Bit-swapping Oriented Twin-memory Multi-view Clustering in Lifelong Incomplete Scenarios
Authors: Shengju Yu
Pei Zhang
Siwei Wang
Suyuan Liu
Xinhang Wan
Zhibin Dong
Tiejun Li
Xinwang Liu
Venue: NeurIPS 2025 poster ()
Keywords: Incomplete Multi-view Clustering
Lifelong Learning
Graph Learning
Multi-view Clustering
Primary area: general_machine_learning

Abstract: Although receiving notable improvements, current multi-view clustering (MVC) techniques generally rely on feature library mechanisms to propagate accumulated knowledge from historical views to newly-arrived data, which overlooks the information pertaining to basis embedding within each view.  Moreover, the mapping paradigm inevitably alters   the values of learned landmarks and built affinities due to the uninterruption nature, accordingly disarraying the hierarchical cluster structures. To mitigate these two issues, we in the paper provide a named BSTM algorithm. Concretely, we firstly synchronize with the distinct dimensions by introducing a group of specialized projectors, and then establish unified anchors for all views collected so far to capture intrinsic patterns. 
Afterwards, departing from  per-view architectures, we devise  a shared bipartite graph construction via indicators to quantify similarity, which not only avoids redundant data-recalculations  but alleviates the representation distortion caused by fusion. 
Crucially, there two components are optimized within an integrated framework, and collectively  facilitate knowledge transfer upon  encountering  incoming views.  Subsequently, to flexibly do transformation on anchors and meanwhile maintain numerical consistency, we develop a bit-swapping scheme operating exclusively on 0 and 1. It harmonizes anchors on current view and that on previous views through one-hot encoded row and column attributes, and the graph structures are correspondingly reordered to reach a matched configuration. Furthermore, a computationally efficient four-step updating strategy with linear complexity is designed to minimize the associated loss. Extensive experiments organized  on publicly-available benchmark datasets with varying missing percentages confirm the superior effectiveness of our BSTM.

Bit-swapping Oriented Twin-memory Multi-view Clustering in Lifelong Incomplete Scenarios
Shengju Yu', Pei Zhang', Siwei Wang"; Suyuan Liu', Xinhang Wan', Zhibin Dong', Tiejun Li Xinwang Liu
National University of Defense Technology. "Intelligent Game and Decision Lab yu-shengju@f oxmail com, (vangsiwei ii,,iiiiin @nudt. edu cn
Abstract
Although receiving notable improvements, current multi-view clustering (MVC) techniques generally rely on feature library mechanisms to propagate accumulated knowledge from historical views to newly-arrive data, which overlooks the infor- mation pertaining to basis embedding within each view. Moreover, the mapping paradigm inevitably alters the values of learned landmarks and built affinities due the uninterruption nature, accordingly disarraying the hierarchical cluster structures. To mitigate these two issues, we the paper provide a named BSTM algorithm. Concretely, firstly synchronize with the distinct dimensions by introducing group of specialized projectors, and then establish unified anchors for all views collected so far to capture intrinsic patterns. Afterwards, departing from per- view architectures, we devise shared bipartite graph construction via indicators to quan- tify similarity, which not only avoids redundant rettllloalls but alleviates the representation distortion caused by fusion. Crucially, there two components are optimized within integrated framework, and collectively facilitate knowl- edge transfer upon encountering incoming views. Subsequently, to flexibly do transformation anchors and meanwhile maintain numerical consistency, develop a bit-swapping scheme operating exclusively on 0 and It harmonizes anchors current view and that previous views through one-hot encoded row and column attributes, and the graph structures are correspondingly reordered to reach matched configuration. Furthermore, a computationally efficient four-step updating strategy with linear complexity is designed to minimize the associated loss. Extensive experiments organized on publicly-availatee benchmark datasets with varying missing percentages confirm the superior effectiveness of our BSTM.
Introduction
As information technology advances, multi-view data, typically referring to the characterization of the same object derived from diverse domains, is becoming increasingly ubiquitous [35] 83] 55 52 42
Naturally, extracting meaningful patterns from these data has sparked substantial research interest
5. Owing to the superior heterogeneous data integration capability, multi- effective methodology for tackling multi- view data and is deployed in various fields like financial analysis, community recommendation, intelligent diagnosis, etc (37 16. 60 84
12
41
73
46
78
view clustering (MVC) is generally recognized
51 28) It seeks partition samples without requiring any labels into distinct groups such that the intra-group similarity is maximized while the inter-group dissimilarity maintained, thereby uncovering potential data relationships [91 19 80 g].
To enhance the partition quality, recently researchers have developed numerous innovative methods [53 58 43 92 79 (85. For sample, Chen al. [2) learn hybridized representations to build a fused
"Correspondngg Authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

sparse similarity measure based on Euclidean rendering, and continuously calibrate a dynamic set with collaborative representation residuals. et al. [2] establish a common embedding space through sample transformation to refine the knowledge repository, and incorporate the geometric structure
of streaming views into the consistency similarity matrix. Wen et al. [66] devise a confidence- based neighbor graph for incomplete views to regularize consensus graph learning, and leverage multiple connected bub-graphs to reveal group-wise cluster-aware topological patterns. Lin et al. [33 assimilate incomplete feature inference and self-representation recoupling to discover latent consistent cluster partition, and employ the tensor decomposition to explore high-order cross-view correlations.
Although achieving impressive enhancements in clustering effectiveness from multiple perspectives, most studies usually employ feature library mechanisms to disseminate formulated knowledge from prior observations to newly-arrived aawiyeerrieed data, which fails to account the characteristics about basis embedding within each view, whether for historical views or new views. This is not conductive to deriving expressive and comprehensive representations as there generally exist valuable geometric features and essential cluster topologies in the basis embedding. Additionally, due to the inherent non-separable continuum attribute, the mapping paradigm currently adopted unavoidably distorts the learned landmarks and established affinities. Not only does this disrupt the anchor topology structures but disarrays the hierarchical cluster formations, accordingly limiting the clustering ability of models.
2
Incomplete data
UAM
Resutts
DIB FIET
SBG
IN-1
IN-2
IN-3
N-
Spectaaf
Figure 1: Pipeline of the designed BSTM. It firstly harmonizes diverse dimensions via projectors [G.). and then builds unified anchor matrix (UAM) for all received views to extract latent patterns. Subsequently, it designs shared bipartite graph (SBG) paradigm based on constructed indicator matrices IN-t and IN-A to establish similarity. This avoids view-data recalculating and alleviates fusion distortion. Also, UAM and SBG collectively do knowledge transfer. Further, it devises bit-swapping scheme consisting of 0 and to rearrange anchors and meanwhile maintain numerical consistency. All components are jointly optimized through an integrated learning mode. IN-t: The indicator matrix built for the 1-th view; IN-A: The indicator matrix built for all historical ( views.
In response these two challenges, we in the paper develop named BSTM algorithm, and Fig. ! presents its overall pipeline. Specifically, we begin with harmonizing disparate dimensions through set of specialized view-specific projectors, and then construct unified anchors over all arrived (incomplete) views to exploit underlying patterns. Subsequently, rather than conventional pie-view architectures, we introduce shared bipartite graph paradigm based on devised indicator matrices to measure similarity, which not only effectively eliminates view-data recomputing but also mitigates fusion-caused representation distortion. More significantly, both unified anchors and the shared bipartite graph possess memory functions, and collectively transfer knowledge when encountering incoming views. After that, in order to flexibly transformation on anchors to alleviate mismatching with new views and at the same time preserve numerical consistency, we design bit-swapping

---

strategy that operates exclusively on {0, 1) space. It introduces a matrix with one-hot encoded row and column properties for all historical views to rearrange anchors according to the characteristies of current view. Correspondingly, the graph structures undergo topological reordering to reach matched configuration while maintaining value invariance. It is noteworthy that all of these components are co-optimized in one common framework, enabling mutually reinforcing interactions. Thereafter, to minimize the associated loss, we give a computationally-efiia linear complexity. The clustering results acquired by conducting spectral partitioning on the produced bipartite graph. Finally, to adequately evaluate the effectiveness of presented BSTM, we earry out extensive contrast experiments with diverse missing data ratios several public datasets. Briefly stated, the contributions of this paper mainly include
four-step solving scheme with
We propose a twin-memory paradigm to facilitate knowledge transfer, which incorporates underlying basis-pattern representations and eliminates redundant view-data recalculating as well as mitigates fusion-induced distortion.
We introduce a bit-swgpiing strategy to flexibly transform anchor topologies and graph structures while preserving numerical consistency.
We optimize all components in an end-to-end manner, and provide a comell-copplextty solver to ensure computational efficiency. Extensive experiments validate the effectiveness of our designed method.
2
Related Work
To boost clustering performance, MVC research community has developed a series of innovative
algorithms from different perspectives 34 induced partition through late fusion for incremental knowledge integration, and substitute average partition with alignment maximization to consolidate prior patterns. On this basis, Yan er al. [77] introduce discrete category learning by constrained matrix factorization to progressively uncover latent clustering structures as the optimization progresses. Rather than kernel combinations, Wan el al. (56) employ an orthogonal coefficient matrix to integrate view data, and dynamically refine this matrix via an information propagation mechanism that synergistically couples established representations with streaming view observations. Qu et al. [49] utilize principal component analysis to standardize the dimension variations, and apply orthogonal permutation matrices to reorganize learned prototypes according to their underlying structural properties. Together with space correlation, Cai et al. M design view-wise codebooks and embedding codebooks to extract patterns based on spectral clustering paradigm, and aggregate multi-view information via adaptive fusion mode. Sun et al. [50] leverage orthogonal repository and feature dictionary to identify potential cluster centers and uncover shared manifolds, and derive the encoding matrix by maximally transferring knowledge from them. In place of vanilla graph, Yin el al. [8I) integrate sparse similarity learning with connectivity-prrserviii learning simultaneously accomplish noise suppression and intra-cluster structure maintenance after reconstruction. Wang et al. (62 harness multi-level consensus representations to maintain heterogencous distributions and inter-view relationships, and leverage a view-consistency matrix to reveal the similar underlying patterns among views. Under relation consistency learning, Yuan er al. (86) utilize contrastive learning-driven view coherence maximization paradigm to compensate for data incompleteness, and mitigate noisy influence through discriminative prototype learning. Xu et al. (76) adopt adaptive feature rendering to bypass data imputation requirements, and extract cluster structures through joint maximization of mutual information and minimization of mean discrepancy.
45 For instance, Wan al. [54] preserve a kernel-
3 Preliminaries
With the newly-arrived t-th (incomplete) view data D, Rdden, where de denotes the data dimension and n, denotes the number of observed samples, the basic clustering model can be mathematically described as
min AREPpxaR AEREXR
Σ D - DD AN CC, p. A)
1=1
(1)
s.t. A, 0, A p Inp Imp: [Apli 0, 1, npp
A 2 0, A T 1n = 1,,
[Aks = 0, 1,
3

---

Ap is the affinity generated on view p. Cp E x=x", is the built indicator matrix, and consists of [Cpli,) if [wp]] i else [Cplk = 0. 1. ny where W E I is the given index vector on view p. is the number of samples and greater than equal to Mp- A is the generated fused affinity. The function V denotes certain fusion strategies, and the hyper-parameter plays role in balancing reconstruction error item and fusion item. After obtaining A, the data grouping results can be acquired by conducting spectral clustering on it.
4 Methodology
Firstly, we associate a projector G, E IRdixm for new view data D, to harmonize its dimension, and then introduce anchor matrix B, Rmxm and bipartite graph Q E [R=x* exploit potential intrinsic structures where m is the number of anchors. Accordingly, we formulate the loss as
Lo min
[Di G.B.Quli
Q.
(2)
s.t. G. G. Im. B,B, =
I Q 2 0, 1m
1m I
The orthogonality aims enhancing the discrimination, while the non-negativity and column-sum constraints guarantee it satisfies similarity requirements.
Subsequently, rather than recomputing all historical views, utilize anchor matrix and bipartite graph to collaboratively extract features across views. However, due to the incompleteness, the graph size is not compatible for different views. To get out of this dilemma, matrix H, E Th X for current view where 7i is the number of samples observed on all & views. Specially,
establish tailored indicator
construct W, W, U W Wt E R is the given index vector on view while W E Ri is the constructed index vector union on all previous t views. At initial stage, W1 = W1. Then, we define [H,l., as if [welj = [W]]s else as 0; í = 1,2, .. Majj = 1, 2, .. ni- On this basis, devise the loss as
L = min
[D. G.B. Q.H.
G. Q
(3)
S.L. G, G. Im. B.B, = Im Q 2 0, views to new view avoiding
Q 1m = 1
where B, E Rmxm and Q: E Rmma, are the unified anchor matrix and shared bipartite graph respectively, and collectively transfer knowledge from historical view-data recalculating and meanwhile eliminating fusion-caused distortion. In particular, Q.H, gmxa; can be regarded as the graph measure for view t.
Afterwards, due to the unsupervised nature of clustering tasks and the potential heterogeneity in data distributions on different views, anchors on the current f-th view could mismatch with that generated on previous / views. To remap anchors while maintaining their values, introduce bit-swapping transformation which operates exclusively on binary space. If anchors are matched, we optimize the corresponding element as 1 otherwise O. Especially, associate the anchor matrix B,-1 produced on previous t views with learnable S E R which is devised exactly contain single 1 element in each row and column, to transform anchors. For the anchor transfer branch, consequently, we mathematically define the loss as
L2 min S
B. B.B.S.... 1
(4)
BBB Im S.1. 1 E (0, 1). ST. 1m S. 1m 1m
Further, considering that variations in the anchor order will alter the graph structure, in order to make the graph keep pace with anchors, we employ S to reorganize the graph Q E Rmx., that shared for all previous t views. In conjunction with the fact that the rows of Q correspond to anchors, accordingly. we can adjust the graph by ST Next, we need to build the relation between Q and S Due to the presence of missing samples, the sizes of these two parts may encounter incompatibility. To this end, we customize an indicator matrix
E,-1 E IR x Specially, the element [E,-1]i.j is devised 1 if [w]] [w-1]] else as 0.

---

Then, Q E Rmx;, can be seen as the parts corresponding to the graph on all previous t - 1 views. Therefore, for the graph transfer branch, we design the loss as
Ls min Q.
E|Q 1 S..QQ.111 Q.11
(5)
s.t. Q
2 0, Q 1m
1, S E {0. 1), 1m; 1m 1m
Based on the above exploration, we formulate the final loss as
= Li AL2 + BL3.
(6)
5 Alternating Optimization
adopt the idea of alternating optimization to minimize (
Step-1 Updating G.. With B,, Qu and S held constant, the objective (6) becomes
min
[D; - G,B.Q,
(7)
G G
Expanding F-norm and deleting irrelevant items, have the following equivalent problem,
max
Tr
Q Q.
(8)
G2 G,=Im
The optimal solution is UVT, both of which are the singular matrices of D,H, B,
Remark 1. Due to D. E Rdxxn and H, E Roxx*, directly calculating D,H,, Q, will need at least (( computational cost. square with respect to the number of samples, and consequently unsuitable for large-scale applications. Instead, construct of de ny and then assign its columns using the column elements of D, via corresponding indexes observed on the I-th view. Accordingly, calculating D.H, Q B, needs (dgūgm + dem²) cost. Since the data dimension de is irrelevant ny and greatly smaller than the number of samples, the computational overhead about updating G2 will be O(n), iee, linear to the number of samples.
matrix with the size
Step-2 Updating B, With G., Qi and S held constant, the objective 6 becomes
nin B.B =Im
[D, G.B.Q.H, + + B. B B 1
(9)
After irrelevant item removing, it is equivalently simplified as
Tr ((G, Q + +AB,-IS.1)) B.)
max B. Im
(10)
Accordingly, the optimal solution of B, is UVT, where the matrices U and V are the SVD outcomes of G, D.H, Q + AB.-IS--1-
Remark 2. Rather than directly constructing the term D.D.H. + AB. which needs at least ((m)) computational cost, note that D, and H. remain unchanged throughout the entire optimization procedure, we utilize the established D,H, in updating G, to construct this term, which only takes O(mdiñ h + m2 n + m²) cost. Therefore, the computational overhead about BN is O(n).
Step-3 Updating Q. With Gg B, and S held constant, the objective (6) becomes
min 2.000 1m 1m=
|D: - G GBB. B ST E_
(11)
After expanding, it can be further simplified as
min Q.20.. In =n=
Tr Q. J.G.GBBBHHHHH.. + +0 E.
(12)
-2 @2 B. G. D.H.
अ Q.
5

---

Remark 3. Due to H.H, E R and Ei-1 E RR 1, the matrix products H,H,H, and E, will incur ((mū)) and (m) computational complexities, which square and cubic with respect to the number of samples respectively. To decrease them, observed that He consists of {0, and each column contains only one 1 as well the columns thogonal, we have that H is diagonal matrix with elements 0 and 1. Therefore, have Q,H,H, Qt Jr where J. 1m [H)= 1 1 HH Similarly for Et-1, have Q,E is equal Qi Mr where M, ( Then, combined with Q: E Rmxas
1m
E [E.-1]1,5, " after this equivalent transformation, both of computational complexities are decreased to O(n).
Then, combining the constraints about Q., B, and G., we can update Q on column-by basis. Accordingly, we can deduce
B,
H.H.H
+ ST Q E
min
2
Q
[
20,
:f
ja + E1=1
E1-1
(13)
Remark 4. Note that H, measures whether the samples are available on the t-th view and E,-1 measures whether the samples are on all previous views. Consequently, we have E H
EE-1 means that the sample j must be in views. Thus, this coefficient must be non-zero.
Further, we equivalently have
min Q [ [0.
Q1 .id
T
(14)
1m=1
/
where T.
B. G.
D.H. 3S, Q.- ET
Hel +
E
It has the following closed-form solution,
-(T.s
1m 1 T
TT..
1.2. ,e.
(15)
Remark 5. The computing overhead is mainly from the construction of T, numerator term. Constructing the terms B, G, D and ST 1, needs at least de+ md,n m)( and 0(m2ñ,11 mū cost respectively, both of which are square with respect to the number of samples. To reduce them, utilize the D,H, built in the updating of G. to construct B, G, D.H,, which takes Omndgūz). For Q inspired by the {0, 13 characteristic and column orthogonality of Et-1, have that Q, means taking the columns of Q--1 to generate a matrix with the same size as Q Therefore, we can establish 1 by first creating matrix with the size of m T4 and then assigning its columns using the columns of Q under corresponding indexes. Accordingly, constructing Q. ET_1 lakes Omm
T, especially from the
Step-4 Updating S. With G., B, and Qe held constant, the objective becomes
min
A B
B B. S
ST 111 (16)
S (0. (J.I).LT, 1
1. 1m
can be further equivalently transformed as
Tr B. -0
)
max
(17)
8, 17,001,,.7,,11111...1 11m=1m
Via the matrix vectorization transformation Vec(.), we have
Vec ( ((AB. B, +.Q.E._..T..)) Vec (S-1))
max
S. (0.1( ST
(18)

---

which is an integer linear programming problem and can be solved by existing software. Since S with the size of m m and m is largely smaller than the number of samples, solving this problem requires minor computing cost.
Remark 6. The computing cost about S 1 is mainly from constructing XB, B which takes Omm² + m + m²) To reduce it to linear, noticed that there is only one in each column of Et-1 and other elements all O we have that Q; indicates picking out certain columns of Q₁ to build a smaller matrix. Thus, we establish an auxiliary matrix, and utilize the columns of Q₁ to do element assignment. Accordingly, the computing cost reduced to O(m2
Steps Under Initial View. When facing only one view, the loss (6) degenerates into 3 which can be deemed as the special case of 6 with and taking and not involving S. Therefore. G2 and B, can be updated via (8) and (10 Additionally, H, (i.e., H1) is an identity matrix. Correspondingly
the term E1=1 [He]5, +
E E 111 in (13) is non-zero. Thus, Q still be updated via
Algorithm ggives the overall procedure of BSTM where flose (1) is the loss value at the [-th iteration. Remark 7. The overall computational complexity of the proposed BSTM is linear with respect the number of samples, which accordingly renders it well-suited for large-scale implementations
Remark 8. Updating G., Br, Qi and S takes (d + d,m), O( + mmu + m²), O(d - md, + mān), O(m² + mm memory cost respectively. So, BSTM's space complexity is also linear.
Algorithm 1 Bit-swapping Oriented Twin-memory Lifelong Incomplete MVC (BSTM)
Input: Incomplete multi-view data D, with index vector w.. hyper-paramettrs À and B; Initialize: G1, B1. Q1, S1;
Output: Performing spectral partitioning on Q to produce clustering results;
1: for t = 1 to do
2: it == then Setting À and as 0. 4: end if
3:
5: == O:
6: repeat
7:
[ [= 1;
8:
Updating the guidance variable G, via 8
9:
Updating the unified anchor variable B, via 10
10:
Updating the shared bipartite graph Q₂ via 15 if then
11:
12:
Updating the swapping variable S.1 via (8)
13:
end if
until 1 1 and (1o==(1-1)-fonn)) (1) S
14:
Roo (I-1)
end for
6 Experiments
Table 1:
Details of the Datasets Utilized in Experiments
NC
NV
NC
NV
PROKARYO
551
438/3/393
4
3
PROTEINF
694
27/27/../22/22
27
WIKIFEA
2866
128/10
10
2
NUSWIENE
4095
128/73/144/225/64
33
5
CALTEALL
9144
48/10/254/51//922
102
YOUTUTEN
38654
944/576/512/6400
YOUTUTWE
63896
944/576/511/666 12/640
20
4
FAMNISIX
70000
1376/512/537//5777/ 23395537
10
We conduct experiments 8 public datasets, with their key characteristics summarized in Table DD is the data dimension. NS, NC and NV are the numbers of samples, clusters and views, respectively.
12 classical methods, GSRMC 226] FLSD 70 MVTSC 71
MVCBG
65 AGCMC [69
NGSPL. [72], PIMVC 7 TCIMC 77), TMBSD 29). PSMVC 24 MKKMC 40 and LRGMV 66
chosen as the baselines. Their descriptions are presented in Section F due to the space limit.

---

6.1 Results and Interpretations
Table 2: Comparative Evaluation of Clustering Method Performance
Dutseet
PROKARYO
PROTEINI
MR
0.1
0.4
0.7
0.1
0.4
0.7
Method
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
AACC
PUR
FSC
ACC
PUR
FSC
GSRMC
27.37
56.81
30.42
39.79
57.00
35.97
45.59
64.24
40.48
32.00
36.19
17.39
51.34
38,70
16.95
29.53
34.00
12.13
FLSD
52.74
64.75
57.67
56.46
61.16
55.87
53.99
61.77
$1.56
27.06
34,56
15.90
25.45
32.62
14.24
24.57
31.28
13.32
MVTSC
49.76
61.52
48.78
50.72
59.51
48.68
48.52
99.56
46.60
30.23
36.99
17.45
28.75
34.65
15.15
25.56
31.44
14.33
MVCBG
55.56
67.20
64.55
56.87
68.50
45.37
53.18
66.26
64.36
29.16
36,97
16.63
28.34
33.85
15.92
26.26
31,56
13.95
AGUMC
77.19
63.65
10.89
25.61
19.37
10.35
NGSPI
90.35
25.48
12.82
22:50
10.75
66.10
45.06
44.0%
18.82
30.01
13.54
58.81
30.23
29.52
32.45
16.36
3.86
16-12
14.63
TMBSD
39.66
47.46
39.08
32.04
40.26
33.03
14.91
20.58
20.42
21,96
19:32
16.14
25.30
22.15
14.11
PSMVC
53.18
65. 70
44.03
79
43.05
51.11
63.70
40.34
28.70
34,00
14.73
78.34
33.94
14.59
26 12
30.01
13:25
MKKMC
50.20
42.27
38.79
39.55
33.57
20.72
37,63
32.14
12.56
14.36
17.15
8.88
14.31
16.12
9.45
15.63
17:23
9.43
LKGMV
30.22
55.85
32.60
28.71
56.43
31.31
31,25
56.82
52.97
14.15
41.28
21.30
32.65
37.78
17.87
29 59
35.59
12.69
Oues
74.95
82.31
64.79
72.78
79.13
62.82
$2.09
74.59
49.59
36.26
41.70
21.81
33.57
37.89
18.41
30.07
35.07
14,41
WIKIFEA
NUSWIENE
GSRMC
47.09
50.18
35.00
38:22
42.73
25.61
35.96
39.61
23.54
10.18
32.19
6.74
11.42
32.33
7.32
11:10
31.56
7.40
FLSD
52.112
58.16
45.45
49
54,01
38.35
39.96
44.65
25.45
10.06
30.21
9.16
11.14
25.47
9.27
12.63
29.36
14.16
MVTSC
51.85
57.97
45.38
45.10
50.63
37.98
40.46
44.63
25.57
10:22
32.74
6.50
9.51
33.65
6.43
6.39
31.34
6.05
MYCBG
51.26
58.42
49.16
53.92
38.84
40.91
44.72
30.60
6.54
3.97
7.12
3.94
6.38
9.29
AGCMC
35.68
37.66
25.91
35.64
40.06
25.60
39.45
44.00
25.28
10.19
31.22
7.07
9.59
29:59
10.39
30.89
8.77
NGSPL
56.75
45.64
30.00
30.40
13.78
10.98
54.89
46.85
34.91
10.88
6.09
31.32
31,66
6.75
TCMM
16:27
19.44
15.93
1529
19.84
15.81
19.52
10-35
28,91
7,06
23.89
9:04
12:40
28,96
14,09
TMBSD
43.93
37:30
36,0
37.93
$2.35
31.31
25.09
6.5
3.94
10.52
6.28
3788
9.54
598
3,60
8.01
PSMVC
52.88
58.36
46.15
50.15
53,69
38.22
39.79
45.0
26.48
9.8
32,26
6.96
10.25
12.27
5.17
9.9
32:25
6.40
MKKMC
54.34
57.44
46.27
48.33
38.82
40.14
42.95
26.48
9.77
32,59
6.92
10.55
31.04
6.61
9:34
32.06
6.38
LRGMM
49.89
56.97
41.04
46.32
52.88
35.84
36.51
43.29
26.93
10.33
32,41
0.90
10.77
32.16
6:83
9.97
32.99
6.59
Ouess
54.22
59.74
47.13
50.17
$4.50
39.21
41,70
46.41
27.03
10.99
33.57
7.59
12.48
33.52
9.87
15.41
33.15
15.10
CALTEALL
YOUTUTEN
GSRMC
22.67
31.52
15.09
21.29
31,46
13.95
19.66
28.07
9:68
FLSD
18.08
34.18
14.46
16.17
33.41
12.38
14.38
28.80
9.19
52.71
55.87
59.57
47.98
$3.98
59.38
45:23
52.34
57.42
MVTSC
21.57
34.34
13.74
22.78
31,23
12.53
21.23
27.21
10.21
MVCBG
24.77
34.13
16.12
23.54
32.65
11.83
20.19
31
9.68
74,07
73.53
64.35
72.55
77.46
65:47
71.22
75.94
61.05
AGUMC
34.62
18.52
17.39
10.74
NGSPI
33.07
15.51
8.76
29.06
56.49
48.93
53.88
61.37
55.03
TCMC
TMBSD
18.58
13.34
15.36
19.57
12.60
12:72
18.52
13.67
9.56
PSMVC
19.02
33.44
14.72
19.11
32.57
13.33
16.58
28.21
9.11
71.56
77.35
68.32
73.77
73.49
05.36
70.09
79.09
62.03
MKKMC
20.34
34.96
15.86
16.13
31.18
11.11
13.19
27.46
5.43
LEGMV
22.71
33.51
15.59
21.54
38.29
13.32
19.74
28.47
8888
Ours
25.93
35.75
17.28
23.24
33.51
14.27
20.27
29.34
9.57
73.23
78.94
67.54
74.14
79.56
67.43
72:21
78.51
64.77
YOUTUTWE
FAMNISIX
GSRMC
FLSD
MVTSC
MVCBG
68.79
69.25
66.85
68.41
08.85
61.82
68.55
69.17
63.26
56.23
56.89
44.82
54.63
57.49
44.36
55.08
56.45
43.70
AGCMC
NGSPL
PINYC
TCTC
TMRSD
PSMVC
65.44
73.34
61.67
71.85
76.75
61.77
67,67
74.17
60.63
49.56
54,45
42.87
49.66
53.87
41.68
48.00
51.36
39.93
MKKMC
T.RGMV
Ours
71.23
76.86
64.34
73.86
79.51
62.06
68.62
76.91
62.90
57.97
58.35
47.84
56.34
57.27
46.89
$4.52
58.43
45,93
To reflect the performance sufficiently, we record the clustering results under missing ratio as 0. 0.4 and 0.7 respectively, with three metrics, ACC, Purity (PUR), Fscore (FSC), as shown in Table 2 The notation 'f' denotes cases where the method fails to process the dataset due to its excessive complexity or itself limitations. Combined with this table, we can acquire the following observations,
1. Our BSTM makes more favorable results in most cases. For instance, it is the best in PUR on PROKARYO, WIKIFEA, CALTEALL and YOUTUTWE. For PROTEINF, WIKIFEA, NUSWIENE, YOUTUTWE and FAMNISIX, there are only two sub-optimal cases on each dataset. The consistent performance confirms BSTM's effectiveness in tackling incomplete multi-view clustering problems.
2. The competitors GSRMC, FLSD, MVTSC, AGCMC, NGSPL, PIMVC, etc, are not able to handle YOUTUTWE and FAMNSIX. By contrast, we operate normally in all scenarios while delivering competitive performance, which indicates that our BSTM possesses a wider range of applications.
3. For inferior results, such as on PROTEINF in PUR, possible reasons could be that we produce the clustering results by partitioning spectral embedding rather than directly by formulating the discrete cluster labels, which deteriorates the data diversity and accordingly harms the model performance.
8

---

6.2
Resource Usage and Component Ablation
20
DSAMC
F156
1100L
MYC
TCMC
TW955
1130W
Kun
15
Ingg() in seconds
10
PROKARYO
PROTEINF
WIKIFEA
NUSWIENE
CALTEALL
YOUTUTEN
YOUTUTWVE
FAMNISIX
Figure 2: Execution Time Comparison (log2() (.) in seconds)
To illustrate the execution efficiency, we summarize the running time in Fig. As seen, owing to not involving view-data recalculating, BSTM usually requires less time overhead. Methods PSMVC and PIMVC in some cases run faster, possibly because they do not integrate basis embedding patterns and also not employ permutation rearrange anchors. Despite time-saving, combined with Table 2 they typically yield less favorable outcomes. Then, about the space usage, please refer to Section
Table 3: Ablation Results about Twin-memory and Bit-swapping on PROKARYO and PROTEINF
PROKARYO
PROTEINP
0.4
PSC
Ab-8
17.08
Ab-Q
72.78
30.76
62.80
61.34
68.97
49.03
66.64
43.22
35.61
40.44
21.70
35.3 35.34
15.66
32.81
12:07
Ab-bi
51
72.41
46.39
42.83
56.64
43.60
44.11
56.61
41.51
35.17
40.66
21.27
20:97
35 70
16.49
27.51
31.74
12:28
Ours
74.95
82.21
64.79
72.78
79.13
62.82
$2.09
74.59
49.59
36.26
41.70
21.81
33.57
37.89
18.41
30.07
35.07
14.41
T demonstrates the effectiveness of twin- memory and bit-swapping (bs). Ab-B and Ab-Q denote the ablation with memoryless B, and Q: respectively. Ab-bs denotes not employing bs strategy. As seen, each component facilitates the performance. Besides, Fig. 3 visualizes the learned bs $ Yellow denotes 1. As observed,
(a) PROKARYO
(b) PROTEINE
generated S not an identity matrix, meaning that it rearranges anchor topology and graph structure. More ablations are in Section
Figure Visualization of Learned S.
7 Limitations
and need extra efforts to do fine-tuning. So, parameter-free version will improve the practicality. Additionally, the paradigm formulating spectrum and then doing partitioning may degrade the data diversity. Directly producing cluster labels from original samples could further boost the performance.
Conclusion
This work provides a MVC method termed BSTM to address two limitations, basis embedding overlooking and value-distortion mapping. Rather than previous feature library mechanisms and pir-view architectures, it designs a twin-memory paradigm to do knowledge transfer, not only incorporating underlying basis patterns but also eliminating redundant view-data recomputing and avoiding fusion. Further, it introduces a bit-swapping scheme that operates exclusively binary space to adaptively transform anchor topologies and graph structures while well maintaining numerical consistency. All parts are jointly learned in an end-to-end manner, enabling mutually reinforcing interactions. Then, an efficient four-step solver developed minimize the resulting loss, and experiments several datasets with varying incomplete percentages validate BSTM's effectiveness.

---

Acknowledgment
This work was supported by the National Natural Science Foundation of China under Grant No. 62406329, 62476280, 62441618, 62325604, 62276271.
References
[1] Hecheng Cai, Yuze Tan, Shudong Huang, and Jiancheng Lv. Lifelong multi-view spectral clustering. In Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, pages 3488-3496, 2023.
[2] Jie Chen, Shengxiang Yang, and Zhu Wang. Multi-view representation learning for data stream clustering. Information Sciences, 613:731-746, 2022.
[3] Man-Sheng Chen, Chang-Dong Wang. Dong Huang, Jian-Huang Lai, and Yu Philip. Concept factorization based multiview clustering for large-scale data. IEEE Transactions on Knowledge and Data Engineering, 36(1 1):5784-57798 2024.
[4] Man-Sheng Chen, Chang- Dong Wang, Dong Huang, Jian-Huang Lai, and Philip Yu. Effi- cient orthogonal multi-viee view subspace clustering, In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 127-135, 2022.
[5] Zhaoliang Chen, Lele Fu, Jie Yao, Wenzhong Guo, Claudia Plant, and Shiping Wang. Learnable graph convolutional network and feature fusion for multi-view learning. Information Fusion, 95:109-119 2023.
[6] Jinrong Cui, Yulu Fu, Cheng Huang, and Jie Wen. Low-rank graph completion-based incomplete multiview clustering. IEEE Transactions on Neural Networks and Learning Systems, 35(6):8064 8074, 2024.
[7] Shijie Deng, Jie Wen, Chengliang Liu, Ke Yan, Gehui Xu, and Yong Xu. Projective incomplete multi-view clustering. IEEE Transactions on Neural Networks and Learning Systems, 2023.
[8] Zhibin Dong, Dayu Hu, Jiaqi Jin, Siwei Wang, Xinwang Liu, and En Zhu. Selective cross-view topology for deep incomplete multi-view clustering. IEEE Transactions Image Processing, 0144792-8055. 2025.
[9] Yu Feng, Weixuan Liang, Xinhang Wan, et al. Incremental multi-view clustering: Exploring stream-view correlations to learn consistency and diversity. IEEE Transactions Knowledge and Data Engineering, 2025.
[10] Yu Feng, Weixuan Liang, Xinhang Wan, et al. Incremental nyström- multiple kernel clustering. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 16613-16621, 2025.
[11] Yulu Fu, Yuting Li, Qiong Huang, Jinrong Cui, and Jie Wen. Anchor graph network for incomplete multiview clustering. IEEE Trunsactions on Neural Networks and Learning Systems, 2024.
[12] Zhibin Gu and Songhe Feng. From dictionary to tensor: A scalable multi-view subspace clustering framework with triple information enhancement. Advances in Neural Information Processing Systems, 37:103545-1033 2024.
[13] Zhibin Gu, Zhendong Li, and Songhe Feng. Edison: Enhanced dictionary-induced tensorized incomplete multi-view clustering with gaussian error rank minimization. In International Conference on Machine Learning, pages 16548-16567. PMLR, 2024.
[14] Wenjue He, Zheng Zhang, Yongyong Chen, and Jie Wen. Structured anchor-inferred graph learning for universal incomplete multi-view clustering. World Wide Web, 26(1):375-32) -399, 2023.
[15] Cheng Huang, Jinrong Cui, Yulu Fu, Dong Huang, Min Zhao, and Lusi Li. Incomplete multi- view clustering network via nonlinear manifold embedding and probability-induce loss. Neural Networks, 163:233-244 2023.
10

---

[16] Dong Huang, Xiaozhi Deng, Ding-Hou Hua Chen, Zihao Wen, Weijun Sun, Chang-Don Wang, and Jian-Huame Lai. Deep clustering with hybrid grainedr contrastive and discriminative learning. IEEE Transactions on Circuits and Systems for Video Technology, 2024.
[17] Dong Huang, Chang-Dong Wang, Jian-Huang Lai, and Chee-Keong Kwoh. Toward multidiver- sified ensemble clustering of high-dimensional data: From subspaces metrics and beyond. 2022.
IEEE Transactions on Cybernetics, (((1)):22311-223
[18] Zhao Kang, Xinjia Zhao, Chong Peng, Hongyuan Zhu, Joey Tianyi Zhou, Xi Peng, Wenyu Chen, and Zenglin Xu. Partition level multiview subspace clustering. Neural Networks, 122:279-288 2020.
[19] Jinghuan Lao, Dong Huang, Chang-Dong Wang, and Jian-Huang Lai. Towards scalable multi- view clustering via joint learning of many bipartite graphs. IEEE Transactions Big Data, 10(1):77-91 2024.
[20] Haobin Li, Yunfan Li, Mouxing Yang, Peng Hu, Dezhong Peng, and Xi Peng. Incomplete multi-view clustering via prototype-based imputation. In Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, pages 391 1-3999,, 2023.
[21] Haoran Li, Zhenwen Ren, Yulan Guo, Jiali You, and Xiaojian You. Lsve: A lifelong learning approach for stream-view clustering. IEEE Transactions on Neural Networks and Learning Systems, 2024.
[22] Jing Li, Quanxue Gao, Qianqian Wang, Ming Yang, and Wei Xia. Orthogonal non-negative tensor factorization hased multi-view clustering. Advances in Neural Information Processing Systems, 36, 2024.
[23] Jing Li, Qianqian Wang, Ming Yang. Quanxue Gao, and Xinbo Gao. Efficient anchor graph factorization for multi-view clustering. IEEE Transactions on Multimedia, 2023.
[24] Miaomiao Li, Siwei Wang, Xinwang Liu, and Suyuan Liu. Parameter-free free and scalable incomplete multiview clustering with prototype graph. IEEE Transactions on Neural Networks and Learning Systems, 35(1)3300-310, 2024.
[25] Miaomiao Li, Jingyuan Xia, Huiying Xu, Qing Liao, Xinzhong Zhu, and Xinwang Liu. Local- ized incomplete multiple kernel k-means with matrix-inducee regularization. IEEE Transactions on Cybernetics, 53(6):3479-3492 2023.
[26] Xiang-Long Li, Man-Sheng Chen, Chang-Dong Wang, and Jian-Huang Lai. Refining graph structure for incomplete multi-view clustering. IEEE Transactions on Neural Networks and Learning Systems, (5(2):3300-233 2024.
[27] Xingfeng Li, Yinghui Sun, Quansen Sun, and Zhenwen Ren. Consensus cluster center guided latent multi-kernel clustering. IEEE Transactions on Circuits and Systems for Video Technology, 33(6):2864 2876, 2023.
[28] Yan Li, Xingchen Hu, et al. A vertical federated multiview fuzzy clustering method for incomplete data. IEEE Transactions on Fuzzy Systems, 33(5):1510-1524, 2025.
[29] Zhenglai Li, Chang Tang, Xinwang Liu, Xiao Zheng, Wei Zhang, and En Zhu. Tensor- based multi-view block diagonal structure diffusion for clustering incomplete multi-view data. In 2021 IEEE International Conference on Multimedia and Expo, pages 1-6. IEEE, 2021.
[30] Zhenglai Li, Chang Tang, Xiao Zheng, Xinwang Liu, Wei Zhang, and En Zhu. High-order correlation preserved incomplete multi-view subspace clustering, IEEE Transactions on Image Processing, 31:2067-2080, 2022.
[31] Weixuan Liang. Xinwang Liu, Yong Liu. Jun-Jic Huang, Siwei Wang. Jiyuan Liu, Yi Zhang, En Zhu, et al. Stability and generalization of kernel clustering: From single kernel to multiple kemel.. Advances in Neural Information Processing Systems, 15:33633-33644 2022.
[32] Weixuan Liang, En Zhu, et al. Scalable multiple kernel clustering: learning clustering structure from expectation. In Proceedings of the 41st International Conference on Machine Learning, pages 29700029719, 2024.
11

---

[33] Jia-Qi Lin. Xiang- Long Li, Man-Sheng Chen, Chang- Chang-Dong Wang, and Haizhang Zhang. Incom- plete data meets uncoupled case: A challenging task of multiview clustering. IEEE Transactions on Neural Networks and Learning Systems, 35(6):8097-8116 2024.
[34] Yijie Lin, Yuanbiao Gou, Xiaotian Liu, Jinfeng Bai, Jiancheng Lv, and Xi Peng. Dual contrastive prediction for incomplete multi-view representation learning. IEEE Trunsactions on Puttern Analysis and Machine Intelligence, 45(4):4447-4461 2023.
[35] Bao- Yu Liu, Ling Huang, Thang-Dong Wang, Hlan-Huang Lai, and Philip S. Yu. Multiview clustering via proximity learning in latent representation space. IEEE Transactions on Neural Networks and Learning Systems, 34(2):973 3-666, 2023.
[36] Chengliang Liu, Zhihao Wu, Jie Wen, Yong Xu, and Chao Huang. Localized sparse incomplete multi-view clustering. IEEE Transactions on Multimedia, 25:5539-5551, 2023.
[37] Suyuan Liu, Hao Yu. Hao Tan, et al. Efficient federated incomplete multi-view clustering, In Forty-second International Conference on Machine Learning. 2025.
[38] Xinwang Liu. Incomplete multiple kernel alignment maximization for clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1412-1444 2024.
[39] Xinwang Liu, Miaomiao Li, Chang Tang, Jingyuan Xia, Jian Xiong, Li Liu, Marius Kloft, and En Zhu. Efficient and effective regularized incomplete multi-view clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43((0))2634-2644) 2021.
[40] Xinwang Liu, Xinzhong Zhu, Miaomiao Li, Lei Wang, En Zhu, Tongliang Liu, Marius Kloft, Dinggang Shen, Jiamping Yin, and Wen Gao. Multiple kernel k-means with incomplete kernels. IEEE Transactions on Pattern Analysis and Machine Intelligence, 42(5):1191-122) 191-1204, 2020.
[41] Yue Liu, Shihao Zhu, Jun Xia, Yingwei Ma, Jian Ma, et al. End-to-end learnable clustering for intent learning in recommendation. Advances in Neural Information Processing Systems, 37:5913 1799913-5999, 2024.
[42] Jielong Lu, Zhihao Wu, Luying Zhong, Zhaoliang Chen, Hong Zhao, and Shiping Wang. Generative essential graph convolutional network for multi-view semi-supervised classification. IEEE Transactions on Multimedia, 26:7987-7999, 2024.
[43] Yiding Lu, Yijie Lin, Mouxing Yang, Dezhong Peng, Peng Hu, and Xi Peng. Decoupled contrastive multi-view clustering with high-order random walks. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 14193- 14201, 2024.
[44] Juncheng Lv, Zhao Kang, Xiao Lu, and Zenglin Xu, Pseudo-supervised deep subspace clustering. IEEE Transactions on Image Processing, 30:5252-5263 2021.
[45] Ziyu Lv, Quanxue Gao, Xiangdong Zhang, Qin Li, and Ming Yang. View-consistency learning for incomplete multiview clustering. IEEE Transactions on Image Processing, 31:4790-4802, 2022.
[46] Huimin Ma, Siwei Wang, et al. Automatic and aligned anchor learning strategy for multi-view clustering. In Proceedings of the 32nd ACM International Conference on Multimedia, pages 5045-5054, 2024.
[47] Huimin Ma, Siwei Wang, Junpu Zhang, al. Symmetric multi-view subspace clustering with automatic neighbor discovery. IEEE Transactions on Circuits and Systems for Video Technology, 34(9):876688778 2024.
[48] Yalan Qin, Xinpeng Zhang, Liquan Shen, and Guorui Feng. Maximum block energy guided robust subspace clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(2):2652-2666 2023.
[49] Qian Qu, Xinhang Wan, Weixuan Liang, Jiyuan Liu, Yu Feng, Huiying Xu, Xinwang Liu, and En Zhu. A lightweight anchor-based incremental framework for multi-view clustering. In Proceedings of the 32nd ACM International Conference on Multimedia, pages 6662-8661, 2024.
12

---

[50] Gan Sun, Yang Cong, Qianqian Wang, Jun Li, and Yun Fu. Lifelong spectral clustering. In Proceedings of the AAAI conference on artificial intelligence, volume 34, pages 5867-5874, 2020.
[51] Chang Tang, Zhenglai Li, Jun Wang, Xinwang Liu, Wei Zhang, and En Zhu. Unified one- step multi-view spectral clustering. IEEE Transactions on Knowledge and Data Engineering, 35(06):6449-644) 6460,, 2023.
[52] Huayi Tang and Yong Liu. Deep safe incomplete multi-view clustering: Theorem and algorithm.
In International Conference on Machine Learning, pages 21090-21 110. PMLR, 2022.
[53] Xinhang Wan, Jiyuan Liu, Xinbiao Gan, et al. One-step multi-view clustering with diverse representation. IEEE Transactions on Neural Networks and Learning Systems, 36(3).577--5766, 2025.
[54] Xinhang Wan, Jiyuan Liu, Weixuan Liang, Xinwang Liu, Yi Wen, and En Zhu. Continual miewi-view clustering. In Proceedings of the 30th ACM International Conference on Multimedia, pages 3676-3684, 2022.
[55] Xinhang Wan, Jiyuan Liu, Xinwang Liu, et al. Decouple then classify: a dynamic multi-view labeling strategy with shared and specific information. In Proceedings of the 41st International Conference on Machine Learning, pages 49941-49956, 2024.
[56] Xinhang Wan, Bin Xiao, Xinwang Liu, Jiyuan Liu, Weixuan Liang, and En Zhu. Fast continual multi-view clustering with incomplete views. IEEE Transactions on Image Processing. 33:2995- 3008, 2024.
[57] Chang- Wang, Man-Sheng Chen, Ling Huang, Jian-Huang Lai, and Philip S. Yu. Smooth- ness regularized multiview subspace clustering with kernel learning. IEEE Transactions Neural Networks and Learning Systems, 32( (2(11))047750000 2021.
[58] Jing Wang, Songhe Feng. Gengyu Lyu, and Zhibin Gu. graaulgranllrrity contrastive learning for deep multi-view subspace clustering. In Proceedings of the 31st ACM international conference on multimedia, pages 2994-3002, 2023.
[59] Jun Wang, Zhenglai Li, Chang Tang. et al. Multiple kernel clustering with adaptive multi-scale partition selection. IEEE Transactions on Knowledge and Data Engineering, 36(1))))(61)))) 11):11116466666 2024.
[60] Jun Wang, Chang Tang, Zhiguo Wan, Wei Zhang, Kun Sun, and Albert Y Zomaya. Efficient and effective one-step multiview clustering. IEEE Transactions on Neural Networks and Learning Systems, 2023.
[61] Jun Wang, Chang Tang, Xiao Zheng, et al. Fast approximated multiple kernel k-means. IEEE Transactions on Knowledge and Data Engineering, 36(1 (6(11):6711-680) 2023.
[62] Kangru Wang, Lei Wang, Xiaolin Zhang, and Jiamao Li. Continual multiview spectral clustering via multilevel knowledge. IEEE Signal Processing Letters, 2024.
[63] Qianqian Wang, Huanhuan Lian, Gan Sun, Quanxue Gao, and Licheng Jiao. iemsc: Incomplete cross-modie subspace clustering. IEEE Transactions on Image Processing, 30:305-317, 2021.
[64] Qianqian Wang, Wei Xia, Zhiqiang Tao, Quanxue Gao, and Xiaochun Cao. Deep self-supervised t-sne for multi-modal subspace clustering. In Proceedings of the 29th ACM International Conference Multimedia, pages 1748 1755, 2021.
[65] Siwei Wang. Xinwang Liu, Li Liu, Wenxuan Tu, Xinzhong Zhu, Jiyuan Liu, Sihang Zhou, and En Zhu. Highly-efficiens incomplete large-scale multi-view clustering with consensus bipartite graph. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pages 97855 2022.
[66] Jie Wen, Chengliang Liu, Gehui Xu, Zhihao Wu, Chao Huang, Lunke Fei, and Yong Xu. Highly confident local structure based consensus graph learning for incomplete multi-view clustering. In Proceedings of the IEFE/CVF Conference on Computer Vision and Pattern Recognition, pages 15712-15721, 2023.
13

---

[67] Jie Wen, Gehui Xu, Zhanyan Tang, Wei Wang, Lunke Fei, and Yong Xu. Graph regularized and feature aware matrix factorization for robust incomplete multi-view clustering, IEEE Transactions on Circuits and Systems for Video Technology, 34(5):3728-3744 2024.
[68] Jie Wen, Yong Xu, and Hong Liu. Incomplete multiview spectral clustering with adaptive graph learning. IEEE Transactions on Cybernetics, 50(4):1418-1429, 2020.
[69] Jie Wen, Ke Yan, Zheng Zhang, Yong Xu, Jungian Wang, Lunke Fei, and Bob Zhang. Adaptive graph completion based incomplete multi-view clustering. IEEE Transactions on Multimedia, 23:2493 2504, 2021.
[70] Jie Wen, Zheng Zhang, Zhao Zhang, Lunke Fei, and Meng Wang. Generalized incomplete multiview clustering with flexible locality structure diffusion. IEEE Transactions on Cybernetics, 51(1):101-11,, 2021.
[71] Jie Wen, Zheng Zhang, Zhao Zhang, Lei Zhu, Lunke Fei, Bob Zhang. and Yong Xu. Unified ten- sor framework for incomplete multi-view clustering and missing-view view inferring. In Proceedings of the AAAI conference on Artificial Intelligence, volume 35, pages 10273-10281, 2021.
[72] Wai Keung Wong, Chengliang Liu, Shijie Deng, Lunke Fei, Lusi Li, Yuwu Lu, and Jie Wen. Neighbor group structure preserving based consensus graph learning for incomplete multi-view clustering. Information Fusion, 100:101917 2023.
[73] Zhihao Wu, Xincan Lin, Zhenghong Lin, Zhaoliang Chen, Yang Bai, and Shiping Wang. Interpretable graph convolutional network for multi-view semi-supervised learning. IEEE Transactions on Multimedia, 1885993-606,, 2023.
[74] Wei Xia, Quanxue Gao, Qianqian Wang, and Xinbo Gao. Tensor completion-based incomplete multiview clustering. IEEE Transactions Cybernetics, 52(12):13635-33644 2022.
[75] Gehui Xu, Jie Wen, Chengliang Liu, Bing Hu, Yicheng Liu, Lunke Fei, and Wei Wang. Deep variational incomplete mueti-view clustering: Exploring shared clustering structures. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 16147-16155, 2024.
[76] Jie Xu, Chao Li, Liang Peng, Yazhou Ren, Xiaoshuang Shi, Heng Tao Shen, and Xiaofeng Zhu. Adaptive feature projection with distribution alignment for deep incomplete multi-view clustering. IEEE Transactions on Image Processing. 12:1354-1366, 2023.
[77] Xiaoqiang Yan, Yingtao Gan, Yiqiao Mao, Yangdong Ye, and Hui Yu. Live and learn: Continual action clustering with incremental views. In Proceedings of the AAAI conference on artificial intelligence, volume 38, pages 16264-16271, 2024.
[78] Xihong Yang, Yue Liu, Sihang Zhou, et al. Cluster-guided contrastive graph clustering network. In Proceedings of the AAAI conference on artificial intelligence, volume 37, pages 10834-10842, 2023.
[79] Xihong Yang, Siwei Wang, Jiaqi Jin, et al. Generalized deep multi-view clustering via causal learning with partially aligned cross-view correspondence. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 1990-1999, 2025.
[80] Zequn Yang, Han Zhang, Yake Wei, Zheng Wang. Feiping Nie, and Di Hu. Geometric-inspired graph- incomplete multi-view clustering. Pattern Recognition, 147: 10082, 2024.
[81] Hongwei Yin, Wenjun Hu, Zhao Zhang, Jungang Lou, and Minmin Miao. Incremental multi- view spectral clustering with sparse and connected graph learning. Neural Networks, 144:260- 270, 2021.
[82] Shengju Yu, Suyuan Liu, Siwei Wang, Chang Tang, Zhigang Luo, Xinwang Liu, and En Zhu. Sparse low-rank multi-view subspace clustering with consensus anchors and unified bipartite graph. IEEE Transactions on Neural Networks and Learning Systems, 36(1):1433 1438 1452, 2025.
[83] Shengju Yu, Siwei Wang. Zhibin Dong, Wenxuan Tu, Suyuan Liu, Zhao Lv, Pan Li, Miao Wang. and En Zhu. A non-parametric graph clustering framework for multi-view data. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages (6558-16567, 2024.
14

---

[84] Shengju Yu, Siwei Wang, Yi Wen, Ziming Wang. Zhigang Luo, En Zhu, and Xinwang Liu. How construct corresponding anchors for incomplete multiview clustering. IEEE Transactions on Circuits and Systems for Video Technology, 34(4):2845-286) 2024.
[85] Shengju Yu, Siwei Wang, Pei Zhang, Miao Wang, Ziming Wang, Zhe Liu, Liming Fang, En Zhu, and Xinwang Liu. Dvsai: Diverse view-shared anchors based incomplete multi-view clustering. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 16568-16577, 2024.
[86] Honglin Yuan, Shiyun Lai, Xingfeng Li, Jian Dai, Yuan Sun, and Zhenwen Ren. Robust prototype completion for incomplete multi-view clustering. In Proceedings of the 32nd ACM International Conference on Mullimedia, pages 10402-10411 2024.
[87] Changqing Zhang, Yajie Cui, Zongbo Han, Joey Tianyi Zhou, Huazhu Fu, and Qinghua Hu. Deep partial multi-view learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(5):2402-244 2415, 2022.
[88] Chen Zhang, Siwei Wang. Jiyuan Liu, Sihang Zhou, Pei Zhang, Xinwang Liu, En Zhu, and Changwang Zhang. Multi-view clustering via deep matrix factorization and partition alignment. In Proceedings of the 29th ACM International Conference on Multimedia, pages 4156-4164, 2021.
[89] Guang- Yu Zhang. Dong Huang, and Chang-Dong Wang. Tensorized incomplete multi-view kernel subspace clustering. Neural Networks, 179:106529, 2024.
[90] Guang- Yu Zhang, Dong Huang, and Chang-Dong Wang. Unified and tensorized incomplete multi-view kernel subspace clustering, IEEE Transactions on Emerging Topics in Computational Intelligence, 2024.
[91] Pei Zhang, Yuangang Pan, Siwei Wang, al. Max-mahalanobis anchors guidance for multi- view clustering. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 22488-22496, 2025.
[92] Yi Zhang, Siwei Wang, Jiyuan Liu, et al. Dleft-mke: Dynamic late fusion multiple kernel clustering with robust tensor learning via min-max optimization. In The Thirteenth International Conference on Learning Representations, 2025.
[93] Shuping Zhao, Jie Wen, Lunke Fei, and Bob Zhang. Tensorized incomplete multi-view clustering with intrinsic graph completion. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pages 11327-11335, 2023.
15

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: Please see the abstract and introduction parts. We devise novel multi- view clustering method named BSTM by introducing both anchors and shared graph with mnemory-presevvee function. We clearly state existing methods and their drawbacks. To solve the problems, we develop a bit-swapping strategy and twin-memory strategy. Experi- mental results on eight datasets and theoretical analysis demonstrate the effectiveness of our proposed method.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize other settings.
is fine include aspirational goals as motivation long is clear that these goals are not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Please see Section 7 We summarize the limitations of our method, such as srperpparameters and the paradigm formulating spectrum and then doing partitioning. We also provide possible solutions.
Justification:
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors encouraged to create separate "I "Limitations" section in their paper.
The paper should point any strong assumptions and how robust the results to violations of these assumptions (e.g.. independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect the scope of the claims made, e.g., if the approach only tested on a few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't acknowledged the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
16

---

3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [Yes]
Justification: We provide detailed derivation procedure. Please see Section A.1 for Remark 1, Section A.2 for Remark 2, Section A.3 3.33for for Remark 3-5,, Section A..4 for Remark 6. Please
see Section for Remark 7 and Remark 8.
Guidelines:
The answer NA means that the paper does not include theoretical results. All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
The proof's can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proof's provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Answer: [Yes]
Justification: Please see Section and Algorithm
I
We provide all implementation details.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution a specific model and empirical evaluation, may be necessary either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way accomplish this, but reproducibility instructions for how to replicate the results, access to a hosted model (e.g.. in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
also be provided via detailed
While NeurlPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make clear how to reproduce that algorithm.
(b) the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may tricky in some cases, in which case authors welcome describe the particular way they provide for reproducibility.
17

---

In the case of closed-source models, it may be that access to the model is limited in some way (e.g., registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [No]
Justification:
The used benchmark datasets are public. Code will be released under license in the final version.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips.co ca/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https
wtippscc/public//uiiiee guwde// CodeeSumiia iisbimisssiiie onyolicy) for more details.
The authors should provide instructions on data access and preparation, including how access the raw data, preprocessed data, intermediate data, and generated data,
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: Please Section and Algorithm Guidelines:
T All details are provided.
The answer NA means that the paper does include experiments.
The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment statistical significance
Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Answer: [Yes]
Justification: We run 20 times, and count the average value and standard deviation of clustering results. Please see Table and Table TO
Guidelines:
The answer NA means that the paper does not include experiments.
18

---

The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, or statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the enror bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall
with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
It should be clear whether the error bar is the standard deviation or the standard error of the mean.
is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that out of range (e.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes]
Justification: We conduct experiments on Window 10 with 64GB memory and Intel i7 CPU. Please see Fig. for the execution time.
Guidelines:
The answer NA means that the paper does include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary failed experiments that didn't make it into the paper).
9. Code ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics
Answer: [Yes]
Justification: We check the NeurlPS Code of ethics. We conform each aspect of them.
Guidelines:
The answer NA means that the authors have not reviewed the NeurlPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g.. there special consid- eration due to laws or regulations in their jurisdiciio))
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification: We demonstrate that the proposed method is with linear complexity and accordingly suitable for large-scale application, which could impact people's lives.
19

---

Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No. they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied partieular applications, let alone deployments. However, if there is direct path any negative applications, the authors should point it out, For example, it is legitimate to point that improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility of MI...
11. Safeguards
Does the paper deseribe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification:
The paper poses no such risks.
Guidelines:
The answer NA means that the paper poses such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
Justification:
We have discussed and cited relevant papers.
Guidelines:
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset used and, possible, include URL.
The name of the license (c.g., CC-BY 4.0) should be included for each asset.
20

---

For scraped data from a particular source (e.g., website). the copyright and terms of service of that souree should be provided.
assets are released, the license, copyright information, and terms use in the package should be provided. For popular datasets, paperssi thood cww datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
If this information is not available online, the authors encouraged to reach out to the asset's 's creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification: Please see Algorithm for the proposed method BSTM. Please see Section for the implement details.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/model part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset is used.
At submission time, remember anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification:
The paper does not involve crowdsoureing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According to the NeurlPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
Answer: [NA]
Justification:
The paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsoureing nor research with human subjects.
21

---

Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if' applicable), such as the institution conducting the review.
16. Declaration of LLM usage
Does the paper describe the usage of LLMs if is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, originality of the research, declaration is not required.
Question:
Answer: [NA]
Justification: The core method development in this research does not involve LLMS as any important, original, non-standard components.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs as any important, original, non-standard components.
Please refer to our LLM policy (https://neurips: hett::/:/eerrrps.ccc//ooeeereere cc///onfereeeee//222///.... for what should or should not be described.
22

---

Appendices
A
Solution Details
Due the joint non-convexity, we adopt the alternating optimization strategy minimize the original objective loss (6).
A.1 Updating the Guidance Variable G2
Under given B,, Q and St-1, the original objective loss expressed as
6
with respect to G2 can be equivalently
min [D, H.B.Q.H.II..
(19)
s.t. G. G; = Lm- Unfolding F-norm through trace operation, we can have
[D, - G,B.Q. e Tr (D.D. 2D, B, + G.B.Q.HHH,,,BBB.C.
(20)
According to the fact that the data matrix D, is irrelevant to G2 and that the feasible region is orthogonal, we further have
min - H, + max Tr (G, D D.H, G.
(21)
G.
Due to D, E Rdi E Q E R.X and B, E R=xm constructing the term D,H, Q B, will take (d,n, + d + dem²) computational complexity, which is dominated by deneñi since m is generally smaller than n, and 74. When the number samples observed on the t-th view is larger, i.e. the missing ratio is smaller, as time goes on, the complexity will approach On")), resulting in its unsuitability for large-scale applications.
In order to achieve linear scaling, note that 7, is greater than n, and that H, is composed of and and there is only non-zero element in each column. Accordingly. the meaning of D,H, is to construct a bigger matrix with the size of d, x T4 using the columns of D,. The non-zero columns of this bigger matrix correspond to the indexes of samples observed rather than directly calculating D,H, we can firstly create a zero matrix with the size of d, x it and then assign its column elements using the columns of D via corresponding indexes. Since does not involve any element calculating operations and can be constructed before optimization, this will take a constant-order complexity. Consequently, the construction of D.H, Q B, requires only (dema)) linear to the sample size.
the 1-th view. As result,
Let U, and denote the singular matrices of D,H, B. and then we have
max Tr D.H.H.H..... < max Tr (VTG) G.U)).
(22)
G.
Combined with the orthogonality of G; we have that the VTG, U is also an orthogonal matrix. Further, together with the non-negative property of E, we can obtain that Tr (VTG) UΣ) < Tr (E). Therefore, we have that when VT VTG. U I, the equality holds. Accordingly, the optimal solution of G2 is UVT.
A.2 Updating the Unified Anchor Variable B,
Under given G, p, and S, the original objective loss with respect to B, can be equivalently
expressed as
min B.
D. - G. + AJ - B, 1
(23)
s.t. B.B. Im
23

---

Combined with 20 and the orthogonality of B,, we can get
min
Dr G,B.Q, B.
Tr D.H.H,H,
(24)
B.
For the second term i
after F-norm expanding, we have
B, - B S P Tr [BBB - 2B, B. B B, -.
(25)
Due to B,B. Im and
B;- S - being irrelevant to the optimization variable B,, we can derive
min B.
B, B, S.-1S.-112 +
max Tr B.
- B.-.I.....
B,
(26)
Combing
24 and 26
derive that the problem
23
equivalently transformed
max Tr ((G. Q +AB, AAB-IS. S. B,
B.
(27)
s.t. B.B, Im.
Therefore, the optimal solution of B, is UVT, in which U and V come from the SVD results of D.D.H. Q ABB-SS.-I
Directly calculating G, G.D.H,,, Q + AB, will take O(md,n + mmn + m m computational cost. Evidently, it will be square with respect to over time, causing difficulties in tackling large-scale problems. Inspired by the strategy handling D,H, in the optimization procedure of G2, first equivalently calculate D.H, via bigger temporary matrix, and then construct the term G. D,H," Q Accordingly, the complexity reduced (mddii, + m²?, Mr + m²²) Due m generally being smaller than de and ne the computational complexity about B₃ can be formulated as O(dd,nn), which linear to the sample size.
A.3 Updating the Shared Bipartite Graph Q:
Under given G,, B, and S the original objective loss (6) with respect Q can be equivalently expressed as
min D: G.B.Q. B| Q.E. STQQ.-11
(28)
s.t. Q 2 0, Q 1m 1ix.
Together with 20 we can further obtain
min Q
D. G.B. min Tr (o. B. G. G, 2Q, G D.H.
(29)
According to the characteristics of feasible region, we can optimize Q, by column. Specially, we have
min Tr @r G. G.B.Q.H.HH))
min Qdi.
[
B, G. G.B, Q.H.H, :.
(30)
Q
Considering that these is only one non-zero element in each column of H, and that all columns are orthogonal, H.H.T E x will be diagonal matrix with element and Directly cal- culating H.H.H, will need O(m??) computational complexity. As time goes on, it will be quadratic with respect n, and consequently is applicable to large-scale scenes. To decrease the complexity, by virtue of the diagonal property, we can derive Q,H,H. Q c J, where
J. 1m 15 H H.l.. Ene H. H,2,,,....
ni == H.l,,g) Further, we have
Q.H.H.
H
Q
(31)
ji
24

---

Combined with 30 we can equivalently obtain
R1 Hilp G G,B, Q :t
min Tr (r B, G, C.B.H.HHHH..
min Qull..
(32)
Q.
Therefore, for 29 we have the following expression holds.
T4 H.l, B, G. G,B, Q
min Q
D. H.
min [Q:].
Q
: 1=1
(33)
2
Q
B, G
D.H.
:
Then, for the second term in (28 after expanding and deleting irrelevant items, have
min Q ST Q111 min Tr Q. E 2Q, S. Q Q.. (34) Q
Q
Note that E,- Rüxx: 1, the computing of E E,_, will need (f complexity. Over time, this will be cubic with respect to n, severely harming the ability tackle large-scale tasks. Inspired by the scheme disposing of H,, we observe that Eş-1 skinny matrix with binary elements, the columns of which are mutually orthogonal. Consequently, E,- is diagonal matrix with elements as the row sums of E,-1 respectively. Further, we have that 1 is
equal to Q C M,. M, 1m | j==1" [E,-1 Σ E1-....j. En' E 1h. Then, by column- wise decomposition, we have
min Tr Q2 (.E,E-E,T,)
e min Qrl.c
Q
E
Q0
(35)
Q
1=1
and
min Tr Q S
Q.
min
Q
S
Q.-
E.
(36)
Q
Together with
33
34
35
and (36.
we can equivalently simplify 28
as
n
min
Qc
Σ
H
B
G.
G.B. +
Σ
E
Im
Qr
@
:
(37)
-2
Q:
B.
D.H.H.
D.H,
+/3 ST. Q. 1 E
s.t.
Q
0,
1m = 1, j 1,2, nec.
:jj
In conjunction with the orthogonality of Ge and Bú, we can further have the following equivalent optimization problem,
The
8t-1
min Qdla
Σ
E
E
Q.
Q. [o...,
j,
1=1
(38)
2
Q
B. G
D.H,
+
S
Q.
E,
@
2 0,
1m 1, 1,2, Th..
:.j
According to the meaning of H, and É. that H, measures whether the samples are on the t-th view and E,-2 measures whether the samples are on all previous -1 views, we can obtain that En H. + Eiz-" [E.-1jjı indicates the sample must be in all t views. Therefore, we can
25

---

derive that the coefficient Σ characteristic, we can further transform
H.
+ 3
21=1 1E-11]:
R1-1
must be non-zero. On the basis of this
(38) as
B.
D
+B
4t-
E,
min QUl.
Q
W
E Holza +B 1
E
(39)
s.t.
Q :.j
2
0,
Q :j
1m = 1, 1,2. ... n2.
Its Lagrangian function can be expressed as
J (5, = min
@
Tig
+ T [00 [1
((0)) i.
1m -1).
(40)
where
1x
T = B.G.D.DH., + Ō E.
H
+
E
(41)
sp E Rmx1 2 0 and E RIx1 are the Lagrange multipliers.
By virtue of KTT conditions, we have
Q :.
-
T
-1m
=
(42)
and
w/ Q s.j
=0 i 1,2,3,
(43)
According the feasible region characteristic that the column sum is equal 1, we can further obtain
T
(44)
m
Therefore, we have
1m
T... 1m
Q
T +
(45)
ijj
m
1.. TT, 1m 2 Tij otherwise 0, = 1,2,.., m; = 1,2, Thg-
Since it exists closed-form solution, the computational overhead mainly comes from the construction of T.j, especially from B G. D.H,T + Q_T Combined with the matrix size, we have that constructing B, D.H. and Q_ will take O(m2d + mdyn4 + mn.ū)) and Omm2n,1 + mm, computing cost respectively, which are both square with respect to the sample size.
To reduce it, we first construct D.H, via a zero-matrix with larger size and then assign elements as done in the optimization about G,, Consequently, generating B, G. D.H, takes ((md, complexity. Subsequently, for ST_ Q: Q due to Q.-1 Rm and E._, R as well as ūn being greater than or equal to 74-1, combined with the 0-1 property and column orthogonality of E,-1, we have that Q. Q_ indicates taking the columns of Q to construct a larger matrix with the size of m x 7. (i.e., the same as the size Q.). Therefore, instead of directly computing QT we establish a bigger zero-matrix with the size of m x 74 and then assign its columns using the columns of Q.-1 under corresponding indexes. As result, constructing ST ET takes ((m ( computing overhead.
Therefore, we have that the computational complexity of constructing the term B. B.G.D.D. 88 _ Q ET_1 is O(md, + m2) Correspondingly, optimizing Q. will require O 2- m n. computing cost.
26

---

A.4 Updating the Swapping Variable S
Under given G2 B, and Qu. the original objective loss (6 with respect to S can be equivalentl expressed as
min A A| - B, S. 31 - 11 8
(46)
S.t. S E 10,1), - 1m; 11m = 1m.
On the basis of 25 for the term [B - -B.- we have
min B. B min Tr (S. B B 2B, BB--I.--1..
2B,
(47)
8,-1
Combined with the characteristics of feasible region, i.e., S is a square matrix with elements and 1, and there is only one in every column and every row, we can derive
S = Im-
(48)
Therefore, we have
min S,-1
[B
-B,-1
S
max Ir B.-
(49)
S
For the term
Q E ST 12-1112 in (46)
after expanding and removing irrelevant items, we
can obtain
min S,11
Q S Q 11 min Tr
-Q,E,- (T,,
(50)
S
Through trace cycle, accordingly have
max Tr (Q.EE-IQT-IS...
mün S
(51)
$
Together with 49 and
51
have that the problem 46) is equivalently simplified
max Tr ((BB, B + 3Q, Q S 8
(52)
s.t. S E {0. 10,11,,T.11 ST = 1m, 1m = mm
In virtue of the matrix vectorization transformation Vec(-), transform equivalent optimization problem,
52 as the following
Veec
+ -.Q..,
Vec (S.-1)
max S
(53)
s.t. S. {0, 10. 10, = S, 1mm
This an integer linear programming problem, and can be solved within cubic computational complexity with respect to the number of variables via existing software. Kindly note that S in Rmxm and m is greatly smaller than the number of samples. Accordingly. this requires minor computational overhead.
Subsequently, needs construct the term B O(3 m + m cost, which is almost close the square with respect to the sample size n. To decrease it, combined with the fact that there only one in each column of E,-1 and other elements are all 0, we have that the product between Q and E,-1 means picking out some columns of Q to generate smaller matrix. Therefore, rather than direct calculation, establish an auxiliary matrix with the size of x 7;-1, and then utilize the columns of Q to do assignment for it via the sample indexes observed on all t - views. Then, we utilize this auxiliary matrix to construct Q, Q,,,- Accordingly, building AB, B. E, Q will take Om3 + m 1) computational cost.
Direct calculation takes
In conjunction with the fact that is generally greatly smaller than 7 1. can obtain that updating S will take Om cost, which linear to the number of samples and consequently does not damage the large-scale ability.
27

---

A.5
Updating Variables under Initial View
Under f = 1, the swapping variable S is not required, and accordingly the objective loss equiva- lently becomes
min B.B,B Q
DD -
(54)
s.t. G2 G I. B,B, Im Q 2 0, Q 1m 1
which can be seen special case of be optimized.
c when both À and / take O, and only three variables need to
When updating G2, with given B, and Qt. the problem is equivalent to 19 Therefore, we can update G, by solving (21) as does. When updating the variable B,, with given G. and Qr. the
problem (54) is equivalent to (33 with taking 0. Therefore, we can update B, by solving 27 as
previous 2 2 does with À taking 0. When updating Qu. with given G2 and B,. (54) is equivalent to 28 with / taking O. Consequently, we can update Q via (45 with 33 taking 0.
In summary, under the scenario / = 1, we can optimize G, and B, as well as Q: using the updating paradigm in 2 2 with À and /3 taking 0.
B
Complexity Analysis
B.1 Computational Complexity
The computational expenditure is mainly composed of updating G,, B,, Q and S When updating GG, it involves constructing D,H, Q, B, and performing SVD on it, which takes (demg)) and (ddm²) respectively. m largely smaller than 7r, and therefore updating G totally takes (dd computational cost. When updating B, it involves constructing H. O + I and performing SVD on it, which takes O(mdiū.) and O(m²) re- spectively. Therefore, updating B, totally takes Omndeñe). When updating Qu. owing to the closed-form solution, it only needs to construct B, G, D.H,, + Q
which takes Omd,, + m² When updating St-1, it needs to construct AB, B, EQ tak- ing O(m3 + m 1) Based the above analysis. accordingly, the overall computing cost is (dgmmm + m²n, + m² + m²). (.)).A As time goes on, both 7n and ū.-1 approach to n. Moreover, the data dimension d, is not relevant to the number of samples So, the computational complexity of proposed algorithm is On), i.e, linear with respect to the number of samples n.
B.2 Space Complexity
The space expenditure is mainly composed of the memory parts required for optimizing G Bi, Q and S,-1. During optimizing G, due to D, ddd.. H, Ruxxx Q R and B, E Rmxm, it will require (d, + dym) memory cost to store D,H, Q Q. Combined with G, Rd:xm and the fact that m largely smaller than 7t therefore, optimizing G, needs (dd))) memory overhead. During optimizing B,, due to B E Rmmm and S E Rm it will require Odd + mñ, + m²) cost to store G2 D,H, Q + +B, Therefore, optimizing B, takes Oldrū)) memory overhead. During optimizing Q. it will require O'd,ū, + +mdy + mm)) cost to store G.G.D.H. + - Q.- ET_ Accordingly, optimizing Q takes (ddmñ) memory overhead. During optimizing S.-1. it will require Omm + mm,-1) cost to store AB, B + E,, QT Therefore, optimizing S. takes ( memory overhead. Additionally, 7 less than or equal to Based on the above analysis, consequently, we have that the overall memory overhead (d, In conjunction with the fact that the data dimension d, is irrelevant to the number of samples, can obtain that the space complexity of proposed algorithm is (n)).
28

---

C Additional Related Work
To effectively cluster multi-view data, Cui et al. [6] introduce adaptive embedding learning to construct low-rank graph affinities, and impute the missing components by exploiting the latent cross- view correlations to generate complete similarity representations. Fu et al. [1]] establish bipartite graphs through a generative modeling approach to capture potential global structure distributions, and employ a dynamic weighted fusion to mitigate the adverse effects of data incompleteness. Rather individual views alleviate the biased error induced by incompleteness, and utilize the local graph structure refined by tensor means to circumvent explicit feature recovery. Gu et al. [3] build anchor graphs via dictionary learning to improve the robustness against missing data, and concurrently extract local representation and high-order correlations by Gaussian error rank minimization with Laplacian manifold regularization. Zhao et al. (93] develop low-rank representation framework based on intrinsic graphs to infer missing samples, and establish inter-graph correlations through between-view structural consistency to formulate a robust consensus representation. Li et al. [20] employ the view-wise prototype graph learned via dual- stal-mtream framework to model similarity, and conduct data recovery by simultaneously investigating instance-level commonality and view versatility to preserve essential cluster structures. In contrast to separate representation learning, Wen et al. [68) formulate unified representation by combining spectral clustering and graph learning to achieve partial-view balance, and derive low-dimensional embedding using a co-regularizer to reveal inherent structure among data. He er al. [14] utilize anchor-inferred graph to directly produce asymmetrie intra-view similarity, and resolve information deficiency in incomplete data through a paired anchor bridging mechanism.
than the full graph, Li et al. [26) allocate dedicated sub-graphs
Different from graph technique for clustering tasks, Liu et al. [36 leverage the matrix factorization paradigm to mitigate the imbalance factor in incomplete learning, and apply sparse regularizer to capture low-dimensional individual features and construct compact local embedding. Wen er
al. (70) maintain local geometrie similarities via a efficient-weigheee common representation learning, and leverage adaptive view importance assignment to alleviate the bias caused by unbalanced incomplete views. Li el al. [2] explicitly model the between-view relationships through orthogonal factorization to explore the within-view spatial organization, and employ a tensor regularization as rank approximation to capture complementary information. In comparison to individual factorization mechanism, Chen et al. (3) unify coefficient expression and base learning via concept factorization to model the fluster-sampl relations, and build explicit view connections using the projecting learning preserve semantic correlations. Li et al. (30] jointly factorize multiple affinities in a tensor manner to maintain high-order geometrical characteristics, and impose SyyerrLaplaccio constraint
factorization model to facilitate
neighbor samples complement the consistency for incomplete view completion. Wen el al. [67] model the characteristic of each view through feature- aware factorization to mitigate the adverse effects caused by redundancy and noise interference, and boost the feature distinctiveness via an adaptive weighting scheme to produce structured unified representations. Unlike single-layer factorization. Zhang et al. [88] utilize multi-stage factorization paradigm to progressively explore partition-level representations. and aggregate all view information through late fusion to generate common grouping results. Li et al. (23) decrease the between-view errors by orthogonal and low-rank factorization to construct indicators without post-pree post-processing, and employ tensor norm regularization and soft labels jointly to exploit data complementary.
Unlike graph and matrix factorization means, subspace scheme is recently introduced into the grouping of multi-view data. Deng el al. (7] perform learning in low-dimensional subspace to effectively integrate multi-view information, and utilize an ensemble of projection mappings to process new samples with maintained balance. Wang al. (44 map original data through convolutional encoders into a subspace to construct potential representations, and learn soft labels via a self-expressive layer to reveal hierarchical feature structures. Huang et al. [17] collaboratively examine multilevel diversity patterns in random subspaces to form metric pairs, and adopt an entropy-driven mechanism to ensure comprehensive preservation about cluster wise variations in ensemble structures. Kang et al. [18] derive partition-level features across multiple subspaces to mitigate intra-vier view noise and inter-feature inconsistencies, and adaptively assign higher weights to partitions stronger consensus clustering agreement. Lv es al. [44] weight the reconstruction loss via pairwise similarity measures to preserve local structural relationships, and leverage pseudo- labeling to iteratively refine uncertain knowledge derived from subspace learning. Contrary to plain subspace, Qin et al. [48 construct the subspace endowed with both sparse and low-rank properties to mitigate errors in projectors, and take advantages of the block diagonal structure to amplify the
29

---

feature discriminability. Chen et al. 4 model data distribution through essential basis selection to derive cluster partitions in orthogonal subspace, and employ a mutual enhancement mechanism to jointly optimize cluster indicators and data representations. Wang el al. [63] maximize cross-view correlations for consistent subspace learning by canonical analysis, and enforce sample-wise mutual exclusivity via an f12 norm constraint to preserve underlying data structures.
Kernel strategy is also generally deemed as a effective means handle multi-view data. Liu al. (38 leverage cluster assignments to refine incomplete kernel recovery, and integrate the kernel imputation and clustering through alignment maximization
achieve superior data grouping performance. Zhang et al. [90] simultaneously address kernel imputation and space partitioning to reconstruct latent nonlinear view structures, and seamlessly generate low-rank tensor embedding and affinity matrices in an unified framework. Wang er al. [57] transform the concatenated view into kernel space to formulate nonlinear view relationships, and employ a kernelized smoothness regularizer to explicitly maintain locality properties in the feature space. Orthogonal to equally treating kernels, Li et al. 25 explicitly model both diversity and complementarity among base kernels to effectively capture inter-keree correlations, and incorporate matrix-induced regularization to probabilistically favor selection of kernel pairs with optimal dissimilarity. Zhang et al. [89] jointly improve kernel completion and low-rank tensor learning through a co-optimization scheme, and integrate kernel techniques into an incomplete subspace to reliably uncover multi-view structures. Liang et al. [31] approximate the spectral decomposition corresponding to the convex combination of base kernels to generate low-dimensional out-of-sample embedding, and establish rigorous theoretical guarantees for its stability. Liu et al. [3) emphasize learned unified clustering matrix to fill incomplete base matrices rather than operating directly on kernel spaces, and regularize clustering matrix by introducing prior knowledge improve the performance. Li et al [27 adaptively determine the dimension of unified partition in a potential embedding domain to overcome the limitations of fixed- reed-partition dimension, and leverage the latent consensus structure to model distributions among base kernels. Another are also well-researched.
algorithms, for instance, 33 61
59
15
10
87
D Symbol Summary
Table 4 provides summary of the main mathematical symbols and their corresponding meanings utilized in this study.
Table 4: Symbol and Meaning
Symbol
Meaning
D E Rdxe Xn:
the data matrix on the t-th view; the guidance matrix on the I-th view; the unified anchor matrix on all i views; the shared bipartite graph on all views;
G e ddxm
B, E Raxm
Q E Rmxa.
H, E Ra,xa;
the indicator matrix on the f-th view;
S mmxm
the swapping matrix about B (and Q.-1) the indicator matrix on all t 1 views; the identity matrix with the size of m m;
E E Rüix p
I Rmxm
1m E R
the vector with the size of m x 1; the index vector on the 1-th view; the index vector union on all views;
W. E RBxx1
W: R
Th
the number of samples observed on the t-th view; the number of samples observed on all / views; the number of samples;
The
n
the number of anchors; the data dimension on the 4-th view; the hyper- parametess,
de
A and 3
30

---

0.28 x10
x10
0.24
Loss Value
0.26
Loss Value
0.23
0.24
0.22
0.22
0.20
0.20
0.19
5
10
15
20
10
15
20
25
Iteration Step
Iteration Step
PROKARYO
(b) PROTEINF
x10
x10²
0.32
Loss Value
Loss Value
1.50
0.30
0.28
1.40
0.26
1.30
10
10
15
20
Iteration tepp (c) WIKIFEA
Iteration Step
(d) NUSWIENE
x10
x10
5.00
8.00
Loss Value
4.00
Loss Value
7.00
3.00
2.00
4.00
1.00
3.00
5
10
15
20
10
15
20
Iteration Step
lteration S tepp (f) YOUTUTEN
(e) CALTEALL
x104
x103
2.80
Loss Value
Loss Value
2.70
1.50
2.60
1.00
2.50
0.50
2.40
10
15
20
30
Iteration step
Iteration Step (h) FAMNISIX
YOUTUTWE
Figure 4: Evolution of the Loss Value with Respect to Iteration Step
31

---

E Experimental Setting
In experiments, we initialize the variables Gi and SJ using random orthogonal matrix and an identify matrix, respectively. For B1, firstly construct unified space minimizing the reconstruction error, and then employ k-means within this space to generate initial anchors serving as the assignment of B1. For Q1, we utilize one-hot vectors to randomly assign its columns, guaranteeing that the sum of its each column equals
For hyper-parameteet À and B, we fine-tune them in [10-1, 10", 10 102, 10 respectively. For the stopping error we set as 10-1, Then, we execute 20 times and summarize the average clustering results.
Description of Benchmark Methods
This section provides brief description of relevant benchmark methods.
GSRMC: It utilizes precomputed sub-graphs each view instead of feature recovering balance boundary samples, and separates the graph structure by means of nuclear norm to reduce biased error.
FLSD: It develops graph regularizer based factorization mechanism maintain local geometries, and utilizes semantic consistency to homeoregulate the discriminativeness incomplete observations.
MVTSC: It combines manifold space and feature space to restore missing parts, and explores inter- view information by tensor low-rank and graph consistency to formulate expressive representations.
MVCBG: It constructs a potential space via data compression to decreases the noisy impact, and utilizes view information complementarity based random walk principle establish the affinity.
AGCMC; It integrates consensus learning and graph completion to exploit hidden features of missing instances, and employs scale vectors to decrease the imbalance influence induced by incompleteness.
NGSPL: builds up the relations between neighbor group and single sample pair formulate representations, and designs a structure constraint based on neighbors to improve the graph quality,
PIMVC: It extracts sample features in subspace instead of original space to balance information among different views, and devises a scatter matrices based graph learning to capture data structures.
TCIMC: It adopts tensor norm mechanism to mine inter-view structures and complementary features, and utilizes graph connectivity constraint alleviate post-processing grouping operations.
TMBSD: It introduces the membership learning by view consistency to maintain multiple spectral embeddings, and employs tensor norm based regularizer enhance the block-diagonal structure.
PSMVC: It constructs the prototype graph rather than pair-wise graph to exploit data similarity relations, and introduces group of heterogeneous projections to preserve consistent cluster structures.
МKKMC: integrates clustering and imputation to get rid of the limitations base kernel complete- ness, and encourages kernel matrices via joint learning to adaptively populate each other mutually.
LRGMV: It unifies inter-view and intra-view related information recover latent relationships across views, and gives a low-rank regularizer to explicitly extract global structures between views.
Table 5: Space Usage Comparison
Dusaset
GSRMC
FLSD
MYISC
MVCBG
AGUMC
NGSPL
PIMVC
TCIMC
TMBSD
PSMVC
MIKMMC
LRGMV
Ours
PROKARYO
0.12
0.05
0.08
0.04
0.10
0.07
0.05
0.17
0.08
0.03
0.05
0.04
0.83
PROTEINE
0.83
0.11
01.53
0.06
0.20
0.25
0.06
0.90
0.57
0.06
0.34
0.29
0,83
WIKIFEA
2.59
0.48
1.57
0.07
L.13
1.95
0.40
2,70
1.77
0.08
1.22
1.15
0,85
NUSWIENE
36.16
17.21
YOUTUTEN
73.14
4.29
68.91
3.77
2.54
YOUTUTWE
6.52
3.98
4.44
FAMNISIX
37.32
43.07
34.41
G Space Usage
In addition linear time complexity, the proposed BSTM is also with linear space complexity. Sec- tion 6.2 has demonstrated the exccution efficiency. Here, illustrate its space-friendly characteristic,
32

---

we count the memory overhead, as shown in 5 where all results are expressed in GB units. One can see that we consistently receive less memory overhead, which mainly benefits from the fact that we circumvent view-data recomputing and successfully leverage only one bipartite graph with small size, rather than multiple self-expression affiiities with full size, to characterize overall similarity.
H Convergence
To illustrate the convergence of our BSTM, we visualize the loss values, as suggested in Fig. 4 One observe that the loss value is consistently decreasing and gradually reaches stability within forty iterations, which indicates that the presented BSTM is convergent.
40
20
100
10
15
20
15
20
30
40
62
50
100
(a) WIKIFEA
(b) NUSWIENE
(c) CALTEALL
10
20
25
30
25
(d) YOUTUTEN
(c) YOUTUTWE
(f) FAMNISIX
Figure 5: Visualization of S.-1 Learned on WIKIFEA ~ FAMNISIX
Table 6: Ablation Results about Twin-memory and Bit-swapping on WIKIFEA FAMNISIX
WIKIFEA
NUSWIENE
Alb.
0.4
0.7
0.1
0.4
0.7
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
ACC
P1R
FSC
ACC
PUR
FSC
ACC
PUR
FSC
Ab-B
50.98
57.08
44.74
49.07
54.22
38.13
41.13
45.65
26.05
10.74
33.34
7.32
12.10
30.53
9.67
11.79
30.96
9.33
Ab-Q
52.52
59.17
45.12
48
53.22
37.96
40.62
44.10
25.19
10.10
33.28
7.11
12.37
30.53
9.74
15.19
30.28
14.92
Al-hs
50.49
47.81
32.84
8,59
54.22
Ab-B
21.97
32.11
15.23
18.38
31.00
12.56
16.12
26.93
8.58
70.97
76.93
62.67
77. 77.36
63:42
71.31
76.36
62.56
Ah-4)
23 46
32.46
16.56
21.75
$2.40
11:24
19.38
28.79
7.51
71.47
77.12
62.95
71.76
71.87
62.56
71.43
76.55
61.98
Ab
21.78
30.72
14.62
15.59
26.57
10.35
16.96
27.45
9.21
71.13
76.67
61.98
70.67
78, 28.23
63.26
70.95
75.89
02:31
Dars
25.93
36.75
17.28
23.24
33.51
14.27
20.27
29.34
9.57
73.23
78.94
67.54
74.14
79.56
67.43
72.21
78.51
64.77
YOUTUTWE
FAMNISIX
66
Ab-Q
Ab-bs
66.97
68.85
60.42
68
75.47
59.78
66
76.03
39.78
52.18
$2.02
52. $2.16
43.37
50.97
$2.21
42.12
Ours
71.23
76.86
64.74
73.86
79.51
62.06
68.62
76.91
62.90
$7.97
98.35
47.84
$6.34
57.27
46.89
54.52
$8.43
45.93
I Additional Ablation Results
summaazes the ablation results on dataset WIKIFEA ~ FAMNISIX about the effectiveness of twin-memory and bit-swapping strategies. One can see that we receive consistently superior results than other counterparts. Combined with Table Table we can obtain that the devised twin wwn-memory strategy and bit-swapping strategy indeed bring performance enhancement.
33

---

Moreover, we also plot the learned bit-swapping St-1, as shown in Fig. Yellow denotes while blue denotes O. As seen, the produced S conforms to permutation characteristics, constitutes non-identity transformation matrix, and accordingly reorders anchor topology and graph structure.
Next, we provide the ablation results in which S only acts on B, S only acts on Q1, and our bit-swapping transformation is replaced by the value-altering mapping.
I.1 Ablation for S Only Acting on B,
In our model, the bitpswg transformation S 1 is simultaneously applied to both B, and Q to rearrange anchor topology and graph structure. Accordingly. we organize comparative experiments to display the results in which S only acts on one of B, and Q₁.
Table presents the ablation results for S only acting on B, (SonB). As seen, ours is the better in most cases, which means that applying S on Q2 is effective and can promote clustering performance.
Table 7: Ablation Results for S Only Acting on B,
PROTEINF
Abla.
0.1
0.1
0.4
0.7
ACC
PUR
ESC
ACC
PUR
FSC
ACC
PUR
PSC
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
SonB
51.54
72.41
46.39
43.99
56.81
42.67
14.61
56.81
11.62
35.68
10.97
21.31
29.64
35.37
16.14
26.57
31.17
12:25
Oas
74.95
82.21
64.79
72.78
79.13
62.82
53.09
74.59
49.59
36.26
41.70
21,81
33.57
37.89
18.41
30,07
35.07
14.41
WIKIFEA
NUSWIENE
39.70
33.13
Ous
47.23
50.17
41.70
10.99
33.57
33.52
9.87
33.15
15.10
CALTEALL
YOUTUTEN
SonB
22.97
33.14
16.85
15.59
26.57
10.35
16.96
27.45
9.14
72.52
79.50
62.75
70.55
77. 17.30
60.71
71.45
76.58
62.22
Duss
25,93
35.75
17.28
23.24
33.51
14.27
20.27
29.34
9.57
73.23
78.94
67.54
74.14
79.56
07.43
72.31
78.51
64.77
YOUTUTWE
FAMNISIX
SonB
65
68.76
77,05
52.36
40.37
40.28
57.27
45.93
1.2
Ablation for S Only Acting Q
Table
provides the ablation results for S. only acting on Q (SonQ). As observed, we receive better results, indicating that applying S on B, is beneficial for the clustering performance gain.
Table Ablation Results for S. Only Acting on Q.
PROKARYO
PROTEINF
Abla
0.1
0.4
0.7
0.1
01.4
0.7
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
SonQ
47.74
43.42
44.
25
40.21
35.
16.30
12.02
Ours
82.21
64.79
72.78
41.70
21.81
18.41
14.41
WIKIFEA
NUSWIENE
SonQ
50.49
58.80
44.52
48.81
$3.00
37.5
39 60
9.87
32.0 84
6.98
12.01
30.48
9.48
11.23
$0.92
9.23
Ours
54.22
59.74
47.23
50.17
54.50
39.31
41.70
46.41
27.03
10.99
33.57
7.59
12.48
33.52
9.87
15.41
33.15
15.10
CALTEALL
YOUTUTEN
SonQ
23.86
33.85
16.23
15.78
26.21
11.57
17 26
27.00
9.72
71.23
78.12
63.42
70.17
76.12
60.31
70.45
75.28
61.43
23.24
7%.94
78.51
64.77
YOUTUTWE
PAMNISIX
SonQ Ours
67.92
73.26
62.13
69.57
77.22
58
67.5
76.86
58.18
53.67
51.43
41.37
43.69
53.67
12.56
51,47
55.63
41.36
71.23
76.86
64.74
73.86
79.51
62.06
68.62
76.91
61.90
57.97
58.35
47.84
56.34
$7.27
46.89
$4.52
58.43
45.93
I.3 Ablation for Value-altering Mapping
Our bit-swapping transformation is with the ability to maintain numerical-consistenee That is, only reorganizes the topology of anchors and the structure of graph while it does not alter their value. To illustrate strengths, we utilize previous orthogonal permutation transformation (VaM) to replace it, and the ablation results are presented in Table 9 One can observe that produce more
34

---

desirable clustering results than VaM in most cases, which means that our bit-swapping strategy is more North-having.
Table 9: Ablation Results for Value-altering Mapping
Abla.
0.1
0.4
0.7
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
ACC:
PUR
FSC
ACC
PUR
FSC
VaM
72:12
80.42
62.
22.23
79.01
61.37
52.13
72.42
47.12
34,89
00.16
20.66
31.95
31 27.25
18.47
28.45
34,63
14.12
Ours
74.95
82.21
64.79
72.78
79.13
62.82
52.09
74.59
49.59
36.26
41.70
21,81
33.57
37,89
18.4
30,07
35.07
14.41
WIKIFEA
NUSWIENE
47.23
41.70
33.57
CALTEALL
YOUTUTEN
VaM
25.21
34.24
16.96
23.13
32.89
13.43
19.78
28.75
9.36
72.36
77.23
66.62
73.24
78.24
66.24
70.96
77.
65.42
Oces
25.93
35.75
17.28
23.24
33.51
14.27
20.27
29.34
9.57
73.25
78.94
67.54
74.14
79.56
07.43
72.21
78.51
64.77
YOUTUTWE
FAMNISIX
63.5 52
62.31
66.74
56.35
45.23
44.32
57.97
Steadiness
In addition the average value of clustering results, we count the standard deviation demonstrate the steadiness of our model, as suggested in Table I0 According to these results, one can obtain that the presented model is relatively steady and can produce robust clustering results.
Table 10: Standard Deviation of Clustering Results (%)
PROKARYO
PROTEINF
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
ACC
PUR
FSC
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.87
0.89
0.63
0.76
0.58
0.63
0.75
0.78
0.51
WIKIFEA
NUSWIENE
0.01
0.01
0.01 0.00
0.00 0.00
0.00 0.00
0.00
0.37
0.19
0.21 0.16 0.15 0.07
0.19
0.15
0.10
CALTEALL
YOUTUTEN
1.25
2.47
YOUTUTWE
FAMNISIX
0.57
0.42
0.48 0.81 0.50
0.53
0.71 0.38
0.54
0.04
0.04
0.00
0.08
0.07
0.00
0.02
0.02
0.00
K Parameter Sensitivity
Parameters À and 3 play a role in regulating L2 and L3 respectively to formulate favorable clustering representations. To explore the parameter sensitivity, we plot the results under multiple groups of λs and Bs, as shown in Fig. 6 and Fig- One can observe that the clustering performance exhibits no significant fluctuations. Therefore, our model relatively robust with respect to parameters À and B.
L Influence of Anchor Number
To investigate the influence of anchor number, count the clustering performance under diverse anchor numbers, as illustrated Fig. where my ~ my equal to 1k ~ 5k respectively. is the number of clusters. As seen, the performance curve relatively smooth with respect to anchor number, demonstrating that our proposed model is not significantly affected by the anchor number.
35

---

30
PUR (%)
FSC (%)
80
86
40
ACC
16
10"
10
T0
10
109
100
10
be
10a
101
10
tgp
102
10'
T02
10P
(a) PROKARYO-ACC
(b) PROKARYO-PUR
(c) PROKARYO-FSC
40
PUR (%)
FSC 196)
15
ADC
20
20
10
100
TO7
10
100
100
10"1
10
10
10"
10
10
TOP
10
10
10
10
10
10
(d) PROTEINF-ACC
(c) PROTEINT-PUR
PROTEINF-FSC
50
10
40
PUR (86
40
FSC (%))
20
20
80
10
109
9
10
10P
109
10
10
10
100
10
10
100
10
10
100
10
100
10
100
(g) WIKIFEA-ACC
(h) WIKIFEA-PUR
(i) WIKIFEA-FSC
20
40
20
ACC (%)
FSC 196)
80
0
10
10P
10T
t01
10
102
10
10
8 10
101
102
101
100
lo!
101
10
102
10
10
tuo
10
10
100
10a
109
(i) NUSWIENE-ACE
(k) NUSWIENE PUR
()) NUSWIENE-FIE
Figure 6: Parameter Sensitivity on PROKARYO ~ NUSWIENE
36

---

20
PUR (%)
PSC (%)
10
ACC
10
10
10"
10"
TO!
10
10
100
10
D0
100
101
10a
10
10
10
tor
100
10
(a) CAC
(h) CALTEALL-PUR
(c) CALTEALL-FSC
80
80
A00 (%)
8
PUR (S)
60
FSC (96)
80
90
20
10
10
10
T07
10
toc
10
100
102
10
10"
10
10P
10
10
10
10
10
(d) YOUTUTEN-ACC
(e) YOUTUTEN-PUR
YOUTUTEN-FSC
80
80
400 (%)
PUR (S)
60.
FSC (%))
80
20
10
109
10
10
3
10
107
T0P
1ps
10
10P
100
10
107
100
10
10
100
10
10
100
10
g YOUTUTWE-ACC
(h) YOUTUTWE-PUR
(i) YOUTUTWE-FSS
80
80
80
PUR (S)
PSC 156)
400
20
0
10
70P
107
10
10
tup
101
100
102
10
10P
8
10
10
10
toP
10'
101
100
lo!
10a
109
101
10
102
(i) FAMNISIX-ACE ACC
(k) HAMNISIX-PUR
(I) FAMNISIX-FES
Figure 7: Parameter Sensitivity on CALTEALL FAMNISIX
37

---

80
50
ACC - PUR
- FSC
+ ACC - PUR FSC
75
40
Performance
Performance
65
30
60
20
10
60
202
2112
1/56
1714
7055
701
1/6
Anchor Number
Anchor Number
(a) PROKARYO
(b) PROTEINF
36
ACC - PUR -M-FSC FSC
ACC - +
PUR - FS-FSC
50
300
Performance
Performance
40%
26
30
20
20
15
10
700
7712
17ks
1734
1R5
Anchor Number
Anchor Number (d) NUSWIENE
(c) WIKIFEA
+ ACC -e- PUR FSCFSC
+ ACC -0-PUR -X-FSC
30
80
Performance
25
Performace
75
200
70
15
65
10
60
55
100
1192
17g
1774
775
Anchor Number
Anchor Number (f) YOUTUTEN
(c) CALTEALL
ACC - PUR -W- FSC
ACC -PPPUR - FSC
80
Perforance
75
Performacce
589
66
70
54
65
52
60
55
m9
171
1ag
mg
Anchor Number
Anchor Number
YOUTUTWE
(h) FAMNISIX
Figure 8: Clustering Performance under Different Anchor Numbers
38


Reviews:
[{"review_id": "6YhqIW4snY", "reviewer": "Reviewer_hkM5", "summary": "This paper designs an algorithm named BSTM to overcome two limitations in multi-view clustering:  the ignoring of basis embedding and the value-distorting mapping. Unlike traditional feature library mechanisms, it harmonizes disparate dimensions through specialized view-specific projector, and incorporates potential basis patterns during knowledge transfer. This avoids view data recalculating and alleviates fusion-induced distortion. The bit-swapping strategy presented re-render anchor topology and affinity structure by virtue of the one-hot encoded characteristics while preserving numerical consistency. All components are co-optimized in an end-to-end manner, and the updating scheme with linear complexity guarantees the overall efficiency.", "questions": "1. Due to the presence of incompleteness, the graph scale is diverse for different views. How to ensure that it is compatible for history data and newly arrived views?\n2. In the process of updating the bipartite graph variable, as illustrated, it will induce a third-order overhead to the sample number. So, could you please provide more detailed procedures about how it reduces to linear?    \n3. It claims that the coefficient in (13) consisting of $\\mathbf{H}_t$ in (3) and $\\widetilde{\\mathbf{E}} _{t-1}$  is non-zero. How to guarantee this point? or How to derive this conclusion?\n4. The proposed twin-memory paradigm transfers knowledge collectively, so, rather than the employed learning strategy for anchors, how does the current model perform under heuristic search?", "limitations": "As stated, the designed model involves two hyper-parameters, which requires extra efforts to do fine-tuning. Parameter-free version is the future goal.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths** \n1. The structure is well-organized and presented logically. \n2. Experiments conducted are extensive, and validate the method from multiple aspects. \n3. The idea of twin-memory architecture is interesting, and its collaborative knowledge propagating facilitates the discovery of patterns in newly arrived incomplete views.  \n\n**Weaknesses**\n1.  Associating IN-1 and IN-A with the matrix $\\mathbf{H}_t$ in (3) and $\\widetilde{\\mathbf{E}} _{t-1}$ in (5) respectively helps grasp the contributions  of customized indicators better. \n2.  Although harmonizing disparate dimensions, the projectors could bring about extra computational overhead and accordingly reduce efficiency.\n3. The illustration about the topology rendering that consists of column sum and row sum is slightly concise, and more explanations could better enhance its significance.", "was_revised": true, "final_justification": "Thank you for the detailed response from the author, which has answered most of my questions. I have decided to maintain my rating.", "rebuttal": "**Q1:**  Associating IN-1 and IN-A with $\\mathbf{H}_t$ in (3) and $\\widetilde{\\mathbf{E}} _{t-1}$ in (5). \n \n**A1:** Thanks! We will associate these in the next version.\n \n\n**Q2:** The projectors could bring about extra overhead.\n \n**A2:** According to their size $d_t \\times m$, we have that storing them will take $\\mathcal{O}(dm)$ memory overhead. Besides, combined with Remark 1, we have that updating them will take $\\mathcal{O}(n)$ computing overhead. Since $d$ is a constant and $m$ is largely smaller than $n$, we can derive that these projectors do not impact the overall complexity. \n \n\n**Q3:**  More illustration about topology rendering. \n\n**A3:** The topology rendering mechanism requires that in each column and each row, there is only one element equal to 1, while all other elements are zero. These features guarantee that it merely alters anchor order while anchor value remains unchanged. This makes learned anchors well maintain the characteristics of original data. \n \n \n**Q4:**   How to guarantee compatible graph scale? \n \n**A4:**  To derive compatible graph, we construct indicator matrices to pick out certain columns of the common graph for current view to do similarity calculation. Afterwards, to make this graph transferable, we utilize the indicator matrix to construct corresponding small similarity and then compare it with that constructed on all previous views. Kindly note that we do not explicitly establish these tailored indicator matrices, and use them solely for illustrative purposes. Remarkably, we adopt the element-wise value extraction operation via corresponding index to do similarity construction and comparison. \n \n\n**Q5:** How to reduce the cost of bipartite graph to linear?\n \n \n**A5:** Along with the view collection, the size of $\\widetilde{\\mathbf{E}} _{t-1}$ will be close to $n \\times n$. Accordingly, computing $\\widetilde{\\mathbf{E}} _{t-1} \\widetilde{\\mathbf{E}} _{t-1}^{\\top}$ will require a third-order cost. To reduce it to linear, note that $\\widetilde{\\mathbf{E}} _{t-1}$ consists of binary elements, and $\\widetilde{\\mathbf{E}} _{t-1} \\widetilde{\\mathbf{E}} _{t-1}^{\\top}$ is a diagonal matrix. The diagonal elements are each row sum of $\\widetilde{\\mathbf{E}} _{t-1}$. Thus, instead of explicit calculation, we can directly construct the diagonal elements, and then multiply it by the shared graph with the size of $m \\times n$. Consequently, the computing cost is linear. \n\n\n \n**Q6:** How to guarantee the coefficient in (13) non-zero? \n \n**A6:** $\\mathbf{H}_t$ aims at measuring whether the samples are available on current view, while  $\\widetilde{\\mathbf{E}} _{t-1}$ measures whether the samples are on historical views. Note that the current sample either appears in the current view, the historical view, or both. Therefore, we have that each row sum of $\\mathbf{H} _t$ + $\\widetilde{\\mathbf{E}} _{t-1}$ must be non-zero.  Accordingly, we can derive that this coefficient is non-zero. \n \n**Q7:** The performance under heuristic search. \n \n**A7:** The following table presents the performance comparison where HS and LS denote the results based on heuristic search and learning strategy respectively. As seen, HS usually is sub-optimal, possibly because the heuristic search is unable to effectively characterize original data due to the separation from graph generation. \n\n\n|  | PROKARYO |  |  |  |  |  |  |  |  |\n|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n|  | 0.1 |  |  | 0.4 |  |  | 0.7 |  |  |\n|  | ACC | PUR | FSC | ACC | PUR | FSC | ACC | PUR | FSC |\n| HS | 53.54 | 72.23 | 46.74 | 44.10 | 56.81 | 43.37 | 42.86 | 56.13 | 41.41 |\n| LS | **74.95** | **82.21** | **64.79** | **72.78** | **79.13** | **62.82** | **52.09** | **74.59** | **49.59** |\n|  | PROTEINF |  |  |  |  |  |  |  |  |\n| HS | 35.41 | 40.95 | 21.35 | 31.64 | 36.44 | 17.33 | 28.42 | 33.63 | 12.77 |\n| LS | **36.26** | **41.70** | **21.81** | **33.57** | **37.89** | **18.41** | **30.07** | **35.07** | **14.41** |\n|  | WIKIFEA |  |  |  |  |  |  |  |  |\n| HS | 53.98 | 58.06 | 46.45 | 49.21 | 54.22 | 39.13 | 41.66 | 45.11 | 26.02 |\n| LS | **54.22** | **59.74** | **47.23** | **50.17** | **54.50** | **39.21** | **41.70** | **46.41** | **27.03** |\n|  | NUSWIENE |  |  |  |  |  |  |  |  |\n| HS | 10.85 | 33.26 | 7.41 | 12.42 | 30.45 | 9.79 | 13.02 | 31.07 | 10.98 |\n| LS | **10.99** | **33.57** | **7.59** | **12.48** | **33.52** | **9.87** | **15.41** | **33.15** | **15.10** |\n|  | CALTEALL |  |  |  |  |  |  |  |  |\n| HS | 21.37 | **35.85** | 15.16 | 18.33 | 31.11 | 12.67 | 17.60 | 29.24 | **9.64** |\n| LS | **25.93** | 35.75 | **17.28** | **23.24** | **33.51** | **14.27** | **20.27** | **29.34** | 9.57 |\n|  | YOUTUTEN |  |  |  |  |  |  |  |  |\n| HS | 72.75 | 78.62 | 62.97 | 73.80 | 79.37 | 64.34 | **72.23** | 76.36 | 64.51 |\n| LS | **73.23** | **78.94** | **67.54** | **74.14** | **79.56** | **67.43** | 72.21 | **78.51** | **64.77** |\n|  | YOUTUTWE |  |  |  |  |  |  |  |  |\n| HS | 70.06 | 75.51 | 55.73 | 68.28 | 76.79 | 56.56 | 68.53 | 76.86 | 58.27 |\n| LS | **71.23** | **76.86** | **64.74** | **73.86** | **79.51** | **62.06** | **68.62** | **76.91** | **62.90** |\n|  | FAMNISIX |  |  |  |  |  |  |  |  |\n| HS | 52.16 | 55.72 | 41.26 | 50.14 | 53.70 | 39.34 | 43.00 | 43.11 | 25.66 |\n| LS | **57.97** | **58.35** | **47.84** | **56.34** | **57.27** | **46.89** | **54.52** | **58.43** | **45.93** |"}, {"review_id": "r7jfMji6Uw", "reviewer": "Reviewer_TZU6", "summary": "This paper tackles multi-view clustering by proposing a unified framework that simultaneously learns basis embeddings and value-preserving mappings. Distinct feature spaces are first harmonised through dedicated projectors; the model then constructs shared anchors to capture intrinsic patterns and generates bipartite graphs to quantify cross-view similarity, thereby avoiding repeated view-by-view recomputation and fusion distortion. To remain compatible with incoming views, the authors introduce a transformation based on one-hot–encoded row and column attributes of historical views. Anchors and graphs are jointly reordered topologically so that their structures align while their values remain unchanged, and all components are optimised together with overall linear time complexity.", "questions": "- Could the authors elaborate on the mathematical or clustering rationale behind enforcing exactly one ‘1’ in each row and column of $\\widehat{\\mathbf{S}}_t$? What would be the implications—on anchor assignment, similarity computation, and convergence behavior—if this constraint were relaxed to allow multiple or no selections per row?\n\n- What are the key advantages or characteristics of the proposed twin-memory architecture compared to conventional per-view designs, particularly in terms of computational workload, feature extraction, and view-wise information propagation?\n\n- The anchor-alignment transformation can vary from an identity mapping to a complex permutation. Under which data distributions or hyperparameter settings does this transformation collapse to the identity? How does this affect clustering quality and training stability?\n\n- If the guidance mechanism is allowed to relax the one-hot column constraint, does performance on clustering metrics (e.g., NMI, ARI) degrade significantly? Please discuss any observed failure modes such as mode collapse or anchor duplication, and consider including sensitivity curves to illustrate the impact.\n\n- The rationale behind hyperparameter choices is not clearly explained. Since different values can substantially affect performance, a discussion of how these settings were determined would help clarify the method’s underlying principles.\n\n- What is the motivation for introducing matrix vectorization at the specified point in the algorithm? Are there any computational trade-offs or penalties associated with this choice?\n\n- The graph transfer process relies on shared sample observations across views. How does the method behave when a new incoming view has no intersection with historical views? Is anchor transmission or graph transfer still valid in such cases?", "limitations": "Authors have mentioned the limitations in the work. Parameter-free learning and direct cluster label learning could further boost the practicality and performance.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n+The bit-swapping strategy and twin-memory paradigm address common pitfalls of view misalignment and information loss.\n\n+Related work is thoroughly covered, and the optimisation procedure is explained in a step-by-step, easy-to-follow manner.\n\n**Weaknesses**\n\n- As the overall loss function consists of three components, an explicit summary of the contribution of each item is beneficial for highlighting the entire method’s design. \n\n- Giving the inspiration about the tailored indicator matrices is encouraging. Since the main purpose of these matrices is to pick out certain graph columns to do similarity comparison, the behind inspiration will facilitate fundamental understanding of structural similarity.", "was_revised": true, "final_justification": "Thank you for the response and additional results, which address most of my concerns. After considering the other reviewers’ comments, I am leaning positive to the submission", "rebuttal": "**Q1:** A summary on the contribution of each item.\n    \n**A1:** Thanks! $\\mathcal{L}_1$ aims at formulating similarity and extracting basis patterns via reconstruction error minimization. $\\mathcal{L}_2$ renders anchors via current view and historical views while preserving value consistency to reach matching configuration. $\\mathcal{L}_3$ guarantees  graph scale to be compatible and meanwhile reorganizes graph topology. $\\mathcal{L}_2$ and $\\mathcal{L}_3$ collaboratively transfer knowledge at similarity level and embedding level. We will add this summary in the next version.  \n \n \n\n**Q2:**  The inspiration about tailored indicator matrices.   \n \n**A2:** Due to the incompleteness, the graph size is diverse and consequently it is impossible to construct the graph shared for newly-arrived view and previous views. Besides, it also can not do knowledge transfer on graph. To overcome these difficulties, we utilize $\\mathbf{H} _t$ to pick out some columns of the shared graph  for current view to build similarity, and utilize $\\widetilde{\\mathbf{E}} _{t-1}$ to form a smaller graph to compare with previous views. Kindly note that the size of shared graph is dynamically changing as view data is collected.  \n \n\n**Q3:** The underlying principle for $\\widehat{\\mathbf{S}}_t$. \n \n**A3:** This essentially guarantees that anchors are merely rearranged without altering their values. It mainly leverages one-hot characteristics to reorganize anchors. If violated, the learned anchors will be disturbed, potentially destabilizing the entire graph topology. \n \n\n\n**Q4:** The advantages for twin-memory paradigm. \n\n**A4:** Rather than extracting features by view, it builds only one graph across views, and so the computational workload is smaller than current per-view architectures. Besides, it effectively gathers view information during forming features instead of via fusion. Accordingly, the distortion induced by fusion is effectively avoided. \n\n\n \n**Q5:** Could the transformation be a unit matrix?  \n \n**A5:** Yes. When the anchors learned on current view is the same order as those on previous views, topological rendering of anchors becomes unnecessary during transformation. Accordingly, it degenerates into a unit matrix. \n \n \n \n**Q6:** Performance under guidance without column constraints. \n \n**A6:** These constraints aims at discriminating projectors. Without them (WO), the dimension space could be redundant and accordingly the model performance will degrade. The following table gives the comparison results.   \n \n\n|   | PROKARYO |  |  |  |  |  |  |  |  |\n|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n|  | 0.1 |  |  | 0.4 |  |  | 0.7 |  |  |\n|  | ACC | PUR | FSC | ACC | PUR | FSC | ACC | PUR | FSC |\n| WO | 68.36 | 77.24 | 60.62 | 67.47 | 77.02 | 58.56 | 48.32 | 66.32 | 41.21 |\n| Ours | **74.95** | **82.21** | **64.79** | **72.78** | **79.13** | **62.82** | **52.09** | **74.59** | **49.59** |\n|  | PROTEINF |  |  |  |  |  |  |  |  |\n| WO | 32.42 | 38.24 | 19.32 | 30.36 | 35.23 | 16.12 | 26.32 | 32.27 | 13.34 |\n| Ours | **36.26** | **41.70** | **21.81** | **33.57** | **37.89** | **18.41** | **30.07** | **35.07** | **14.41** |\n|  | WIKIFEA |  |  |  |  |  |  |  |  |\n| WO | 52.12 | 54.37 | 45.35 | 48.53 | 52.23 | 37.34 | 37.42 | 43.42 | 24.36 |\n| Ours | **54.22** | **59.74** | **47.23** | **50.17** | **54.50** | **39.21** | **41.70** | **46.41** | **27.03** |\n|  | NUSWIENE |  |  |  |  |  |  |  |  |\n| WO | 9.83 | 32.32 | 6.53 | 11.23 | 31.47 | 9.11 | 13.26 | 30.12 | 14.21 |\n| Ours | **10.99** | **33.57** | **7.59** | **12.48** | **33.52** | **9.87** | **15.41** | **33.15** | **15.10** |\n|  | CALTEALL |  |  |  |  |  |  |  |  |\n| WO | 23.28 | 33.43 | 16.27 | 21.27 | 31.56 | 12.89 | 19.84 | 28.83 | 8.47 |\n| Ours | **25.93** | **35.75** | **17.28** | **23.24** | **33.51** | **14.27** | **20.27** | **29.34** | **9.57** |\n\n \n \n**Q7:** The reasons for hyper-parameter setting. \n\n**A7:** $\\lambda$ plays a role in regulating anchor residual while $\\beta$ regulates graph residual. Because of the consensus structure, these residuals are generally in the same low magnitude. Besides, in experiments, we found that the reconstruction error is usually slightly larger than these residuals. Thus, we search $\\lambda$ and $\\beta$ in a slightly larger same scale range. \n \n \n\n**Q8:** The rationale for matrix vectorization.\n\n**A8:** It primarily transforms the intractable trace problem into an element-wise maximization linear programming problem, thereby enabling solutions via existing packages. \n \n \n\n**Q9:** Is the transfer still valid without view intersection?\n \n**A9:** Yes. The devised transfer mechanism is only related to the union between indexes. Even without view intersection, it still operates properly as long as  the union is not empty."}, {"review_id": "V04QlXCyfY", "reviewer": "Reviewer_e6Ai", "summary": "This work proposes a twin-memory paradigm to overcome the loss of basis patterns during the process of propagating knowledge from historical views to new views, and a bit-swapping mechanism to correspond the topologies of anchors and graphs under numerical consistency. It specializes a group of guidances to synchronize distinct dimensions, and captures intrinsic patterns via transferable anchors.  The collective graph structure is utilized to quantify similarity, eliminating the data-recalculation requirement and fusion distortion. By formulating topology transformation on binary space, it reorders anchor and graph structure without altering value consistency to reach appropriate matching. Subsequently, a four-step alternating updating scheme is designed to minimize the associated loss function.", "questions": "The questions, \n\n- The specialized guidance mechanism serves to mitigate dimensional discrepancies for perspective- invariant feature extraction. Through the tight integration with the anchor framework, it helps anchor representation transfer across modalities.  Can this generalize to raw data? If applicable, would such implementation yield measurable gains? If not, what are the limitations?\n \n- The built indicator matrices play a role in assisting establishing similarity and transferring similarity from previous views to new views. It seems that they have a complementary relation. Is it possible to build one from the other?  This helps achieve additional space savings. Besides, over time, the indicator matrix for similarity transferring is close to the full size. Are there additional means available to decrease it?\n\n- Along with the ongoing propagation of view information, there will lead to continuous accumulation of historical views.  As a result, compared to the new views, the relative proportion of historical views will continue to increase. However, in lifelong learning scenarios constrained by both privacy regulations and memory limitations, these historical views become inaccessible over time. This raises a critical question: How can we calibrate the contributions between incoming new views and unavailable historical views in the learning process?", "limitations": "Extra efforts are required for hyper-parameters. The spectrum partitioning may degrade the data diversity.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The strengths,\n- The motivation and the overall framework are clearly explained. \n\n- The designed linear complexity facilitates the model’s large-scale deployment capacity. \n\n- The algorithm performance is analysed through multiple perspectives.\n\nThe weaknesses,\n\n- The topology transformation may complicate the model, as it requires that each column is composed of one-hot encoder and meanwhile the rows also need to satisfy sum constraints. Moreover, the discrete optimization is usually more challenging to solve compared with continuous counterpart.   \n\n- The need for parameter searching may weaken practical performance, as the model requires manual adjustment of two hyper-parameters. This may result in suboptimal performance when processing data with poorly-defined clusters.  \n\n- In addition to the memory graph, the model involves the memory anchor, which may increase the space cost, especially on resource-limited platforms. Moreover, in propagation, the anchor quality may vary with the arrival of incoming data.  The degenerated anchors will restrict the representation expression ability of the proposed model.", "was_revised": true, "final_justification": "The authors have well solved my concerns and I decide to raise the rating.", "rebuttal": "**Q1:**  The topology transformation and discrete optimization may complicate the model. \n\n**A1:**  Thanks! The topology transformation aims at reorganizing anchor order to alleviate the mismatching dilemma while the discrete optimization is to preserve the value consistency. They collaboratively support the anchor knowledge transfer from historical views to current view.  The topology transformation and discrete optimization are equivalently converted to a linear programming, and can be easily solved by off-the-shelf software. Besides, the theoretical complexity demonstrates that they are with a linear overhead and do not bring about severe computing and storing workload. \n \n \n**Q2:**  The need for parameter searching may weaken practical performance. \n \n**A2:** The hyper-parameters aim at regularizing anchor residual and graph residual to formulate desirable similarity. Although it needs parameter searching, combined with sensitivity figures, we have that the model performance is relatively stable under diverse parameter values on multiple data scenes. Therefore, we can deploy it on different scenes with the given guidelines. In the future, we will strive to devise a parameter-free version to further enhance its practicality. \n \n  \n**Q3:** The memory anchor may increase the space cost.    \n \n**A3:** The memory anchor matrix plays a role in propagating basis embedding from historical views to incoming view. Although it is with memory function, kindly than it has the size of $m \\times m$. In general, $m$ is greatly smaller than $n$. Thus, the space cost caused by the memory anchor matrix is almost negligible compared to the overall cost. \n  \n   \n**Q4:** Can the specialized guidance generalize to raw data?  \n \n**A4:** Yes. The specialized guidance is associated with anchor matrix (AAM) in the proposed model, and it is mainly to alleviate dimension disparity to build transferable space. When generalizing to raw data (GRD), although this is also able to construct transferable space via dimension reduction, it generally degenerates dimension diversity and brings about information loss of view data, accordingly weakening the overall clustering performance. To validate this, we organize relevant comparison experiments, as shown in the following table. One can see that GRD is suboptimal compared to AAM.  \n\n\n\n|  | PROKARYO |  |  |  |  |  |  |  |  |\n|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n|  | 0.1 |  |  | 0.4 |  |  | 0.7 |  |  |\n|  | ACC | PUR | FSC | ACC | PUR | FSC | ACC | PUR | FSC |\n| GRD | 62.12 | 74.32 | 50.32 | 52.17 | 58.72 | 51.32 | 43.21 | 58.32 | 42.83 |\n| AAM | **74.95** | **82.21** | **64.79** | **72.78** | **79.13** | **62.82** | **52.09** | **74.59** | **49.59** |\n|  | PROTEINF |  |  |  |  |  |  |  |  |\n| GRD | 33.42 | 39.52 | 20.56 | 30.82 | 35.83 | 16.21 | 26.52 | 31.47 | 11.84 |\n| AAM | **36.26** | **41.70** | **21.81** | **33.57** | **37.89** | **18.41** | **30.07** | **35.07** | **14.41** |\n|  | WIKIFEA |  |  |  |  |  |  |  |  |\n| GRD | 51.35 | 56.73 | 44.57 | 48.65 | 53.11 | 38.23 | 39.78 | 44.67 | 25.89 |\n| AAM | **54.22** | **59.74** | **47.23** | **50.17** | **54.50** | **39.21** | **41.70** | **46.41** | **27.03** |\n|  | NUSWIENE |  |  |  |  |  |  |  |  |\n| GRD | 10.42 | 31.67 | 7.34 | 11.56 | 31.21 | 8.23 | 13.11 | 31.23 | 10.21 |\n| AAM | **10.99** | **33.57** | **7.59** | **12.48** | **33.52** | **9.87** | **15.41** | **33.15** | **15.10** |\n|  | CALTEALL |  |  |  |  |  |  |  |  |\n| GRD | 22.35 | 33.27 | 15.74 | 21.42 | 32.26 | 12.72 | 18.53 | 28.12 | 8.52 |\n| AAM | **25.93** | **35.75** | **17.28** | **23.24** | **33.51** | **14.27** | **20.27** | **29.34** | **9.57** |\n|  | YOUTUTEN |  |  |  |  |  |  |  |  |\n| GRD | 71.34 | 76.83 | 63.62 | 71.87 | 76.86 | 64.53 | 70.26 | 75.43 | 63.67 |\n| AAM | **73.23** | **78.94** | **67.54** | **74.14** | **79.56** | **67.43** | **72.21** | **78.51** | **64.77** |\n|  | YOUTUTWE |  |  |  |  |  |  |  |  |\n| GRD | 69.83 | 76.12 | 58.73 | 69.16 | 75.72 | 58.92 | 66.21 | 74.52 | 58.43 |\n| AAM | **71.23** | **76.86** | **64.74** | **73.86** | **79.51** | **62.06** | **68.62** | **76.91** | **62.90** |\n|  | FAMNISIX |  |  |  |  |  |  |  |  |\n| GRD | 54.24 | 54.76 | 44.52 | 52.31 | 53.52 | 42.73 | 51.32 | 53.32 | 43.78 |\n| AAM | **57.97** | **58.35** | **47.84** | **56.34** | **57.27** | **46.89** | **54.52** | **58.43** | **45.93** |\n\n\n**Q5:**  Is it possible to build one indicator matrix from the other?  Are there means available to decrease its overhead?\n\n**A5:**  Yes. The construction of indicator matrices is based on the union set of observed sample indexes. Therefore, the indicator matrix about current view can be built through that about historical views, vice versa. Besides, although the indicator matrix about historical views is close to full size over time, kindly note that we do not explicitly build and calculate these indicator matrices, and only utilize them for illustration. In practical, we select certain columns from the shared graph via corresponding indexes to establish similarity for current view and do graph propagation for historical views. All these operations are proven to only require linear complexity.\n \n\t\n**Q6:** How to calibrate the contributions between incoming new views and unavailable historical views?\n \n**A6:** Due to privacy protection or memory limitation, the historical views become inaccessible over time. Consequently, it can not directly weight historical views and incoming new views. To calibrate the contributions, note that during propagation, it inherently involves anchor transfer and graph transfer from historical views to new views. These components hierarchically characterize view data representation. Therefore,  instead of view data, we can calibrate anchor and graph respectively.  Specially, we can adjust anchor importance  in $\\mathcal{L}_2$ and graph importance in $\\mathcal{L}_3$ to balance view contributions. This dual-calibration mechanism ensures equitable weight allocation across views while preserving structural hierarchies."}, {"review_id": "mHBSKA9e8s", "reviewer": "Reviewer_o1Vu", "summary": "This paper addresses the challenges of incomplete multi-view clustering (MVC) by proposing the BSTM algorithm. It introduces a Twin-memory paradigm and a Bit-swapping strategy. The Twin-memory paradigm, consisting of a Unified Anchor Matrix (UAM) and a Shared Bipartite Graph (SBG), enables knowledge transfer to avoid redundant computation and fusion distortion. The Bit-swapping strategy reconstructs the anchor topology and graph structure based on binary operations. Experiments on 8 public datasets show that BSTM outperforms 12 baseline methods in most cases, especially in PUR and FSC metrics, and has linear complexity suitable for large-scale scenarios. However, there are still areas for improvement in theoretical analysis, experimental comparison, and expression.", "questions": "1.Theoretical Rigor: The theoretical explanation of the cooperation mechanism between the core components (UAM and SBG) is insufficient, and the assumption conditions and limitations of the model are not clearly stated. \n2.In formula (6), the hyper-parameters  and  are merely stated to \"balance the reconstruction error and the fusion term\". It is suggested to supplement: ablation experiments investigating the influence of different (,) combinations on the convergence behavior should be included in the appendix.\n3.This work lacks an analysis of the interactions between core components (UAM and SBG), particularly failing to investigate the performance degradation when UAM and SBG are used individually. It is recommended to conduct additional ablation experiments to quantitatively analyze the performance contributions of UAM and SBG in isolation, such as evaluating the metrics when only UAM or SBG is employed.\n4.While the paper mentions a complexity analysis, it does not provide an explicit comparison of computational complexity with other methods. Please supplement a comparative analysis of time complexity and computational complexity between BSTM and state-of-the-art methods (e.g., MVTSC, AGCMC).", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "The proposed Twin-memory paradigm and Bit-swapping strategy are innovative. The UAM and SBG effectively address the issues of ignoring basic embedding information and mapping distortion in existing MVC methods, with a self-consistent logical framework. Adequate Experimentation: Comprehensive experiments on multiple datasets, comparing with a large number of baseline methods, and testing under different missing rates, which can well verify the performance of the algorithm. The linear complexity analysis also shows its potential for large-scale data. Clearly points out the problems in existing MVC methods and proposes corresponding solutions, which has certain guiding significance for the development of the field. However, theoretical derivation details, extreme scenario analysis, and clarity of expression still leave much to be desired. The supplementation of absent comparative experiments and mechanistic explanations is expected to further enhance its academic influence and universality in practical applications.", "was_revised": true, "final_justification": "The authors have provided a well-prepared rebuttal that addresses most of the concerns raised in the initial review. Their clarifications and additional experimental results have improved the overall clarity and completeness of the paper. I appreciate the effort the authors have made in responding to the feedback. After considering the rebuttal, I have decided to maintain my original score.", "rebuttal": "**Q1:** Theoretical explanation on the cooperation mechanism between  UAM and SBG;  the assumption conditions; the limitations. \n\n**A1:** Thanks! UAM and SBG collectively transform knowledge via one common learnable framework. UAM aims to do propagation at embedding level while SBG does propagation at similarity level. They seamlessly integrate representations from historical views and newly-arrived data to facilitate clustering. Kindly note that they can cooperate with each other via $\\mathcal{L}_1$, or via $\\mathcal{L}_2$ and $\\mathcal{L}_3$ using the swapping matrix, or via both.\n\n\nAbout the assumption conditions, we assume that views are independent of each other. This is rational since in practice, view data is usually collected from diverse sensors. Based on this assumption, we customize a guidance for each view to harmonize disparate dimensions  and thereby construct transferable anchors and bipartite graph. \n \n\nAbout the limitations, there are two hyper-parameters in our model, which could to some extent weaken its practicality. The paradigm that firstly formulates spectrum and then conducts partitioning may degenerate view data diversity. Besides, we at this point do not learn to adjust the representation contributions between newly-arrived data and historical views. As data collection progresses, inaccessible historical views will account for an increasing proportion compared to new view. Therefore, balancing them will further boost the model performance. \n \n\t\n**Q2:** The influence of different hyper-parameter combinations  on the convergence behavior.   \n \n**A2:** We employ an alternating optimization strategy to minimize the formulated loss function that is lower-bounded by zero. Under different hyper-parameter combinations, the loss still can be lower-bounded by zero. Additionally, the solutions of all variables still can be obtained by Eqs.(8), (10), (15) and (18) respectively, even both of hyper-parameters as zero (as illustrated in Steps Under Initial View). Therefore, during updating each variable, it is monotonically decreasing. Combined with monotonicity and boundedness, consequently, our algorithm is theoretically convergent for different hyper-parameter combinations. We will add the convergence curves under diverse hyper-parameter combinations in the next version. \n\n\n\n**Q3:** \tThe interactions between UAM and SBG; the performance contributions of UAM and SBG in isolation. \n \n**A3:**  UAM and SBG work within one integrated framework, and they negotiate with each other during the learning process. Owing to the joint-optimization, UAM and SBG establish a tightly-coupled relationship through bidirectional collaborative mechanisms. Specially, UAM guides SBG in capturing global clustering structures, while SBG refines UAM through its connection patterns to eliminate view-specific biases. This synergistic interaction enhances clustering robustness, particularly when handling incomplete views, where the memory function of UAM and the topological elasticity of SBG effectively preserve clustering performance. \n\t\n\t\n\t\nAbout the performance contributions, the following table gives the ablation results. As seen, UAM and SBG collaboratively improve the clustering performance. \n\n\n|  | PROKARYO |  |  |  |  |  |  |  |  |\n|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|\n|  | 0.1 |  |  | 0.4 |  |  | 0.7 |  |  |\n|  | ACC | PUR | FSC | ACC | PUR | FSC | ACC | PUR | FSC |\n| SBG | 51.54 | 72.60 | 46.61 | 43.99 | 56.81 | 42.66 | 44.61 | 56.98 | 41.62 |\n| UAM | 72.78 | 80.76 | 62.80 | 61.34 | 68.97 | 49.03 | 51.24 | 66.64 | 43.22 |\n| Both | **74.95** | **82.21** | **64.79** | **72.78** | **79.13** | **62.82** | **52.09** | **74.59** | **49.59** |\n|  | PROTEINF |  |  |  |  |  |  |  |  |\n| SBG | 36.49 | 41.92 | 21.67 | 31.99 | 36.53 | 17.08 | 28.65 | 33.17 | 12.51 |\n| UAM | 35.61 | 40.44 | 21.70 | 30.43 | 35.34 | 15.66 | 28.09 | 32.81 | 12.07 |\n| Both | **36.26** | **41.70** | **21.81** | **33.57** | **37.89** | **18.41** | **30.07** | **35.07** | **14.41** |\n|  | WIKIFEA |  |  |  |  |  |  |  |  |\n| SBG | 50.98 | 57.08 | 44.74 | 49.07 | 54.22 | 38.13 | 41.13 | 45.65 | 26.05 |\n| UAM | 52.52 | 59.17 | 45.12 | 48.22 | 53.22 | 37.96 | 40.62 | 44.10 | 25.19 |\n| Both | **54.22** | **59.74** | **47.23** | **50.17** | **54.50** | **39.21** | **41.70** | **46.41** | **27.03** |\n|  | NUSWIENE |  |  |  |  |  |  |  |  |\n| SBG | 10.74 | 33.34 | 7.32 | 12.10 | 30.53 | 9.67 | 11.79 | 30.96 | 9.33 |\n| UAM | 10.10 | 33.28 | 7.11 | 12.37 | 30.53 | 9.74 | 15.19 | 30.28 | 14.92 |\n| Both | **10.99** | **33.57** | **7.59** | **12.48** | **33.52** | **9.87** | **15.41** | **33.15** | **15.10** |\n|  | CALTEALL |  |  |  |  |  |  |  |  |\n| SBG | 21.97 | 32.11 | 15.23 | 18.38 | 31.00 | 12.56 | 16.12 | 26.93 | 8.58 |\n| UAM | 23.46 | 32.46 | 16.56 | 21.75 | 32.46 | 11.24 | 19.38 | 28.79 | 7.51 |\n| Both | **25.93** | **35.75** | **17.28** | **23.24** | **33.51** | **14.27** | **20.27** | **29.34** | **9.57** |\n|  | YOUTUTEN |  |  |  |  |  |  |  |  |\n| SBG | 70.97 | 76.93 | 62.67 | 70.97 | 77.36 | 63.42 | 71.31 | 76.36 | 62.86 |\n| UAM | 71.47 | 77.12 | 62.95 | 71.76 | 77.87 | 62.56 | 71.43 | 76.58 | 61.98 |\n| Both | **73.23** | **78.94** | **67.54** | **74.14** | **79.56** | **67.43** | **72.21** | **78.51** | **64.77** |\n|  | YOUTUTWE |  |  |  |  |  |  |  |  |\n| SBG | 67.21 | 68.32 | 60.47 | 68.49 | 76.21 | 59.84 | 66.76 | 75.05 | 59.23 |\n| UAM | 67.47 | 70.43 | 62.98 | 70.87 | 76.63 | 60.62 | 67.23 | 75.87 | 60.18 |\n| Both | **71.23** | **76.86** | **64.74** | **73.86** | **79.51** | **62.06** | **68.62** | **76.91** | **62.90** |\n|  | FAMNISIX |  |  |  |  |  |  |  |  |\n| SBG | 51.23 | 51.64 | 42.79 | 50.94 | 51.43 | 42.14 | 51.52 | 52.02 | 41.28 |\n| UAM | 51.08 | 51.73 | 44.86 | 51.78 | 51.76 | 40.78 | 51.23 | 52.24 | 41.17 |\n| Both | **57.97** | **58.35** | **47.84** | **56.34** | **57.27** | **46.89** | **54.52** | **58.43** | **45.93** |\n\n\n\n**Q4:** Complexity comparison between BSTM and comparison methods. \n \n**A4:** Thanks! We summarize the complexity comparison in the following table. Please check it. We will add this in the next version. \n\n|  | Time Complexity | Space Complexity |\n|:---:|:---:|:---:|\n| GSRMC | $\\mathcal{O}(vn^2(v+\\log(n)))$ | $\\mathcal{O}(vn^2)$ |\n| FLSD | $\\mathcal{O}(nd^2)$  | $\\mathcal{O}(n^2v+dnk)$ |\n| MVTSC | $\\mathcal{O}(vn^3+vn^2\\log(n)+v^2n^2)$ | $\\mathcal{O}(mn^2+mnk)$ |\n| MVCBG | $\\mathcal{O}(ndk+ndm+dmk)$ | $\\mathcal{O}(dk+mk+mn)$ |\n| AGCMC | $\\mathcal{O}(n^2k)$ | $\\mathcal{O}(vn^2+nk+v^2)$ |\n| NGSPL | $\\mathcal{O}(n^2k)$ | $\\mathcal{O}(mn^2+(m+1)nk)$ |\n| PIMVC | $\\mathcal{O}(n^3+dk^2)$ | $\\mathcal{O}(mn^2+dk^2)$ |\n| TCIMC | $\\mathcal{O}(n^3+n^2v\\log(n))$  | $\\mathcal{O}(n^3+mn^2)$  |\n| TMBSD | $\\mathcal{O}(nk^2+k^3+n^3)$ | $\\mathcal{O}(mn^2+mnk+k^3)$  |\n| PSMVC | $\\mathcal{O}(dm^2+nm^2+dmn)$ | $\\mathcal{O}(nd+mn+m^2)$ |\n| MKKMC | $\\mathcal{O}(n^3v)$ | $\\mathcal{O}(n^2v+nkv)$ |\n| LRGMV | $\\mathcal{O}(nk^2)$ | $\\mathcal{O}(mn^2+nk)$ |\n| Ours | $\\mathcal{O}(dnm + m^2n + m^3)$ | $\\mathcal{O}(dn)$ |"}]

Author rebuttal:

Meta-review: This paper proposes a novel Bit-swapping Oriented Twin-memory (BSTM) framework for lifelong incomplete multi-view clustering, featuring a twin-memory architecture for cross-view alignment, a bit-swapping mechanism to harmonize current and historical views, and a linear-complexity update strategy for scalability. Reviewers praised its originality, clear methodology, and comprehensive experimental validation across benchmarks, noting its effectiveness in addressing view misalignment and preserving knowledge. Concerns centered on the justification of one-hot constraints, reliance on hyperparameters, and the need for clearer explanations of certain components and parameters. The rebuttal addressed most issues with additional experiments, complexity analysis, and design rationale, leading two reviewers to recommend acceptance and two to lean borderline accept due to clarity. Overall, the contribution is technically sound and well-supported, warranting acceptance.
Decision: Accept (poster)