Simple yet Effective Incomplete Multi-view Clustering: Similarity-level Imputation and Intra-view Hybrid-group Prototype Construction
Authors: Shengju Yu
Zhibin Dong
Siwei Wang
Pei Zhang
Yi Zhang
Xinwang Liu
Naiyang Guan
Tiejun Li
Yiu-ming Cheung
Venue: ICLR 2025 Spotlight (2025)
Keywords: incomplete multi-view clustering
mulit-view clustering
clustering
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Abstract: Most of incomplete multi-view clustering (IMVC) methods typically choose to ignore the missing samples and only utilize observed unpaired samples to construct  bipartite similarity. Moreover, they employ a single quantity of prototypes to extract the information of $\textbf{all}$ views.   To eliminate these drawbacks, we present a simple yet effective IMVC approach, SIIHPC, in this work.  It firstly transforms partial bipartition learning into original sample form by virtue of   reconstruction concept to split out of  observed similarity, and then loosens traditional non-negative constraints via regularizing samples to more freely characterize the similarity.  Subsequently, 
it learns to recover the incomplete parts by utilizing the connection built between the similarity exclusive on respective view and the consensus graph shared for all views.  On this foundation,  it further introduces a group of hybrid prototype quantities for each individual view  to flexibly extract the data features   belonging to each view itself.  Accordingly, the resulting graphs are with various scales and  describe the overall similarity more comprehensively. It is worth mentioning that these all are optimized in one unified learning framework, 
which makes it possible for them to  reciprocally promote.  Then, to effectively solve the formulated optimization problem,  we design an ingenious auxiliary function that is with theoretically proven monotonic-increasing properties.  Finally, the clustering results are obtained by implementing spectral grouping action on the eigenvectors  of stacked multi-scale consensus similarity.  Experimental results confirm the  effectiveness of  SIIHPC.

Published as a conference paper at ICLR 2025
SIMPLE YET EFFECTIVE INCOMPLETE MULTI-VIEW CLUSTERING: SIMILARITY-LEVEL IMPUTATION AND INTRA-VIEN HYBRID-GROUP PROTOTYPE CONSTRUC-
TION
Shengju Yu Zhibin Dong Siwei Wang 2- Pei Zhang
Yi Zhang Xinwang Liu
Naiyang Guan ', Tiejun Li 1x Yiu-ming Cheung
National University of Defense Technology, PIntelligent Game and Decision Lab
National Innovation Institute of Defense Technology, "Hong Kong Baptist University
yu pa-shengjjue jue foxma com (wangsiwe 13, xinwangliu, tjli @nudd edu. cn
ABSTRACT
Most of incomplete multi-view clustering (IMVC) methods typically choose to ignore the missing samples and only utilize observed unpaired samples to construct bipartite similarity. Moreover, they employ single quantity of prototypes to extract the information of all views. To eliminate these drawbacks, we present simple yet effective IMVC approach, SIIHPC, in this work. It firstly transforms partial bipartition learning into original sample form by virtue of reconstruction concept split out of observed similarity, and then loosens traditional nen-negative constraints via regularizing samples to more freely characterize the similarity. Subsequently, it learns to recover the incomplete parts by utilizing the connection built between the similarity exclusive on respective view and the consensus graph shared for all views. On this foundation, it further introduces group of hybrid prototype quantities for each individual view to flexibly extract the data features belonging to each view itself. Accordingly, the resulting graphs are with various scales and describe the overall similarity more comprehensively. It is worth mentioning that these all are optimized in one unified learning framework, which makes it possible for them to reciprocally promote. Then, to effectively solve the formulated optimization problem, we design an ingenious auxiliary function that is with theoretically proven monotonic-inereasing properties. Finally, the clustering results are obtained by implementing spectral grouping action on the eigenvectors of stacked multi-scale consensus similarity. Experimental results confirm the effectiveness of SIHHPC.
INTRODUCTION
Incomplete multi-view clustering (IMVC). representative unsupervised learning approach, is grasping increasing concerns owing to its effectiveness in grouping heterogeneous data containing missing samples (Lin et al. 2021 Zhang al. 2021a Chen et al. 2024a Tang & Liu 2022 Gu et al. (0024). It aims to under no any label information divide all samples into distinct sets such that samples within the same have relatively higher similarity while different
are with significant
differences, thereby discovering the latent pattern relations embedded inside samples (Liu et al.) 2020
Huang et al., 2021 Ma et al. 2024aa Yu al., 2024a Pan & Kang 2021 Li al. 2025 Chen et al.
2024b Yu et al. (023b). To generate high-quality results for IMVC, recently series of eye-catching
algorithms have been carefully devised (Zhang al. 2022 Wang et al., 2021c| Yu al.) 2024d
Yang et al. 2023a Chen et al. 20233] Yu et al. 2024c). For instance, Li et al. (2024a) describe the
relationship between existing samples and prototypes through an incomplete graph instead of the full pair-wise instance graph improve the computational efficiency, and produce the uniform similarity under parameter free searching. Long et al. (2024) utilize the prototypes in potential feature subspace to do low-rank approximation for the view correlations, and preserve the consistencies between views by decreasing the rotation sensitivity in the embedded space. Rather than the distance-orientee
"oorreponndigg Authors.

---

Published as a conference paper at ICLR 2025
Obserrod Samples
Missing Samples
Incomplete
T.BL
Biparitiio Leamingg
Teansfarriing Ponie
latra-Yiew Hykedd-
Ravso
Group Protets
Suckkr
Prstoyge
Observel Similanky
Multi-eale
Incemplete view
VireSpeeite Goaph
SG
Sudarrty
PISEE
Lad Imputation
Camaanuu Graph
Spectial Gropping
Incomplete VIew
Suillnit Papuraioo
The overall framework of proposed SIIHPC. It firstly utilizes T-PBL to split out of observed similarity and then conducts SLI based the connection between CG and view-specifie similarities. Further, combined with IVHGP, generates MSVSG to flexibly extract features on respective view.
Figure 1:
weighting, He et al. (202)) construct an asymmetric matrix by structural prototype based metric learning to expand the late fusion, and accelerate the spectral generation through prototype inferred graph learning. Li et al. (2023) maintain the view versatility and instance commonality via a double stream learning framework, and use view-wise prototypes to exploit cluster-specifie representations.
These approaches successfully achieve clustering result improvement from various perspectives, nevertheless, they typically choose to ignore the missing samples and only take advantages of observed samples to achieve the construction of bipartite similarity. This will miss out latent useful information from the missing samples, resulting in the generated similarity not that accurate. Also, due to the randomness of sample missing, the remaining observed samples are usually unpaired, which could lead to unbalanced cluster distribution and deteriorate the graph structure. Besides, they usually employ single quantity of prototypes to extract all view information. This is apparently unreasonable since each view generally owns unique features, and single quantity of prototypes could be not competent to adequately characterize all views, accordingly weakening the view information diversity,
To eliminate these issues, we present simple yet effective IMVC method, SIIHPC, in this paper. The overall framework is described in Fig. I Concretely, we firstly transform partial bipartition learning under prototype orthogonality into the form containing original samples by utilizing the data reconstruction concept to split out of observed similarity. and then relax conventional non-negative constraints through sample regularization skill to make the measure of similarity more free. Based on the criterion that one object appears on at least one view, we further introduce the learnable consensus graph, which is shared for views, to provide unified structure. Afterwards, relying on the connection built between all view-specific bipartition similarities and the consensus graph, gather the information from other views at the similarity level to assist imputing the incomplete parts of similarity on each view. On this basis, rather than single prototype quantity for all views, associate a group of hybrid prototype quantities for each individual view so that it can flexibly exploit features according to the characteristics of each view. Accordingly, the resultant graphs have various scales and in addition to balancing views, they also can more comprehensively characterize the particular, we achieve these goals within one unified learning framework such that they are able to negotiate with each other towards the direction of mutual reinforcement. Then, to minimize the objective function, we adopt the alternate optimization idea and design an ingenious four-step solution scheme that cleverly solves the sub- cob-problem through an auxiliary function with theoretically and experimentally proven monotonic-increasing properties. Subsequently, we stack all obtained multi-scale consensus graphs and perform spectral grouping action on the feature embedding that consists of the eigenvectors to generate the clustering results. After that, to demonstrate the multiple datasets and under different missing
overall similarity.
effectiveness of SIIHPC, organize experiments percentages. Numerous experiment results suggest that our SIIHPC has the ability to effectively cluster incomplete data. Main novelties in this paper follows:
2

---

Published as a conference paper at ICLR 2025
Unlike previous methods disregarding the missing samples when constructing bipartite similarity, this paper successfully imputes incomplete parts at the similarity level. Not only does this alleviate the adverse impacts caused by the unpairing of observed samples but also can take advantages of the potential useful information of missing samples to help characterize the similarity more accurately.
Instead of single prototype quantity for all views, this paper successfully generates group of hybrid prototype quantities for each individual view to flexibly extract data features according to the characteristics of each view itself. The resulting graphs are with diverse scales and besides balancing views, they are also able to more comprehensively describe the overall similarity.
To optimize the objective function, this paper carefully designs an alternate solving scheme, which decomposes the entire problem into four parts and solves the sub-problem via an ingenious auxiliary function with theoretically proven monotoniccincrraainn properties.
2
RELATED WORKS
As the information age progresses, multi-view data which commonly stems from diverse descriptions
of the same instances is becoming increasingly widespread (Ma et al. 2024b Peng et al. 2019 Kang
et al.
2020b; Yu et al. 2023a Qin et al.) 2023: Zhang et al. [202c] Yang et al.
[023bb] Lu et al.
2024 Accordingly, clustering technology receives growing interest owing to its ability effectively
grouping multi-view data without needing label information (Wan et al.] 2024
Liang et al. 2024
Kang et al. 2020a Lin et al.) 2023b, Wang et al.) 2021a] Huang et al., 2022 Yu al. 2024b).
However, due to factors like sensor breakdown or environment change, is inevitable that some
samples are missing//mcommee /incomlltte on certain views, causing traditional clustering methods not working properly and inducing the IMVC problem (Wang al.) 2022b Zhang al.) 2019 Xu et al. 2024
Zeng et al. 2024 Ly et al.
2022). For effectively tackling this problem, many remarkable works have
been proposed successively from various perspectives, such (Zhao et al. 2023 Yang al. 2024
Zhang et al. 2024a Wang et al. 2021b; Huang et al. 2023 Xu et al. 2022 Zhang et al. (024bb)
V== denote the overall data and indexes of observed data respectively, then, the basic IMVC framework can be expressed as
Let matrices (Du E Rd.xa)y
)==
===1 and vectors (ru RR"
min D.W. - H. + +AIIX.13 s.t. X.1 1, 20,
(I)
where the indicator matrix W. E RRxx, measures the incompleteness of view v, and elements consist of Wolls = 1 when [rul] = i otherwise [Wo]as = 0, Vj 1,2, Re. H. e Rd.xmm denotes the prototype matrix on view v, and is intended to approximately characterize the data D... X, E R.mx denotes the incomplete similarity matrix on view v. The clustering results can be obtained by first fusing all learned X, and then performing spectral embedding partitioning on it.
Following this paradigm, Chen et al. (023) introduce tensor learning to exploit the low-rankness between views and utilize high-level view correlations captured by tensor to assist the learning of prototypes. Wang et al. (2022a) conduct group of projectors to guarantee the dimension consistency of prototypes and aggregate different view information via an uniform fusion scheme. Xu et al. 2023a)
regard the common features among views as prototypes and perform the distribution alignment by maximizing the mutual information between prototypes and view-wise features. Lin al. (202a))
choose to concatenate view-representations as prototypes on each view and preserve the consistency by minimizing the distance between prototypes and within-cluster instances. WWnn et al. (2021a) adopt the within-view maintenance and between- -iew inference strategy to decrease the adverse impact of information unbalance and encourage cluster structure directly reflected in representations. [Ln et al. (2024) concurrently recoup and infer features in latent embedding space to explore the correlations between views and utilize an exploratory scheme to update all parameters, Xia et al. (2022) employ tensor norm to extract complementary information and introduce connectivity constraint to capture the spatial structure hidden into similarity. Xu et al. (2023b) design a two-branch, common and private, variable strategy to leverage representations and improve the robustness to senseless information via a controllable way. Wen et al. (2021b) devise a graph regularizer to maintain the local geometric similarities between views and utilize semantic coherence constraints to stimulate uniform features.
3

---

Published as a conference paper at ICLR 2025
3 METHODOLOGY
Rethinking T its nature to reconstruct Dr using X under given H., Unlike the fixing strategy, firstly make prototype learnable and then introduce orthogonal constraint strengthen its discrimination, i.e., H H = I. On this basis, we have H Dj W. = X. W.. Then, the observed parts can be splited out through X, W, W H. D. W, W, Notice that the item H, D, can be regarded as the cosine similarity between H. and D. when all columns of D, are unit vectors. Hence, choose do normalization on D.,. which expands the similarity range from [0, 1] to [-1, more freely measuring the similarity. Subsequently, we introduce consensus graph G to aggregate information from different views, and impute the incomplete parts by utilizing H. D. W y W and G. Further, to avoid single prototype quantity for all views, we provide group of hybrid prototype quantities {m,, m2, ... Mss" .... ms) for each view to flexibly extract features according to the characteristics of each view itself. Consequently, we have X.,s W.W. H D.W.D. W. Besides, to adaptively adjust the importance between prototype quantities, we associate a learnable weight, dp for each prototype quantity on each view. Finally, our SIIHPC can be formulated as
Guss ( H
D. W.W. - Q, - -G.ll + | + +33 |A
min A,H A. Qe ==1
s.t. H Ho, Im,: -15 Q 1 -1, 1,0
(2)
where H E Rd,
xm, denotes the prototype matrix with the s-th quantity view u. M, consists of [M =1 when [holj == otherwise [M. j = 0, Vj 1,2, ................................ nu i 1,
n2. by {z|z Ta and z To where T. (1.2. n and T. {[r.) [ol2..... ... [r
Qu,a E R Xn is the imputation matrix with the s-th scale on view v. A E R x5 consists of dg,s.
4 OPTIMIZATION
Due to the non-convexity when jointly considering all variables in (2) we alternatively optimize each variable via the following four-step updating skill.
Step 1:
Optimizing the Prototype Matrix Hu.s
Under fixed Qe,s. G, and A, we can simplify the optimization problem (2 as
max Tr ( H.,,H P.......) s.t. H He. Im.. Ho..
(3)
where the matrix L. poId, Ly, the scalar y represents the largest eigenvalue of Ly, L. D. W. W. W. D.T. Po,s W, W (G, Q.,
Denote the function g ((H,,)) Tr(H, L., H, H U.T.Pook Po,s), its derivative as Vg((H,,s)) the value of Ho at the r-th iteration as (He.))" the singular value decomposition results of (HH.H..))) as (U,.s) (Ev,a)" (VT,)" Then, we have the following two lemmas hold.
Lemma Under (H,,)) taking (Uv,a)" "...)" have
. for the trace of Ho,s and derivative, we [H]..) ((H..))))
Tr -(HH.))""(HHT.)) -H,,)) Vg where Vg ((Ho,))) denotes the derivative value at the r-th iteration. Lemma 2. For the trace Hy
a at the r-th iteration and (r + 1)-th iteration, we have
( E,
++1 (H,
(H),))") 2 Tr (((TT..))
r+1 - (H...) "[, (H,,)") (5)
In conjunction with Lemma and Lemma 2 we have the following theorem holds.
Theorem 1. For the function under any (H,,)) and (H,,.) = (U...)" (VT,)", we have
g(H,,s ) is monotonically increasing.
According to Theorem I we can determine H.,s by comparing the objective value at current iteration and that at previous iteration. Algorithm summaries the overall procedure of optimizing H.,s-
4

---

Published as a conference paper at ICLR 2025
Algorithm 1 The procedure of optimizing Ho.s in (3).
Input:
The matrices He.e. Qu.s. Gs. A, Do. W., M Construct the function ((Hra))
while g( (((...))**)
((H,, "")g, (()g ) S le - do
2: Compute the derivative function Vg ((H v.s)
3: Generate the singular matrices (U,,e) and (V u.s)
4: Assign (Ho,s) )++ by (Ho,)) yr+1 = (U.,s) (V7,))
r+1
0,8)
5:
r r-r+l.
6: end while
Output: The prototype matrices [
s
Remark 1. Due to W. T E R and M, M E RR calculating L, and Pv.s needs at least (nn²) computing overhead. Noticed that W, W and M.M are diagonal matrices with elements or 1, by virtue of Hadamard product, we can transform L. and Pu,s as D ① B, B O D and
,D.
( Wili 2j=1 [W W...j..... E [Wo]aol where B, = 1a, (
L -i=1 [Molns] After transforming, the
and C 1m, -E ". (1 -i=1 [
computing complexity reduced to O(n).
Step 2: Optimizing the Similarity Imputation Matrix Q
Under fixed H.,s, G. and A, we can simplify the problem 12 as
min Q
Qn, M, -J.-ll s.l.
Qu.s 1
(6)
where the matrix Ju,s = G. - H,, D. W M. is an indicator matrix, and therefore we can determine Qu. by taking the value corresponding index of Jr To guarantee the feasible region, can regularize the solution by first comparing it and #1 and then performing truncation operation.
Remark 2. Due to the direct assignment operation, the computing overhead of optimizing Qu, mainly from the construction of Ju..- Inspired by Remark the item H W. W can be transformed as H Dv & B.. Therefore, the computing complexity about optimizing Qu,s is O()..
D.
Step 3: Optimizing the Unified Representation Matrix G. Under fixed Hy,s, Quis and A, we can simplify the problem as
V
min Tr G.
G.
Σ a1 (1 A)Im. -
Σ
av F v,
Fin" G.
s.t.
15 G, 1
where the matrix Fe,. D.W.D.WWW we can equivalently transform the objective
WT Qo After expanding the trace by elements,
V
V av [F Fu,eles
min I.. (G.
Σ
ou.o (1 + Im, [Goli -
Σ [=
G..l...
(8)
For the feasible region, we can split it into -1 S [G.].. < 1,j 1,2,...., Therefore, the problem (7) is transformed as a quadratic programming (QP) problem, and can be effectively solved using existing software packages.
Remark 3. Solving each column vector [G , by QP consumes O(m?) overhead. Therefore, the computing overhead of optimizing G2 is (m) Note that the number of prototypes m, is not related n and usually far less than n, accordingly, the computing complexity of G. is also O(n).
Step 4: Optimizing the Prototype Balance Matrix A
Under fixed H. H. Qu,s and GG, simplify the problem 2
V
s
min
av + +BAA s.l. A1 - 1,0
(9)
5

---

Published as a conference paper at ICLR 2025
Algorithm 2 The procedure of solving the problem (2)
Input: Data matrix D., index vectors by, hyper-parameters and 3, 1,
Construct indicator matrices W. and M
while (Joby (t) foty (t + fob/ (t) <= do
2: Optimize the variable H., by Algorithm
3: Optimize the variable Qu.s by solving (6).
4: Optimize the variable G. by solving 7
5: Optimize the variable A by (TI).
6: end while
Output: The unified representation matrices (G,)a 15
where Po,a D.W.
W.W.W W. +Q.,,,,, - G, + Due to the constraints being
for the row of A, we can further transform the problem (
min
Pe,sPo, + Sa s.t. a 1,0 app
(10)
Gu.
where the vector a denotes the v-th row A. For the above optimization problem, we can get its closed-form solution
1e1-1-11 20
1-1
1
Pe.:
(11)
S
23
where the vector Pe;: is composed of pn,s. = 1,2, ,.
Remark 4. Owing the closed-form solution, the computing overhead is mainly from the con- struction of Pv.:- According to Remark 7 we can obtain that constructing each Pv.s takes O(n).
Accordingly, solving a,; takes (Sn). Solving the overall A will take O(VSn). which is also (()).
We summary the overall procedure for solving the optimization problem in Algorithm foby(t (f) denotes the objective value at the t-th iteration.
2
where
After obtaining the unified representation matrices (G.)s concatenate them by row and subsequently perform spectral grouping on it to generate the data clustering results.
Remark 5.
The overall computing complexity of Algorithm is ((n) since updating Hy, Qu G, and A all take (n)) which consequently enables it to be expanded to large-scale tasks.
Remark 6. Storing the optimization variables He,s. Qu.s. G2 and takes O(m.do), O(..)). (m,,) and OSV),, respectively. Therefore, the space complexity of Algorithm is also (n).
5 EXPERIMENTS
5.1 BASELINES AND DATASETS
We conduct all experiments six public multi-view datasets, and their details presented in Table where SS: Sample Size, NV: Number of Views, FD: Feature Dimension, NC: Number of Clusters.
Table I: Dataset Description
Dataset
SS
NV
FD
NC
BDGPFEA
2500
1000/500/250
NUSOBJECT
6251
5
42//24/145/22666
10
VGGFACEFIFTY
16936
944/576/512/640
50
VGGFACEHUND
36287
4
512/576/640/944
100
YOUTUBEFACE
63896
640/944/576/512
20
FASHMINST
70000
4
576/512/944/640
10
The following methods are used as baselines in this paper illustrate the effectiveness of SIIHPC:

---

Published as a conference paper at ICLR 2025
Localized Sparsity (LSIMVC (Liu et al. 2023)) ) Refined Graph Structure (GSRIMC (Li et al. 2024b)), High- Orderr Correlation (HCPIMSC (Li et al. )022)), Efficient Effective Regularizer (EELMVC (Liu et al. 202T),, Low-Rank Graph (LRGRIMVC CCui et al. 2024)). Consensus Bipartite Graph LIVCCCCG (Wang et al. )022a)), ) Balance Guidance (BGIMVSC (Sun et al.
2023)), Late Fusion (OSLFIMVC (Zhng et al.) 202Tb)), Neighbor Group Structure (NGSPCGL.
WWong et al. (202)), Projections (PIMVC (Deng et al. (023)), Parameter-Fres Scalable Prototype
Graph (PSIMVC et al., (024a)), Structured Anchor-Inferred Graph (SAGL (He al. 2023
Local Structure Consensus Graph (HCLSCGL Wen et al. (203)).
5.2
RESULTS AND DISCUSSIONS
Table 2: Clustering Results on Benchmark Datasets
RIGGFRA
NUSORIECT
Method
30%
30%
70%
SUPS
5016
70%
ACC
NMI
PUR
ACCC
NMI
PUR
ACE
XMI
PUR
ACCC
NMI
PUR
AACC
NM1
PUR
ACC
NM4
PUR
LSIVVC
26.56
6.14
26.56
26.5
7.18
26.81
27,40
8.35
28.07
21.70
9.03
31.33
21.81
8.43
30.99
20.57
7.43
30.52
GSRIMC
36.78
11.22
8.34
20.91
32.04
20.46
31.23
ICPIMSC
34.12
12.65
36.35
32:20
12.41
38.24
33.16
11.81
34.38
21.56
6.38
29.21
21.33
8.93
20.15
22.87
8.07
29.81
ERIVVE
35.70
14.47
36.34
33.23
12.39
36.05
31,012
10.37
33.64
21.51
6.17
13.51
21.07
9.97
133442
20.33
8.14
12.17
LEGRIMVC
34.71
12.58
35.74
31.43
32.63
27.25
4,50
27.27
21.43
1.25
22.62
30.99
30,15
40,05
15.01
38.10
36.76
22.59
21.35
32.85
BGIMVSSC'
22.65
3.19
23.26
26.88
9.6M
27.08
24.04
4.72
24.56
19.16
0.30
22.36
19:13
0.34
22.91
19.06
0.31
22 22.86
OSLFIMYC
30.38
9.58
36.57
31.34
9.12
35.37
31,68
8.50
35.73
21.88
7.67
32.34
20.68
6.91
23.00
18.41
4.63
29.58
NUSPOOLI
7.83
19:97
25.20
PIMIC
34.03
35.99
33.04
12.92
33.54
34,43
11.60
35.41
21.29
9.36
31.07
21.08
5.52
31.12
7389
31.36
PSIMVC
34.00
12.51
35.58
11.08
9.55
33.65
30.12
9.15
52.45
19.65
8.25
29.11
20.09
8.91
30.21
22.07
7.91
50.35
SAGL
23.76
1.69
23.92
23.03
1.41
23.
28.52
4.09
29.56
20.48
7.67
27.46
20.39
6.91
26.16
18.39
6.63
26.47
HELSCGL
24.28
1.54
31.31
38,80
15.21
39.97
40.31
13,88
40.31
11.54
37.30
23.30
9.14
32,87
23.
33.92
8.36
31.49
VOGIFACFFIFTY
VOGFACEHUNND
LSIMVC
8:45
10.78
8.65
7.30
9:83
7.56
6.94
9.08
7.18
GSRIMC
N/A
HCPIMSC
10:33
12.14
10.54
11.90
10:85
9,23
10.16
ERIMVC
6.56
14.03
5.94
5.60
14.15
5.50
5.33
13:20
5:23
3.37
7.32
4.78
3.41
6.89
5.67
3.50
6.27
5.74
LEGRIMVC
9.21
13.25
11.37
10.02
12.48
11.45
9.15
11.58
12.56
NIA
IMVOCBG
12:13
14.25
11.52
12.40
12:35
14,23
7.52
8.25
12.20
7,06
RGIMVSSC
6:49
9.83
7.34
7.19
6.76
9.85
7.19
OSLRIMYC
8:50
5:79
8.96
6.96
6.71
7.58
6.01
5.09
5.60
5.54
9.59
5:97
4.62
7.54
5.05
3,60
5.81
4.08
NOSPOOT
6.50
6.47
7.19
6.34
6.54
6.74
6.08
6.24
6.75
N/A
5.97
12.36
6.72
PSIMVC
12.50
11.58
9.54
11.33
10.49
9.36
10.45
9.92
11.04
5.28
3.89
5.51
6.04
SAGE
8:75
9.33
9:75
6.54
9.68
6.75
5.84
9.65
8:56
5.84
10.54
6.36
4.85
10.13
4.74
3.54
9.32
4.54
HCLSCOI
5.65
9.55
5.74
4,18
8.68
4.62
4.67
8.55
5.01
3.05
10.32
4.36
3.05
10.12
4.13
3.15
9:51
4.02
13.21
YOUTUBEPACE
FASHMINST
LSIMVC
GSRIMC
HCPIMSC
RRCRIMVC
IMVCCRG
74
79.28
77.29
72.39
78.33
77.04
70.61
78.60
77.97
58.18
57.58
62.22
58.01
53.01
61.75
56.27
56.48
60.17
OSLFIMVC
61.85
70.25
69.84
60.78
69
67.46
41.73
36:25
47.38
41.67
34.36
45.37
41
41.33
32.89
44.76
NGSPOOI
PIMVC
N/A
N/A
PSTMVC
75.67
49
74.17
52.23
$4.78
57.73
SAGL
63.48
72.89
72.45
62.47
73.63
73.04
62.65
12.05
73.68
43.47
53.56
53.68
43.35
57.88
55.73
43.58
53.62
51.85
HCLSOOL
N/A
N/A
76.29 82.27
72.60
77.65
71,05
79.19
76.75
61.24
59.52
62.69
62.51
64.64
60.59
58.77
63.18
Table 2 presents the clustering results under multiple missing ratios (30%, 50%, 70%). We can get:
The proposed SIIHPC receives preferable results than many comparison algorithms under multiple missing ratios and metrics. For instance, on the datasets VGGFACEHUND and FASHMINST, SIIHPC is consistently the best; VGGFACEFIFTY and YOUTUBEFACE. SITHPC obtains only two sub-optimal results totally: on BDGPFEA and NUSOBJECT, SITHPC also makes desirable results. Therefore, SITHPC can effectively tackle IMVC tasks.
LSIMVC, GSRIMC, HCPIMSC, BEIMVC, LRGRIMVC, BGIMVSC, NGSPCGL, PIMVC and HCLSCGL can not normally run on slightly- larger dataset VGGFACEFIFTY, VG- GFACEHUND, YOUTUBEFACE or FASHMNIST, while the proposed SIIHPC is not only able to work properly under these circumstances but also makes favorable results. Therefore, SIHHCC is with relatively stronger practicality.
7

---

Published as a conference paper at ICLR 2025
5.3 TIME AND MEMORY OVERHEAD COMPARISON
For illustrating SIHHPC's friendliness to computing resource and storage resource, we compare the running time (min) and memory overhead (GB) between all as reported in Table 3 According to this table, we can observe that:
IMVC methods,
SIIHPC consumes fewer resources against most methods. For example, on datasets YOUTUBEFACE and FASHMINST, the algorithms OSLFIMVC and SAGL require 126.28GB, 82.96GB, 123,42GB and 99.01GB memory respectively while SIIHPC only needs 6.01GB and 5.1.GB. In other situations, the time overhead and memory over- head of SIIHPC are still relatively small. Therefore, SIIHPC is resource-friendly.
In some cases, PIMVC, PSIMVC and IMVCCBG take lower running time and/or memory overhead, possibly because PIMVC learns representation common -owdiimesiional space instead of in diverse original space, PSIMVC employs only one bipartite graph to characterize the correlation between all views, and IMVCCBG utilizes the landmarks with a single dimension to extract features. Despite resource-saving they generally can not integrate information from missing samples, accordingly giving inferior clustering results.
Table 3: Running Time and Memory Overhead Comparison
BDGPFBA
NUSORIECT
VGGFACEFITTY
VGGFACEHUND YOUTUBEFACE FASHMINST
Method
Time
Memo
Time
Memo
Memo
Time
Memo
Time
Memo
Time
Memo
LSIVVC
0.03
0.32
0.13
2.42
0.55
15.18
GSRIMC
2.10
2.82
28.88
28.07
N/A
HCPIMSC
2.79
1.93
43.33
17.25
741.45
104.84
N/A
N/A
EEIMVC
0.02
0.80
0.33
5.06
2.99
30.97
238.01
98.84
ERGRIMVC
3,35
1.11
60.59
10.09
492.37
61.87
N/A
IMVCCBG
0.02
0.17
0.05
0.20
0.56
1.73
2.46
3.96
1,23
6.16
1.27
6.41
BGIMVSC
4.85
1.27
15.76
8.75
132.67
135.70
N/A
N/A
N/A
OSLFIMVC
0.09
0.30
0.18
1,51
3.23
10.02
20.00
41.96
13.54
126.28
12.27
123.42
NGSPCGL
0.97
1.79
11.42
13.43
111.29
89.09
N/A
N/A
N/A
PIMVC
0.01
0.46
0.40
2.53
0.36
17.20
76.58
PSIMVC
0.16
1.62
5.22
1.57
6.42
1.95
SAGL
0.22
0.40
0.41
7.54
16.29
45.06
26.96
38.39
82.96
30.07
HCLSCGL
0.17
1.84
4.14
13.92
309.87
91.51
4838.55
133,20
N/A
N/A
Ours
0,06
0.14
0.11
0.22
1.86
2.84
6.22
10.32
3.31
6.01
3.57
5.13
5.4 ABLATION
We utilize the similarity level imputation (SLI) to capture the latent useful information from missing samples and thereby improve the clustering performance. To verify its effectiveness, we do result comparison under these two situations, as shown Table where AB: Ablation, MR: Missing Ratio, NSLI: No-SLI. As seen, SLI results always preferable. Therefore, our SLI scheme is functional.
Table 4: Similarity-level Imputation Effectiveness
A8
MR
BLGPFEA
NUSOBJECT
VOGRACFFITY
VOGRACCHUUD
YOUTUBEFACE
FASHMINST
ACDC
NMI
PLR
XLCC
NMI
PUR
A3C
NML
PUR
ACC
NMI
PUR
ALC
NMI
PUR
ACC
NML
PUR
NSLI
28.15
30.38
22.60
31.85
7.22
9,33
40:95
49.41
38.80
39.97
32.87
14.91
82:27
61.24
62.69
NSLI
50%
20.74
3.97
10.08
21.09
6.20
31.10
5.33
4.45
6.00
3.73
6.89
4.36
26.07
16.16
28.60
37.85
24.03
40.85
SLJ
40.31
13.88
40.31
22.38
9.21
33.92
12,31
14.48
13.21
7.55
13,85
9.39
72.60
79.60
77.65
62.51
60.22
64.64
26.39
25.15
27.31
36.04
11.54
37.30
21.46
8.36
31.49
11.18
13.35
11.96
6.82
12.69
7.55
71.05
79.19
76.75
60.39
58.77
63.18
Unlike a single prototype quantity (SPQ) for all views, we introduce group of hybrid prototype quantities (HPQ) [1k, 2k. ... 5k] for each view to flexibly exploit features where l: is the number of clusters. The ablation results are shown in Table 5 where PQ: prototype quantity. It can be seen that
the HPQ results consistently superior to any SPQ ones. Therefore, HPQ scheme is effective.
Further, we adaptively adjust the importance of each prototype quantity via learnable weight to more flexibly extract features. To verify its effectiveness, present the ablation results in Table
8

---

Published as a conference paper at ICLR 2025
Table 5: Hybrid-group Prototype Quantity Effectiveness
NUSORIECT
VOCIFACRRITTY
VOGFACERUND
YOUTUREFACE
FASHMINST
NMI
0.70
13.93
10.42
12:57
11:23
5.67
11.54
78.24
75.30
55.01
SPQ
9076
11
34.43
26.71
11.46
6.70
35.65
30.60
16.88
15.15
4.56
3.64
24.36
27.12
11.29
11.18
13.35
13.60
12.06
12.04
6.41
6.48
12.27
12.80
7.36
7.27
68.36
70.68
80.63
76.85
74.42
76.57
$3.50
56.94
58,71
58.61
$7.34
58.40
14.84
9.74
16.15
17:46
4.21
27:17
12.00
14.03
13.90
7.065
12.56
7.44
69.31
76.88
75.33
56.12
$5.80
59.85
10.08
53.41
21
10.77
11.71
11.31
24.15
71.43
50.97
SPQ2
30%
m1:48
10:33
34.95
34.59
5.95
9.44
34.59
15.74
20.19
19.25
7.01
6.21
29.56
30.80
11:24
11:12
13.51
13:31
12.17
11.93
6.54
6.01
11.68
11.74
5.68
6.76
67.05
70.21
23.99
77.21
74.64
72.04
55.62
58.47
58.39
58.09
57.25
59.34
11-58
34.25
9.22
76.55
19.04
6.01
31.08
11.33
13:25
12,16
0,88
11:89
7.43
70.55
76.25
75.53
61.01
58,45
62.85
TIPQ
40.31
22.35
35,91
14.48
13.21
7.55
13.85
8.39
72.00
79.60
77.45
62.51
08.22
64.44
64.60
36
52.31
206
m=
10-4
30.38
6.91
32.76
14.06
15.37
3.53
25.58
10.08
9:69
12.13
11:27
10.98
10.50
6.00
5.84
10.69
10.55
6.03
08.09
76.77
73.13
70:46
53.57
55.76
56.62
57.78
60.05
31.90
7.87
35.75
16.93
3.58
26.81
10.53
12:24
11.35
6.06
10.54
6.34
09.55
75.94
73.29
52.69
53.91
57.57
BPV
35.04
11.54
37.30
21.46
8.36
31.49
11.18
13.35
11.96
6.82
12.69
7.55
71.05
79.19
76.75
60.59
58.77
63.18
where ETPQ: Equally Treating Prototype Quantity, AWPQ: Adaptively Weighing Prototype Quantity. Evidently, our AWPQ scheme makes performance improvement.
Table 6: Hybrid- Hybrid-group group Prototype Quantity Weighting Effectiveness
AB
MR
BUGIPPEA
NUSOBIECT
VIGBACCEFFTY
VGGBACEHUND
YOUTUBEFACE
FASHMINST
ACCC
NMI
PUR
ACC
NMI
PUR
ACCC
NM1
PUR
ACC
NMI
PUR
ACCC
NMI
PUR
ACC
NMI
PUR
ETHP
509
33.28
36.33
11.21
13.08
78.50
AWP)
38.80
39.97
13.4
76.29
59.52
XWPQ
ETHP
50%
37.70
40.31
13.88
12.37
39.04
40.31
21.37
22.38
9.21
7.24
31.79
33.93
11.29
12.31
13.44
14.48
12:13
13:21
7.31
7.55
12387
13,85
7.54
8.39
71.32
72,60
78.93
79.60
75.67
77.65
62.08
02.51
59.90
60.22
64,84
64.64
ETP
70%
34.70
35.09
28.10
10:37
12.58
10:22
6.26
11:08
08.62
78.38
75.92
50.35
59.42
00:54
AWPQ
35.04
37.30
31.49
11.18
11.96
7.55
71,05
79.39
76.75
60.59
58,77
5.5
CONVERGENCE
We draw the objective value evolution of Algorithm 2 to illustrate the convergence of SIIHPC. From
Fig. 2
we can know that monotonically decreases and gradually stabilizes within twenty iterations.
1.12
8.8 20
Objectiv Value
1820
Objective Value
bjectvve Value
2.28
64ce
3.06
2.04
83
2.02
10
Iteration Number
Iteration Number
Iteration Number
(a) BDGPFEA
(b) NUSOBJECT
(c) VGGFACEHIFTY
Figure 2: The objective value of Algorithm 2 on BDGPFEA, NUSOBIECT and VGGFACEFIFTY.
5.6 MONOTONICITY OF FUNCTION g
To experimentally verify the monotonicity of function g. we draw its objective value evolution in Fig. Evidently, is monotonically increasing. Further, we also give the change of during each iteration of Algorithm 2 Taking Fig. 2 (a) as an example, Algorithm| iterates totally 10 times. 2
the 2-th ~ 10-th iteration respectively. As seen, it is also monotonically increasing. Moreover, it can be observed that as the upper-loop Algorithm? iterates, the number of iterations required for the inner-loop Algorithm gradually decreases, which A Algorithm 2 the optimization variable in the inner-loop gradually reaches to its optimal solution and accordingly Algorithm needs fewer iterations.
Fig. presents the change of when Algorithm
is mainly because along with the iteration of

---

Published as a conference paper at ICLR 2025
132
820
Objective Value
K000
Objective Value
1.13
Objective
aco
2500
1.14
113
620
520
1.22
426
Iteration Number
Iteration Number
Iteration Number
(a) BDGPFEA
(b) NUSOBJECT
(c) VGGFACEFIFTY
Figure 3: The value change of function g when Algorithm 2 is at the 1-th iteration.
Objective Value
973
Objective Value
079
Objective Value
853.2
833.8-
853.1
063
853.6
355.8
390
0534
8567
3568
Iteration Number
Iteration Number
Iteration Number
(a) Algorithm 2
at 2-th iteration
(b) Algorithm at 3-th iteration
(c) Algorithm
2
at 4 thth iteration
947.4
3452
854
Objective Value
847.5
Objective Value
Objective Value
843.
847.3
8/5
843.
944.9
647
3450
3418
095.
1.
1.4
1.8
18
811.7
1.6
1.
1.4
1.6
Iteration Number
Iteration Number
Iteration Number
(d) Algorithm
at 5-th iteration
(e) Algorithm 2 at iteration
(f) Algorithm
2
at 7-th iteration
Objective Value
bjjcclvve Value
$49.2
842.9
842.75
Objectvve
443.55
642.7
$48.8
141.05
8/2
813
B42:55
10399
642.8
803
Iteration Number
Iteration Number
Iteration Number
gg) Algorithm 2
at 8-th itcration
(h) Algorithm
2
at 9-th iteration
(i) Algorithm at 10-th itcration
Figure 4: The value change of function g on BDGPFEA.
CONCLUSION
We propose simple yet effective IMVC method named SIIHPC in this paper. Rather than only utilizing observed unpaired samples to construct bipartite similarity, successfully imputes incom- plete parts at the similarity level via partial bipartition learning transformation to integrate the latent useful information from missing samples. Then, instead single prototype quantity for all views, it introduces group of hybrid prototype quantities for each view to flexibly extract data features according to the characteristics carefully decomposes the entire optimization problem into four sub-parts and devises auxiliary function with theoretically and experimentally proven monotonic-inerealn properties. Experimental results six popular datasets with various missing ratios demonstrate the effectiveness of SIIHPC.
respective view itself. To minimize the formulated objective,
10

---

Published as a conference paper at ICLR 2025
ACKNOWLEDGMENT
This work was supported in part by the Research Grants Council (RGC) Joint Research Scheme under grant: N 1 the General Research Fund of RGC under the grants: 12202622 and 12202924, and the National Natural Science Foundation of China under Grant No. 62406329, 62476280, 62441618, 62325604, 62276271.
ETHICS STATEMENT
This paper does not involve any potential ethics issues.
REFERENCES
Jie Chen, Yingke Chen, Zhu Wang. Haixian Zhang, and Xi Peng. Spectral embedding fusion for incomplete multiview clustering. IEEE Transactions on Image Processing, 33:4116-4130, 2024a.
Man Man-Sheng Chen, Xi-Ran Zhu, Jia-Qi Lin, and Chang- Wang. Contrastive multiview attribute graph clustering with adaptive encoders. IEEE Transactions on Neural Networks and Learning Systems, 2024b.
Yongyong Chen, Xiaojia Zhao, Zheng Zhang, Youfa Liu, Jingyong Su, and Yicong Zhou. Tensor learning meets dynamic anchor learning: From complete to incomplete multiview clustering. IEEE Transactions on Neural Networks and Learning Systems, 2023.
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.
Shijie Deng. Jie Wen, Chengliang Liu, Ke Yan, Gehui Xu, and Yong Xu. Projective incomplete multi-view clustering. IEEE Transactions on Neural Networks and Learming Systems, 2023.
Zhibin Gu, Zhendong Li, and Songhe Feng. Edison: Enhanced dictionary-induced tensorized incomplete multi-view clustering with gaussian error rank minimization. In Forty-first International Conference on Machine Learning, 2024.
Wenjue He, Zheng Zhang, Yongyong Chen, and Jie Wen. Structured anchor-inferred graph learning for universal incomplete multi-view clustering. World Wide Web, 36(1):375-33)) -999 2023.
Cheng Huang, Jinrong Cui, Yulu Fu, Dong Huang, Min Zhao, and Lusi Li. Incomplete multi- view clustering network via nonlinear manifold embedding and probability-induee loss. Neural Networks, 163:233 243,333-33,,.. 2023.
Dong Huang, Chang-Dong Wang, Jian-Huang Lai, and Chee-Keong Kwoh. Toward multidiversified ensemble clustering of high- dinenssinniil data: From subspaces to metrics and beyond. IEEE Transactions on Cybernetics, 52(11)) 2022.
Zhenyu Huang, Joey Tianyi Zhou, Hongyuan Zhu, Changqing Zhang, Jiancheng Lv, and Xi Peng. Deep spectral representation learning from multi-view data. IEEE Transactions on Image Process- ing, 30:5352-5362, 2021.
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 2020a.
Zhao Kang, Wangtao Zhou, Zhitong Zhao, Junming Shao, Meng Han, and Zenglin Xu. Large-scale multi-view subspace clustering in linear time. In Proceedings of the AAAI Conference Artificial Intelligence, volume 34, pp. 4412-4419, 2020b.
Haobin Li, Yunfan Li, Mouxing Yang. Peng Hu, Dezhong Peng, and Xi Peng. Incomplete multi-view clustering via prototype-basee imputation. In Proceedings of the Thirty-Second International Joint Conference Artificial Intelligence, pp. 391 1919,, 2023.

---

Published as a conference paper at ICLR 2025
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):300-310, 2024a.
Xiang-Long Li, Man Shnng Chen, Chang-Done Wang, and HunnHuung Lai, Refining graph structure for incomplete multi-view clustering. IEEE Transactions Neural Networks and Learning Systems, 35(2):2300-2313, 2024b.
Yan Li, Xingchen Hu, al. A vertical federated multi-view fuzzy clustering method for incomplete data. IEEE Transactions on Fuzzy Systems, 2025.
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, 31:2067-2088, 2022.
Weixuan Liang, En Zhu, et al. Scalable multiple kernel clustering: learning clustering structure from expectation. In Forty-first International Conference Machine Learning. 2024.
Jia-Qi Lin, Xiang-Long Li, Man-Sheng Chen, Chang-Done Dong Wang, and Haizhang Zhang. Incomplete data meets uncoupled case: A challenging task of multiview clustering. IEEE Transactions on Neural Networks and Learning Systems, 35(6):8077-8110, 10, 2024.
Yijie Lin, Yuanbiao Gou, Zitao Liu, Boyun Li, Jiancheng Lv, and Xi Peng. Completer: Incomplete multi-view clustering via contrastive prediction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 11174-11183, 2021.
Yijie Lin. Yuanbiao Gou, Xiaotian Liu, Jinfeng Bai, Jiancheng Lv, and Xi Peng. Dual contrastive prediction for incomplete multi-view representation learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, (5(4):4447-446) 2023a.
Zhiping Lin, Zhao Kang. Lizong Zhang, and Ling Tian. Multi-view attributed graph clustering. IEEE Transactions on Knowledge and Data Engineering, 38(2):1872- 18800 2023b.
Chengliang Liu, Zhihao Wu, Jie Wen, Yong Xu, and Chao Huang. Localized sparse incomplete multi-view clustering. IEEE Transactions on Multimedia, 25:5539-55511 5551, 2023.
Xinwang Liu, Xinzhong Zhu, Miaomiao Li, Lei Wang. En Zhu, Tongliang Liu, Marius Kloft, Dinggang Shen, Jianping Yin, and Wen Gao. Multiple kernel kk-means with incomplete kernels. IEEE Transactions on Pattern Analysis and Machine Intelligence, 42(5):1191-122) 2020.
Xinwang Liu, Miaomiao Li, Chang Tang, Jingyuan Xia, Jian Xiong, Li Liu, Marius Kloft, and Zhu. Efficient and effective regularized incomplete multi-view clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43(00)):634-2646 2021.
Zhen Long, Ce Zhu, Pierre Comon, Yazhou Ren, and Yipeng Liu. Feature space recovery for efficient incomplete multi-view clustering. IEEE Transactions on Knowledge and Data Engineering, 36(9); 4664-4677, 2024.
Yiding Lu, Yijie Lin, Mouxing Yang, Dezhong Peng, Peng Hu, and Xi Peng. Decoupled contrastive multi-view clustering with high-order random walks. Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 14193-1422 2024.
Ziyu Lv, Quanxue Gao, Xiangdong Zhang, Qin Li, and Ming Yang. View-consistency learning for incomplete multiview clustering. JEEE Transactions Image Processing, 014499--4800 2022.
Huimin Ma, Siwei Wang. Junpu Zhang, et al. Symmetric multi-view subspace clustering with automatic neighbor discovery. IEEE Transactions Circuits and Systems for Video Technology, 2024a.
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, pp. 5045- 5054, 2024b.
12

---

Published as a conference paper at ICLR 2025
Erlin Pan and Zhao Kang. Multi-view contrastive graph clustering. Advances in neural information processing systems, 34:2148-21 2159, 2021.
Xi Peng, Zhenyu Huang, Jiancheng Lv, Hongyuan Zhu, and Joey Tianyi Zhou. Comic: Multi-view clustering without parameter selection. In International Conference on Machine Learning, pp. 5092-5101. PMLR, 2019.
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): 2652-2659, 2023.
Lilei Sun, Jie Wen, Chengliang Liu, Lunke Fei, and Lusi Li. Balance guided incomplete multi-view spectral clustering. Neural Networks, 166:260-272, 2023.
Huayi Tang and Yong Liu. Deep safe incomplete multi-view clustering: Theorem and algorithm. In International Conference Machine Learning, pp. 21090-21110, PMLR, 2022.
Xinhang Wan, Jiyuan Liu, Xinwang Liu, Yi Wen, et al. Decouple then classify: A dynamic multi-view labeling strategy with shared and specific information. In Forty-first International Conference on Machine Learning. 2024.
Chang-Dong Wang, Man Man-Sheng Chen, Ling Huang, Jian-Huang Lai, and Philip S. Yu. Smoothness regularized multiview subspace clustering with kernel learning. IEEE Transactions on Neural Networks and Learning Systems, 32(11):544755060 2021a.
Qianqian Wang, Zhengming Ding, Zhiqiang Tao, Quanxue Gao, and Yun Fu. Generative partial multi-view clustering with adaptive fusion and cycle consistency. IEEE Transactions on Image Processing, 30:1771-1783, 2021b.
Qianqian Wang, Huanhuan Lian, Gan Sun, Quanxue Gao, and Licheng Jiao. iemse: Incomplete cross-modal subspace clustering. IEEE Transactions on Image Processing, 30:305-317, 2021c
Siwei Wang, Xinwang Liu, Li Liu, Wenxuan Tu, Xinzhong Zhu, Jiyuan Liu, Sihang Zhou, and En Zhu. Highly-efficiene incomplete large-scale multi-view clustering with consensus bipartite graph. In Proceedings of the IEFF/CVF Conference on Computer Vision and Pattern Recognition, pp. 9776-9785, 2022a.
Yiming Wang, Dongxia Chang, Zhiqiang Fu, Jie Wen, and Yao Zhao. Incomplete multiview clustering via view relation transfer. IEEE Transactions Circuits and Systems for Video Technology, 33(1):367-378, 2022b.
Jie Wen, Ke Yan, Zheng Zhang, Yong Xu, Junqian Wang, Lunke Fei, and Bob Zhang. Adaptive graph completion based incomplete multi-view clustering. IEEE Transactions on Multimedia, 23: 2493-2504, 2021a.
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):
101-114, 2021b.
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 IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp.
15712-15721, 2023.
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.
Wei Xia, Quanxue Gao, Qiangian Wang, and Xinbo Gao. Tensor completion-based incomplete 2022.
multiview clustering. IEEE Transactions Cybernetics, 52(12))
Gehui Xu, Jie Wen, Chengliang Liu, Bing Hu, Yicheng Liu, Lunke Fei, and Wei Wang. Deep varia- tional incomplete multi-view clustering: Exploring shared clustering structures. In Proceedings of the AAAI Conference Artificial Intelligence, volume 38, pp. 16147-16155, 2024.
13

---

Published as a conference paper at ICLR 2025
Jie Xu, Chao Li, Yazhou Ren, Liang Peng, Yujie Mo, Xiaoshuang Shi, and Xiaofeng Zhu. Deep incomplete multi-view clustering via mining cluster complementarity. In Proceedings of the AAAI Conference Artificial Intelligence, volume 36, pp. 8761-8769, 2022.
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. IEFE Transactions on Image Processing, 32: 12:1354-3366 2023a.
Jie Xu, Yazhou Ren, Xiaoshuang Shi, Heng Tao Shen, and Xiaofeng Zhu. Untie: Clustering analysis with disentanglement in multi-view information fusion. Information Fusion, 100:101937, 2023b.
Mouxing Yang. Yunfan Li, Peng Hu, Jinfeng Bai, Jiancheng Lv, and Xi Peng. Robust multi-view clustering with incomplete information. IEEE Trunsactions on Pattern Analysis and Machine Intelligence, 45(1):1055- 2023a.
Xihong Yang, Yue Liu, Sihang Zhou, Siwei Wang, Wenxuan Tu, Qun Zheng, Xinwang Liu, Liming Fang. and En Zhu. Cluster-guided contrastive graph clustering network. In Proceedings of the AAAl conference on artificial intelligence, volume 37, pp. (0834-10842, 2023b.
Zequn Yang, Han Zhang, Yake Wei, Zheng Wang, Feiping Nie, and Di Hu. Geometric-inspine graph-based incomplete multi-view clustering. Pattern Recognition, 147: 10082, 2024.
Shengju Yu, Suyuan Liu, Siwei Wang, Chang Tang, et al. Sparse low-rank multi-view subspace clustering with consensus anchors and unified bipartite graph. IEEE Transactions on Neural Networks and Learning Systems, 2023a.
Shengju Yu, Siwei Wang, Yi Wen, Ziming Wang, et al. How to construct corresponding anchors for incomplete multiview clustering, IEEE Transactions on Circuits and Systems for Video Technology, 34(44)2845 2860, 2023b.
Shengju Yu, Zhibing Dong, Siwei Wang, Xinhang Wan, et al. Towards resource- -ssurce-frreenll. extensible and stable incomplete multi-view clustering. In Proceedings of the st International Conference on Machine Learning, pp. 57415-574555 2024a.
Shengju Yu, Siwei Wang, Zhibin Dong, Wenxuan Tu, et al. A non-parametric graph clustering framework for mueti-view data. In Proceedings of the AAAI conference on artificial intelligence, volume 38, pp. 16558-16567, 2024b.
Shengju Yu, Siwei Wang, Pei Zhang, Miao Wang, et al. Dvsai: Diverse view-shared anchors based incomplete multi-view clustering. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 16568-16577, 2024c.
Shengju Yu, Pei Zhang, Siwei Wang, Zhibin Dong, et al. Differentiated anchor quantity assisted incomplete multiview clustering without number-tuning. IEEE Transactions Cybernetics, 2024d.
Pengxin Zeng, Mouxing Yang, Yiding Lu, Changqing Zhang, Peng Hu, and Xi Peng. Semantic invariant multi-view clustering with fully incomplete information. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(4):2139-211 2150, 2024.
Changqing Zhang, Zongho Han, Yajie Cui, Huazhu Fu, Joey Tianyi Zhou, and Qinghua Hu. Cpm-nets: Cross partial multi-view networks. Advances in Neural Information Processing Systems, 32, 2019.
Changqing Zhang, Yajie Cui, Zongbo Han, Joey Tianyi Zhou, Huazhu Fu, and Qinghua Hu. Deep partial vuew learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44 (5):2402-2415, 2022.
Guang- Yu Zhang, Dong Huang, and Chang- Wang. Tensorized incomplete multi-view kernel subspace clustering. Neural Nenworks, 179:106529, 2024a.
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, 2024b.
14

---

Published as a conference paper at ICLR 2025
Yi Zhang, Miaomiao Li, Siwei Wang, Sisi Dai, et al. Gaussian mixture model clustering with incomplete data. ACM Transactions on Multimedia Computing, Communications, and Applications, 17(1s):1-14, 2021a.
Yi Zhang, Xinwang Liu, Siwei Wang, Jiyuan Liu, Sisi Dai, and En Zhu. One-stage incomplete multi-view clustering via late fusion. In Proceedings of the 29th ACM International Conference on Multimedia, pp. 2717-2725, 2021b.
Yi Zhang, Fengyu Tian, Chuan Ma, Miaomiao Li, et. Regularized instance weighting multiview clustering via late fusion alignment. IEEE Transactions on Neural Networks and Learning Systems, 2024c.
Shuping Zhao, Jie Wen, Lunke Fei, and Bob Zhang. Tensorized incomplete multi-view clustering with intrinsic graph completion. In Proceedings of the AAAI Conference Artificial Intelligence, volume 37, pp. 11327-11335, 2023.
15

---

Published as a conference paper at ICLR 2025
APPENDIX
A EXPERIMENTAL SETTING
In the paper, we fine-tune and {10-7, 10000000... ;... 1102) } and {102, 10 10...... 107} respectively. The hybrid prototype quantities each view set [1k, 2k, 3k, 4k, 5k). To demonstrate the effectivennes of our SIIHPC in clustering incomplete multi-view data, we conduct experiments under missing ratio 30%, 50% and 70% respectively.
Some reasons about hwper-yarameeee parameter setting are here. In our model, the hyper-parameters À and aim at fine-tuning | and || respectively. Note that G, E Rm, and A E V where mg n. V and S denote the numbers of prototypes the s-th group, samples, views and prototype quantity candidates, respectively. Generally, V S m, and S < Therefore, we have that the size of G2 is much greater than that of A. Besides, combined with the feasible regions, have that the absolute values of the elements in GN and A are all within the range [0, 1], Therefore, we can get that ||G,, Il is much larger than || F. Based on these, search À within small range while searching within a relatively large range.
B SYMBOL SUMMARY
V: the quantity of views;
S: the element quantity of hybrid prototype group;
d,: the feature dimension view
n: the quantity of samples;
k: the quantity of clusters;
no the quantity of observed samples on view o;
m,: the s-th prototype quantity each view;
D.: the data matrix on view v, d, X vı;
x, the incomplete similarity matrix on view v, X m
x the incomplete similarity with the s-th scale on view v, m, X m
W,; the constructed index matrix on view v, n X Nl;
H. the prototype matrix on view v, dg m;
H. the prototype matrix with the s-th quantity on view do x m
Qu the imputation matrix with the s-th scale on view v, m. n;
M.: the constructed index matrix on view v, n X (n n.);
G: the consensus graph, m ni;
G the consensus graph with the s-th scale, m, X ng
A: the prototype quantity weighting matrix, V S;
L temporary variable, d, d,:
Lp temporary variable, d, x dyi
P : temporary variable, d, m,i
Jo.:: temporary variable, m. x n;
F u temporary variable, m,
16

---

Published as a conference paper at ICLR 2025
C
TERMINOLOGY SUMMARY
In the paper, utilize some terms like T-PBL, IVHGP, OS, MSVSG, etc. Here, provide more detailed descriptions about them.
T-PBL represents transforming partial bipartition learning into original sample form to split out of observed similarity.
IVHGP represents introducing group of hybrid prototype quantities for each individual view to flexibly extract the data features belonging to each view itself, i.e., intra-view hybrid-group prototypes.
OS represents the observed similarity on each individual view.
MSVSG represents the generated graphs with various scales on each view, i.c., multi-scale view- specific graphs.
SLI represents learning to recover the incomplete parts by utilizing the connection built between the similarity exclusive respective view and the consensus graph shared for all views, Le., similarity- level imputation.
CG represents the learned consensus graph that is shared for all views.
SG represents conducting spectral grouping on the graph generated by stacking multi-scale consensus graphs.
D PROOF OF LEMMA
Recall the function, g.
g (H,,))) = Tr (H. L. b. + H.,,Po..))
(12)
where L, = Ia L,, L, DD D,W, W W. W.D.J. and then, together with the symmetry of Ly, we have that its derivative V.H.,,.)) is
Vg(Ho..) = L., L. H + Pu.s H + P E.S.
(13)
Denote the value of H.,s at the r-th iteration as (H,,)), the SVD of Vg((H,,)))) as (Uv.s)" (Eu,a)" holds,
(VT,))" (VT,))
Then, for the Hy at any iteration number, we have the following equality
Tr H (H( ))) Tr H (U,,)" (Ee,s) (VT.)")
(14)
Tr (V...) H (Un.)) (Em,s))
Considering that (V H (U,,)) (U,,.) Ho,s (V,,a)* " = I, we have 0.5) H. (U.,.)" orthogonal. Additionally, the diagonal elements of (Er,,)" are all non-negative. Therefore, have
Tr (H. Vo((H,,,)")) S Tr ( ((E,,)))
(15)
In particular, when (VT Therefore, under (H,,a) taking (U (U,,a)" (VT,.) we have the following inequality always holds,
b.s (U,,s) i.e., Ha.s takes (Ue.s)" (VT,)", the equality holds.
V Tr Vo
(16)
At the (r + 1) iteration, accordingly, also always have
Tr (H...))* ++1 Vo((H),,)))) Tr ((H,,.) "V 2 0.
(17)
Consequently, Lemma Temmaaholde holds.
17

---

Published as a conference paper at ICLR 2025
E
PROOF OF LEMMA 2
According to the fact that L, is positive semi-definite, we have Ly can be expressed as Y Y matrix decomposition. On this basis, can further obtain
via
Tr
(Ho
Ly
(Ho.s) (Ho,,)")
Tr [(H))))t1 (Hop))"
YYT (Ho - (Hm,,)))
(18)
(H. -H.,))
Y 20.
Therefore, have the following inequality holds,
Tr H 0,6) L. (He,s)
Ly (Ho,e)
(H L (H H n.s) Ly (Ho..)")
Tr
(H r+1
(H (H
m,5) (7) (Ho.a)) Ly (H |+ (H [H.,)' 2 0.
L
(H m
r+1
(19)
Tr
(Ho..)
Merging common items yields
Tr (H....) r+1 L, (H...)*tt (H. (H. E, (HH (Hmn))²) 20. (20)
Furthermore, in conjunction with the symmetry of L. we have
Tr ((H L Therefore, we have the following inequality holds,
H (H.,)*++ (H.,)""] Tr ([ (TT r+1 - (H (H, L (Hu.)))) (21)
Tr (H L (H,,))** (H,,,)" H (H,,,) )" L, (Ho,,)") 2 0. (22)
Consequently, Lemmal 2 holds.
F PROOF OF THEOREM 1
Proving that the function g (H,,s) is monotonically increasing is equivalent to proving g ((Ho.))*) ((Ho,))) for any iteration number
According to Lemma] Tand the derivative of function we can get ((H (H. 22L, (H..)) + +PM.))
2
(23)
Therefore, the following inequality holds,
r+1
2Í, (Ho + +Po.s)
(HTT)" L, (Ho,))) 3
(24)
(H] 0..) L. (H,.s)" + (H. Pr.ss)
According to Lemma
we can get
r+1 Lg
(H r+1 (H,,))") (HT))) r+1 Poo)) 2
(25)
Th [H. 1.8) (HT.)) ) L. (Ho.)" ) + (H.
r+1
yrrl Po.s)
18

---

Published as a conference paper at ICLR 2025
Therefore, have
Tr H Ly (H ) (H (HT Tr (2
Po.s)
(26)
" Ly (Hoss) (H!,)" Ey (Hu,a) (H (t Pnn))
Further, we have the following equality always holds,
Tr (2(2H...) r+1 L. (Ho.)" (H v,0) " Ly (Ha,)) + (H,,)) r+1 po.s)
(27)
Tr r+1 (2L, (Ho,.) - + Pu.s) (H Ly (Ho,s)))
Noticed that s((H,,s))) Tr
(HH Ep (Ho,s)"
and g HH v. )r+1)
Tr (H )
r+ Lp (Hu.s) r+] (H. )+t
r+1 Pm,s) and conjunction with (24). (26 and (7), we
can get
Pu.e Tr (H. Lu (Ho.e) r + (H Pu.s) Tr (H. L. (Ho,)) )"+ (H, 'PP..
(28)
That is, (HH) ((Hr,))") The proof is complete.
G DERIVATION PROCEDURE OF OPTIMIZATION VARIABLES
Optimizing the Prototype Matrix Hsss
Fixing Qu,ar Gg and A, equivalently transform the original optimization problem (2)
min H 0,5
D. W. W + Qu - -G
(29)
s.l.
0.8 Ho.s = I,.
Using trace operation, obtain
H H D. WT M, G.llE +
min
H.,
(30)
min Tr H 0.0 H. + 2H D. W.W. M,M, - -G.) ")
H.,
where L. D.W. W. W. D.D. Denote the largest eigenvalue of L, as Pv. and in conjunction
with 0,0 H = I,,- we have
min iI (H. L, 2H D. W. (Q., GG.) -G,))) +
H...
min Tr (H... (Ly lol. H 2H D.W. (Q..MMM,.... -G.) + H...
(31)
max Tr H. Hy H P.,.PuP. H...
where L, = Poldd - L.. P 2D, W. WT = -G. M.,M. Then, in conjunction with
Theorem we can obtain that the objective value in (31) is monotonically increasing. Therefore, we can determine the value of H.,s by comparing the objective values (H,,))*+ and (H,,,)" where denotes the r-th iteration.
G.2 Optimizing the Similarity Imputation Matrix Q.,=
Fixing Hy,s, G, and A, we can equivalently transform the optimization problem ? as
W.W.W.WW. W. + Q.,M.M,, G. H 2.8
min
(32)
s.t. - 15 Q < 1.
19

---

Published as a conference paper at ICLR 2025
G, H. W.W.W. and then obtain that the value is equal to || D.W. M, G Accordingly, the objective value of 32) can be minimizing by making Qu M.M. and Ju as close as possible. Therefore, can determine Qu,a using the value of corresponding index of vv,. Subsequentl, to ensure that the solution is within the feasible region, we regularize by first comparing it and and then conducting truncation.
Denote the matrix J Ju,
- Jn,s M
G.3 Optimizing the Unified Representation Matrix G.
Fixing H. Hg,s Qu and A, equivalently transform the problem (2)
[HH.D.WW + M., G. G. +
min
(33)
s.t. - G,
Expanding the objective using trace operation yields
D. M, GollE +AIGG.IP)
min
Gs,8
min G.
0g,s (Tr (G (1+ mmmm G, 2F bss
G.)) a
(34)
1=1
V
min Tr
G
T
0g (1 + 1) G2 2
Σ
(a F Fi.s) G
D=1
o=1
where the matrix Fu, D. can obtain
M. After expanding the trace by elements,
min Tr
G
Σ
a1 + 1) G, - Σ
Fu,s) TG.
G +
u=l
t=1
(35)
min
[.
T
Σ
au,s (1 + Im, Galli |
Σ
au.a F Fualls
v=l
Consequently, together with 34 and 35 we can further transform 33
[G.l.. Ga
min
Σ ae,s (1 + A) Im, [Gol.s Σ av Fo
[Goliv
(36)
s.t. 1 [Gel.. 1
which is classical quadratic programming problem, and be solved by present software packages.
G.4 Optimizing the Prototype Balance Matrix A
Fixing Ha,as Qu.s and G., we can transform the problem 2 as
min Σ O (I HH
D.W.W.W. + Q. - G.ll +*](G.13) + 1B1A
(37)
==1==1
s.t. A1 -1
The scalar Po.s D.W. Q.. G.I + || is constant with respect Gg,s. Besides, the constraints are for the rows of A, and therefore optimize A row by row. In
20

---

Published as a conference paper at ICLR 2025
particular, can equivalently transform (37
min Avg
av,sPo,s + |a..:
(38)
s.t. a 1,0 S ap,:
where the vector an, denotes the v-th row of A. We can further transform (38 as
P
min
Bv.
23 F
(39)
s.t. agg 1 1,0 S ap,
where the vector Pe,: consists of Pu,s 8 1,2, ... S.
S. The Lagrangian function of (39) is
Pa.:
C (a Ki 1) av.
+ K (a., 1) + a
(40)
28
F
where the scalar & and vector μ E RRS denote Lagrangian Multipliers. In conjunction with KKT conditions, can obtain
an.: +
Pv. 233
+ kl
T 0, an.: O p = =
(41)
Therefore, we have
Pv.:
a 28
x1
C2 = 0, s = 1,2, ,.
(42)
Then, conjunction with constraint of row sum, we can obtain
P
an,:
P
x1
K
28
(43)
2,3
S
0o.1111 22
Therefore, we have ap;:
Pvo:
3
H OTHER CONVERGENCE EXAMPLES
During alternatively updating the optimization variables H..., Qu.s, G, and A, their solutions can
be acquired by Algorithm 6). and (II) respectively. This indicates that the objective value of
Algorithm iss monotonically reducing during optimizing each variable. Besides, the objective in (2) has the lower bound, for example 0. In conjunction with the monotonie-reducing and lower bound properties, therefore, our Algorithm is convergent.
Besides the convergence examples in Fig. Algorithm on datasets VGGFACEHUND. YOUBUBEFACE and FASHMNIST, as shown in Fig. It can be seen that these examples also convergent.
also present the change in the objective value of
Objective Value
Objective Value
8.5
Objective Value
8.5
10
8.4
8.4
3.3
8.3
8.3
8.5
81
0000000000000
Iteration Number
Iteration Number
Iteration Number
(a) VGGFACEHUND
(b) YOUBUBEFACE
(c) FASHMNIST
Figure 5: The objective value of Algorithm on VGGFACEHUND, YOUBUBEFACE and FASHM- NIST.
21

---

Published as a conference paper at ICLR 2025
1 MORE EXAMPLES ABOUT THE FUNCTION 9
The function g monotonically increasing. To further illustrate this point, besides the examples in Fig. 3 and 4 we also give its objective value evolution datasets VGGFACEHUND, YOUBUBE- FACE and FASHMNIST, as shown in Fig. 6 and Fig easy to see that the function g is indeed
monotonically increasing.
5.6
Objective Value
Objjeclive Value
Objective Value
2-9--
5.5
5.5
54
5
18
15
15 Iteration Number
Iteration Number
Iteration Number
(a) VGGFACEHUND
(b) YOUBUBEFACE
(c) FASHMNIST
Figure 6: The value change of function y VGGFACEHUND, YOUBUBEFACE. and FASHMNIST when Algorithm is at the 1-th iteration.
Table 7: Performance Comparison under Missing Ratio 40%
Method
BIGPFEA
NUSOBJECT
VOGRACEFITYY
VOGRACEHUND
YOUTUBEFACE
FASHMINST
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
LSMMVC
26.68
6.80
26.68
21.65
8.92
31.54
7.55
10.11
7.78
39.03
33,05
RCPIMSC
33.63
14.14
57.16
21.99
3.92
29.84
9.66
12:22
11.15
NIA
N/A
ELIMYC
33.40
12.08
35.74
22.00
6.12
13.59
5.85
14.65
5.74
3.37
7.17
4.50
LEGRIMVVC
NIA
IMVCCBG
40,72
14.13
39.35 36
22.03
8:22
31,15
11.78
13.70
12.68
7.69
13.81
74.79
79.01
77.30
56.76
57.41
60.19
RGIMVSS
23.60
6.79
24.20
19.01
0.30
22.5 83
7.34
1041
7.76
NIA
NIA
N/A
OSLEIMVC
31.85
8.58
35.67
20.96
6.62
32.11
8.04
4.94
8.39
5,42
59.67
69.78
70.15
40.78
36.57
46.37
28.58
29:47
28.36
5.77
NIA
PIMVC
32.15
12.98
33.34
19.02
9.04
31.13
9.14
13.04
11.13
6.12
13:25
7.31
PSIMYC
37.05
12.64
58.56
20.27
8.26
29.02
10.14
11.78
10.98
5.45
10.27
6,00
71,85
74.66
76.75
$3.56
56.45
$7.45
$4.63
HCLSSOL
27.28
9.02
3.06
NIA
Oues
41.03
14.27
42.43
22.32
8.50
31.97
12.68
14.85
13.45
7.77
14.26
8.80
75.34
79,89
79.97
61.92
60.86
65.38
Table 8: Performance Comparison under Missing Ratio 60%
BDGPFEA
NUSORJECT
VOGPACEFIFTY
VOGFACEHUND
YOUTUBEFACE
FASHIMINST
Mathod
PUR
NMI
NMI
NMI
LSIMVC
27.16
6.51
27.16
8.10
31.21
7.17
9.33
GSRIMC
35.53
13.29
36.35
20.47
7.78
30.87
N/A
NIA
SCPIMSC
32.75
20.70
10.34
NIA
32.90
54.02
14:01
13.73
RRGIRMVC
50.20
8.34
$1.54
21.32
7.66
50.75
9.80
12.38
11.26
NIA
IMVCCBG
36.09
10.82
55.97
22.05
7.34
32.00
11.19
12.92
12:10
7.13
12,74
7.67
74.33
78.55
78.33
$7.99
$7.62
61.14
N/A
OSLFIMYC
31.64
8.24
36.45
20.27
4.76
30.14
6.54
5.74
7.17
4.01
6,62
4.54
61.39
68.37
69.18
40.18
33.56
43.47
NGSPOGL
PIMVL
27.24
4.23
27.73
18.75
3.33
26.43
30.92
6.03
12.08
6.25
5.66
KIA
NIA
N/A
PSIMVC:
53.52
30.14
11.12
5.20
72.70
57.86
SAGIL
23.11
1.29
23.36
19.39
6.76
25.90
6.15
9:22
6.85
2.04
10.57
4.64
63.39
72.16
74.18
42.57
58.76
54.56
HCLSOOI
20.80
1.46
20.80
20.42
7.74
31.19
4.57
8.30
5.88
2.06
10.45
4,01
NIA
N/A
J MORE RESULT COMPARISON ON OTHER MISSING RATIOS
To further reveal the ability of our SIIHPC to effectively tackle incomplete multi-view data, we also organize the comparison experiments under missing ratio 40%. 60% and 80%. The results are reported in Table 7 g and 9
clustering results in most respectivel. It can bee seen that SIIHPC still receives preferable under fairly high missing ratio (like 80%). There results illustrate that the proposed SIIHPC is able to effectively deal with incomplete multi-view data with diverse missing ratios.
22

---

Published as a conference paper at ICLR 2025
Table 9: Performance Comparison under Missing Ratio 80%
NUSOIVECT
VGGFACEFIITY
VOGFACEHLUND
YOLTUBEFACE
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
FUR
ACC
NMI
PUR
ACC
NMI
PUR
LSIMVC
28.33
5.92
25.78
19.87
7.05
30.14
6.36
5.88
7.12
GSRIMC
34.52
30.93
N/A
NIA
33.34
54.37
8,88
NA
EEIMVC
50.49
9.80
52.89
20.56
7.75
13:13
5.14
12:71
505
3.27
6.42
3.57
LRGRIMVC
26.84
3.97
27.45
21.83
29:37
9.04
11.78
11.33
NIA
35.56
34.01
30.53
11.95
BGIMVSC
20.88
1.45
21.32
19.07
2.05
22.93
6.81
10.18
7.28
NIA
NIA
N/A
OSLFIMYC
30.37
8.7
54.64
18.91
4.16
30.00
5.49
4.56
6.31
3.42
5.33
3.87
60.79
68.28
68.36
42,22
36.14
43,60
NGSPOGL
NIA
N/A
PIMVC
32,46
31.88
11:62
11.58
PSIMVC
$2.13
861
$2.95
19.86
7.78
30.20
9:37
10.09
9.96
5.24
9.81
5.68
66.47
72.15
74,60
54.36
54.31
$7.62
SAGL
27.56
5.25
30.80
17.38
26.25
5.44
9.18
7.58
3.85
8.36
4.36
71.57
72.47
44.53
53.67
55,01
HICLSCGL
OuES
36.79
10.71
37.91
21.38
7.19
31,75
11.20
13.17
12.03
6.60
12.12
7.37
70.40
77.78
75.72
66.15
60.96
66.15
K HYPER-PARAMETER SENSITIVITY
To explore the sensitivity of our SIIHPC to hyper- panee-ppramettrs and 3. collect the clustering results under different combinations of À and B, and present them in Fig. One can observe that for any fixed 8, there no significant fluctuation in the clustering performance. On the other hand, for any fixed X, although the clustering performance is fluctuating with the change of [8, it is still tolerable to some extent. Therefore, our SIIHPC is not significantly affected by X and $3
4075
19%
10%
10%
5%
0%
0%
10
1015
top for to?
10
tgp tor to?
10
10
10a toi
101
10
10t Tox
10e for fox tor
(a) BDGPFEA
(b) NUSOBJECT
(c) VGGFACEFIFTY
50%
307
MOD
300
40%
ADC
20%
107
10
10
1o3 10r 108 19t to
104
10-4
1g2 for 162 10t to?
10s
109 top
for
10
to
to
(d) VGGFACEHUND
(c) YOUBUBEFACE
(f) FASHMNIST
Figure 7: The clustering results of SIIHPC under different hyper-parameters.
L THE INFLUENCE OF HYBRID PROTOTYPE QUANTITIES
In this paper, the hybrid prototype quantities on each view are set as [LA, 2k, 3k, 4k, 5k). We consider that too few prototype quantities are not adequately to exploit data features, while too many prototype quantities could lead to information redundancy and the increasing of running time. To explore the influence of hybrid prototype quantities on the clustering performance, we conduct multiple comparison experiments and collect the clustering results under [1k, 2k). [IA: 2k, 3k).
[1k: 2k, ... 8k) respectively, as shown in Table 10 Prototype Quantities. It be seen that when mi mg take [1k, 2k). the obtained results
11 and 12 where SHPQ: the Setting of Hybrid
inferior than that m, ~ my taking [1k, 2k, ... 5k], [1k: 2k, ... 6kk and [1k, 2k, ... 7k) in most instances. For instance, VGGFACEFIFTY with missing ratio 30% 50% and 70% in ACC,
23

---

Published as a conference paper at ICLR 2025
NMI and PUR, the results under [1k, 2k] lower than that under [1k, 2k. .k]]
5k). [1, 2k. 6k)
and [1k, 2k.... ... 7k] by (1.16%. 1.39%, 1.28%, 0.77%. 0.86%, 0.77%, 1.15%. 1.45%, 0.96%). (1.35%, 1.64%, 1.48%, 0.74%, 0.85%, 0.58%. 1.24%, 1.44%, 1.07%) and (1.14%, 1.27%, 1.20%, 0.81%, 0.88%, 0.80%, 1.30%, 1.72%, 1.23%), respectively. There illustrate that too few prototype the improvement of clustering results. On the other hand,
quantities could be not conductive when my ms take [1k, 2k, ... Skj. the obtained results are also inferior than My mg taking [1k, 2k....... 5k] and [1k, 2k..... 6k] in
cases. For example, on FASHMINST with missing ratio 30%, 50% and 70% in ACC, NMI and PUR, the results under [1k, 2k, ... 8k] are lower than that under [1k, ...... 5k] and [1k. 2k...... 6k] by (9.50%, 2.69% 6.48% 6.57%. 2.46%, 4.30% 20% 0.91 %. 0.84%) and by (9.13%, 2.40%. 6.02%. 1.45%, 0.36%, 0.71% %. 3.00%, 0.25%, 2.02%), respectively. Also, the running time (in second) under [1k. 2k: ... 8k) is also relatively higher than that under 11, 2k: ... 5k] and [1A, 2k, 6k). In addition to these, combined with Table 2 we know that SIIHPC is able to beat most of comparison algorithms when mi ~ ms take [Ik 2k, 5k]. Based these, we hold that my mg taking [1k, 2k. ,5k] is worth recommending in our SIIHPC.
Table 10: The Influence of Prototype Quantity on Performance (Results on BDGPFEA)
30%
50%
70%
SHPQ
ACC
NMI
PUR
Time
ACC
NMI
PUR
Time
ACC
NMI
PUR
Time
my ~ my
[1 2
39.32
13.36
40.64
5.54
38.83
9.30
38.83
1.81
32.49
5.84
33.62
1.62
my ~ my [1A 3k
35.11
11.83
38.21
8.74
38.59
10.47
38.59
1.94
34.50
35.35
1.87
m1 my
k 2k,
13.35
36.37
8.29
38.95
34.39
my ms 11.. 2N.
38.80
15.21
39.97
7.16
40.31
13.88
40.31
2.02
35.04
11.54
37.30
1.45
ms 24.
6k
39.20
15.65
39.91
10.16
40.39
13.32
42.58
3.81
38.80
9.61
38.80
3.06
2A,
37.55
16.12
39.54
13.54
36.98
13.44
38.93
3,70
39.12
10.01
39,12
4,28
mi ma
[R. 24,
.88
37.18
15.24
38.61
15.02
41.04
14.11
41.41
4.58
39.06
10.71
39.06
3.77
Table 11: The Influence of Prototype Quantity on Performance (Results on VGGFACHFIFTY)
30%
70%
SHIQ
NMI
PUR
Time
ACC
NMI
PUR
ACC
NMI
Time
my ma
[lk, [k
11.36
13.52
12.16
60.74
11.54
13.62
12.44
61.48
10.03
11.90
11.00
48.74
[1k 24, 36]
12.05
14.18
12.86
85.43
12.07
14,20
12.81
85.75
10.49
12.66
11.33
75.81
my ~ mg [L 3A, 48)
12.08
14.36
12.90
115.63
11.99
14.27
12.87
115.57
11.14
13.16
12.01
107.57
mi ma = [Lk 2k, 5k]
12.52
14.91
13.44
112.19
12.31
14.48
13.21
113.03
11.18
13.35
11.96
109.47
ma [1,,2k,
13.64
13.02
215.13
2R,
12.50
14.79
13.36
263.73
12.35
14.50
13.24
262.95
11.33
13.62
12.23
257.53
mi ma
1k, -
.88]
12.61
13.02
13:47
343.71
12.41
14.62
13.27
352.80
11.44
13.51
12.31
353.56
Table 12: The Influence of Prototype Quantity on Performance (Results on FASHMINST)
30%
50%
70%
SHIQ
ACC
NMI
PUR
Time
ACC
NMI
PUR
Time
ACC
NMI
PUR
Time
my
11. 26
55.22
59.34
59.54
137.94
54.90
58.55
60.45
139.56
56.23
59.16
60.48
162.99
= [k. 2k. 3k)
55.98
58.32
59.86
195.92
55.43
57.54
39.55
193.96
62.21
55.65
62.21
201.49
du ~ mg = L, 2k, Akc]
56.02
59.30
60.11
242.65
62.14
56.38
62.26
251.98
59.60
53.82
62.19
255.66
my my
[.k 2k,
59.52
62.69
62.51
213.51
213.26
my mg
[ 2K,
60.87
59.23
62.23
371.20
57.39
58.12
61.05
376.81
61.49
58.11
64.36
383.28
1k, 2k,
7k
57.95
59.24
61.86
451667
$5.66
58.74
39.95
453.26
61.24
60.20
64.35
450.35
my mg 2K,
88]
51.74
56.83
56.21
540.36
55.94
57.76
60.34
522.42
58.49
57.86
62.34
534.14
M STABILITY AND RELIABILITY
To highlight the stability and reliability our SIIHPC's performance, we count the standard deviation
(%) of clustering results under diverse missing ratios, shown in Table T and Table
As seen, even under diverse missing rations, our standard deviation is small, which illustrates that our SITHPC is robust under varying data conditions.
24

---

Published as a conference paper at ICLR 2025
Table 13: The Standard Deviation Results (%) (Part One)
BDGPFEA
30%
50%
70%
ACC
NM1
PUR
ACC
NMI
PUR
ACC
NMI
PUR
0.25
0.16
0.37
0.24
0.02
0.24
0.32
0.01
0.06
NUSOBIECT
0.30
0.13
0.17
0.09 0.14
0.20
0.13
0.06
0.16
VGGFACEFIFTY
0.30
0.35
0.33
0.32
0.31
0.27
0.36
0.31
0.29
VGGFACEHUND
0.25
0.25
0.25
0.24
0.25
0.22
YOUTUREFACE
2.46
1.07
1.58
2.09
1.30
1.88
2.55
0.82
1.67
FASHMINST
0.00
0.00
0.00
0.00
0.01
0.01
0.00
0.28
0.00
Table 14: The Standard Deviation Results (%) (Part Two)
BDGPFEA
40%
60%
80%
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
0.18
0.06
0.09
0.09
0.01
0.13
0.06
0.06
0.06
NUSOBJECT
0.18
0.19
0.12
0.52 0.09
0.09
0.18
0.07
0.14
VGGFACEFIFTY
0.32
0.23
0.31
0.47
0.33
0.29
0.51
0.35
0.41
VGGFACEHUND
0.22
0.24
0.19
0.16
0.19
0.15
0.17
0.20
0.16
YOUTUBEFACE
2.07
0.83
1.47
2.97
0.82
1.50
2.42
1.26
2.18
FASHMINST
0.48
0.00
0.01
0.01
0.00
0.01
0.02
0.01
0.02
N WEIGHTS OF HYBRID PROTOTYPE QUANTITIES
Instead of single prototype quantity for all views, we generate group of hybrid prototype quantities for each view to flexible capture features. Further, we associate a weight variable for each prototype quantity on each view to adaptively balance their contribution. To verify that it learns different weights for prototype quantities, visualize these weights, shown in Fig. S It is easy to see that on each view, each prototype quantity indeed enjoys a different weight, which makes it more flexibly combine these prototype quantities extract features.
O PERFORMANCE CHANGE W.R.T MISSING RATIO
To illustrate that the clustering performance of our proposed SIIHPC is not significantly affected by the missing ratio, we collect the clustering results under multiple missing ratios, and report them in Fig. 9 As seen, along with the increasing of missing ratio, the clustering performance in most cases is gradually decreasing. This is mainly because the increasing of missing ratio leads to a gradual reduction in available information and the clustering performance is accordingly reducing. Despite
25

---

Published as a conference paper at ICLR 2025
0.25
0.3
02
02-
0.15
0.13
0.05
0.00
0
(a) BDGPFEA
(b) NUSOBJECT
(c) VGGFACEFIFTY
0.25
0.5
0.25
0.2
0.4
0.2
0.15
0.3
2.15
0.2
0.2
2:65
ViCw
Viow
View
View
View
ViEw
VIEw
Vicw
View
View
Vew
View
(d) VGGFACEHUND
(c) YOUBUBEFACE
(f) FASHMNIST
Figure 8: The learned weights of prototype quantities on each view.
all this, from Fig. 9 one can observe that our clustering performance does not fluctuate drastically with the missing ratio.
P LIMITATION AND FUTURE WORK
We aggregate the information of graphs with diverse scales by stacking them and performing SVD to construct splicing eigenvectors, which could weaken the contributions of certain graphs or certain eigen-components. Other ingenious fusion schemes are worth further exploration. Additionally, we utilize the cosine tool to do similarity measure, some other measure approaches can be further studied in the future.
Perfomance
39%
Performance
75%
0.%%
XMI
23%
02%
25%
20%
23%
25%
30%
-2%
50%
60%
15%
93%
30%
45%
50%
50%
70%
55%
30%
45%
55%
60%
10%
55%
Missing Ratio
Missing Ratio
Missing Ratio
(a) BDGPFEA
(b) NUSOBJECT
(c) VGGFACEFIFTY
15%
50%
Performance
[ Performance
80%
erfoommnce
10%
600
70%
50%
65%
305
85%
60%
30%
40%
55%
400
17%
40%
6.0%
10%
Missing Ratio
Missing Ratio
Missing Ratio
(d) VGGFACEHUND
(c) YOUBUREFACE
(f) FASHMNIST
Figure 9: The change in clustering performance w.r.t the missing ratio.
26

---

Published as a conference paper at ICLR 2025
-10
1.37 -72
Objective Value
Objective Value
Objective Value
7.30
7.903
1300
10
15
20
1.5
25
Iteration Number
Iteration Number
Iteration Number
(a) Algorithm
I-th iteration
(b) Algorithm
2
at 2-th iteration
(c) Algorithm
3-th iteration
x10"
x11*
Objectve Value
Objcttvve Value
7:35
bjective Value
2.922
2:30
2,35
7.392
2:31
7:33
7:00
1.89
7312
7332
1,30
1399
Iteration Number
Iteration Number
Iteration Number
(d) Algorithm 2 at 4-th iteration
(c) Algorithm
2
at 5-th iteration
(f) Algorithm
at 6-th iteration
74 212f
7407
7,413
222
Objective Value
Objective Value
7A123
7.300
2.400
7.422
Objective
7A115
2.4000
1402
3.2
2.4
1.5
1.8
1.2
3
16
1.
1.2
3.4
2.6
18
Iteration Number
Iteration Number
Iteration Number
Algorithm 2
at 7-th iteration
(h) Algorithm
at 8-th iteration
(i) Algorithm 2 at 9-th iteration
stt
Objective Value
Objective Value
7,425
Objective Value
7,285
7,720
74475
7.428
7,425
2.477
2.415
7.422
2416
74155
2421
1426
Iteration Number
Iteration Number
Iteration Number
(i) Algorithm 2at at 10-th iteration
(k) Algorithm at 11-th iteration
(l) Algorithm
2 at 12-th iteration
7434 x12*
74386
x28*
74425 2324
Objective Value
Objecttvve Value
7.438
7413
2,4435
74885
bjecttve
7.437
7.4R1
2.433%g
7.40
2/405
122
1.4
1.5 1.3
1.2
3A
1.6
1.2
1.2
3.4
Iteration Number
Iteration Number
Iteration Number
(m) Algorithm 2
at 13-th iteration (n) Algorithm at 14-th iteration (o) Algorithm
2
15-th iteration
Figure 10: The value change of function g YOUBUBEFACE.
27


Reviews:
[{"review_id": "d5AbzVpxWU", "reviewer": "Reviewer_fE1F", "summary": "This paper introduces SIIHPC, an incomplete multi-view clustering method that bypasses traditional missing view recovery by directly imputing similarities. SIIHPC replaces single prototype construction with hybrid-group prototypes, allowing each view to capture unique features within a unified framework. This framework is optimized through a well-designed iterative algorithm with convergence guarantees, ensuring robust and effective clustering.", "questions": "Can the authors clarify the terms used in Figure 1, such as T-PBL, SLI, IVHGP, and MSVSG, and ensure that these terms are defined either in the figure caption or in the text to improve readability?\n\nCould the authors provide a more detailed explanation of the overall process of the clustering algorithm, particularly the final steps for obtaining clustering results and the initial parameter settings?\n\nGiven that the method relies on similarity-level imputation rather than missing view recovery, how sensitive is the model's performance to the quality of the imputed similarities? Could the authors discuss any potential limitations in scenarios with high levels of data incompleteness?\n\nTo better assess the stability and reliability of SIIHPC’s performance, could the authors provide standard deviation metrics for their experimental results? Including this information would help illustrate the consistency of the method across different runs and give a clearer view of its robustness under varying data conditions.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper presents a novel approach SIIHPC to incomplete multi-view clustering through similarity-level imputation, which diverges from conventional methods that focus on reconstructing missing samples or features. This approach serves as an efficient alternative to traditional recovery-based techniques. By addressing incomplete multi-view clustering without explicit missing view imputation, SIIHPC reduces computational overhead and allows clustering methods to function effectively without relying on fully complete data structures.\n\nA key innovation of the paper is the introduction of hybrid-group prototype construction, which replaces single prototypes with a more flexible model that enables each view to capture unique features. This enhances the model’s adaptability to heterogeneous data views, improving clustering performance across diverse datasets and scenarios.\n\nExtensive experimental evaluations on multiple datasets with varying missing ratios highlight the robustness and effectiveness of SIIHPC. The inclusion of ablation studies further enriches the assessment, providing valuable insights into the contribution of each component to the model's overall performance and validating the framework’s design choices.", "weaknesses": "The terminology introduced in the paper is unclear; for instance, terms like T-PBL, SLI, IVHGP, and MSVSG are not properly explained in the captions of Figure 1, making it difficult for readers to follow the framework without additional context.\n\nThe overall process of the proposed clustering algorithm lacks clarity. Specifically, the final steps for obtaining clustering results and the initialization settings for relevant parameters should be clearly defined to improve the reader's understanding of the algorithm’s workflow.\n\nWhile the paper provides strong experimental results, the interpretability of the clustering outputs and the practical implications of hybrid-group prototypes could be explored further. It would be helpful for the authors to discuss how the clustering results or prototype structures might be interpreted in real-world applications, providing insights into the method's broader utility.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "iapUp2JTHS", "reviewer": "Reviewer_3rbh", "summary": "In this manuscript, the authors address the challenge of incompleteness due to missing samples by restoring the missing data at the similarity level. They propose a method that employs a hybrid approach to extract data representations, utilizing multiple quantities of prototypes for each individual view rather than relying on a single quantity across all views. This approach effectively resolves the misalignment of observed samples and incorporates potentially useful information from the missing samples into the bipartition similarity. Additionally, the authors balance contributions from different views while defining overall similarity based on the intrinsic characteristics of each view. These goals are effectively realized within a cohesive learning framework. The proposed method's effectiveness is convincingly demonstrated through experimental results on six public datasets with varying missing ratios.", "questions": "1. Is the auxiliary function $g$ influenced by the percentage of missing samples?  Both $\\mathbf{L} _{v}$ and $\\mathbf{P} _{v,s}$ incorporate the missing percentage, which raises the question of how this affects the function.\n\n2. According to the dataset descriptions in Table 1, FASHMINST has more samples than YOUTUBEFACE. However, the results in Table 3 indicate that SIIHPC incurs a higher memory overhead on YOUTUBEFACE compared to FASHMINST. What factors contribute to this discrepancy?\n\n3. As indicated in Table 3, GSRIMC is limited to operating on only two small-sized datasets and exhibits higher consumption of running time and memory overhead. In comparison with SIIHPC, what is the theoretical complexity of GSRIMC?\n\n4. Beyond the comparison with graph or tensor-based methods, how does SIIHPC fare when compared to deep learning approaches?", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The manuscript presents a logically structured approach, with Figure 1 providing a clear and intuitive overview of the framework.\n\n2.  The authors utilize a variety of missing ratios and metrics in their experiments to evaluate clustering performance effectively.\n\n3. The proposed SIIHPC demonstrates favorable memory and computational efficiency.", "weaknesses": "1. There is an issue with the manuscript's organization where the title of Section 5.5 is found to be identical to that of Section G in the Appendix.\n\n2.  Experiments exhibit that some comparison methods do not function properly on VGGFACEHUND, YOUTUBEFACE and FASHMINST. However, there is a lack of theoretical explanations to substantiate these observations.\n\n3. The space complexity of Algorithm 2 is not described enough.  \n\n4. The manuscript lacks definitions or explanations for certain notations used throughout the text. For instance, the notation $()_{+}$ in (11), N/A in Table 2 and Table 3  are not clarified.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "wZ9aVD0Rrq", "reviewer": "Reviewer_yVBy", "summary": "This paper proposes a new incomplete multi-view clustering method, which reconstructs similarity relationships through the original sample form to capture the intrinsic information of all views. By relaxing traditional non-negative constraints, the method enables more flexible similarity characterizations. Additionally, a hybrid prototype set is introduced for each view, facilitating view-specific feature extraction and contributing to a comprehensive consensus graph. An innovative auxiliary function with monotonic properties is designed to solve the optimization problem effectively. Experimental results on various incomplete multi-view datasets demonstrate the robust clustering performance of SIIHPC.", "questions": "1.The experimental setup lacks sufficient detail, particularly regarding the range and selection criteria of hyperparameters.\n2.The Symbol Summary in the Appendix does not cover all symbols used throughout the paper, which may hinder clarity for readers. It is recommended to include all symbols and provide detailed explanations for each variable to improve readability and understanding of the methodology.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Paper Strengths\n1.The paper is well-organized and easy to follow. The intuition is clearly discussed in the Introduction.\n2.The proposed method performs exhaustive experimental analyses, comparing a wide array of clustering algorithms, thereby strengthening the credibility of the results.", "weaknesses": "Paper Weaknesses\n1.The process for constructing the consensus graph $G$ is not clearly explained, particularly in relation to $G_s$.\n2.Does the dataset include both images and text? Please specify the composition of each view within the dataset.\n3.It would be helpful to discuss how Similarity Level Imputation and Hybrid-group Prototypes specifically contribute to improving clustering performance in Ablation section.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "9ksKjy7t3S", "reviewer": "Reviewer_Gpnt", "summary": "This paper presents an incomplete multi-view clustering (IMVC) algorithm, SIIHPC. To utilize the latent valuable information of incomplete samples, it successfully separates out the observed parts via bipartition learning transformation and relaxes traditional non-negative constraints via sample regularization. It introduces the learnable consensus graphs to provide unified structure, and based on the relationship between consensus graphs and exclusive similarities it imputes the incomplete part at the similarity level. To get rid of the limitations of single prototype quantity, it assigns a group of hybrid prototype quantities for each view, and performs spectral grouping on the resulting multi-scale graphs to generate the cluster labels. Afterwards, it gives a four-step updating scheme to minimize the formulated objective. Overall, the overall organization of this manuscript is clear and easy to follow.", "questions": "1. As descripted, PSIMVC is also based on prototype, what are the differences between the proposed SIIHPC and PSIMVC? Specially, combined with Table 3, PSIMVC can consume less time and/or memory.  \n\n2. Figure 4 show that at each iteration of Algorithm 2, the objective of function $g$ is increasing while at different iterations of Algorithm 2, it doesn't seem like this, such as at the $3$-th, $4$-th, $5$-th iteration respectively. \n\n3. After transformation, why is the complexity about $\\mathbf{H}_{v,s}$ reduced from square to linear?\n\n4. When adopting the prototypes constructed by elicitation sampling, what is the performance of SIIHPC?", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "1. The motivation is good. Incorporating incomplete samples into the construction of bipartite similarity enhances the representation of relationships between different entities.   Diverse prototype quantities facilitate the accurate characterization of different views.\n\n2. The designed auxiliary function is interesting. It equivalently solves one quadratic programming problem with orthogonal constraints and meanwhile is demonstrated to be with monotonic-increasing properties.", "weaknesses": "1. In the paper, the hyper-parameters $\\lambda$ and $\\beta$ are adjusted in $[10^{-7}, 10^{-6}, \\cdots, 10^{-2} ]$  and $[10^{2}, 10^{3}, \\cdots, 10^{7} ]$ respectively. The reasons for setting parameters are not given. \n\n2. Similar to the analysis about Table 3, some reasons for the sub-optimal results in Table 2 should be added. \n\n3. Descriptions about the theoretical space overhead should be more in-depth.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Spotlight)