Aligning Collaborative View Recovery and Tensorial Subspace Learning via Latent Representation for Incomplete Multi-View Clustering
Authors: Youqing Wang
Yu Cao
Jinlu Wang
Xiang Xu
Jiapu Wang
Tengfei Liu
Junbin Gao
Jipeng Guo
Venue: ICLR 2026 Poster (2026)
Keywords: Incomplete Multi-view Clustering
Collaborative View Recovery
Tensorial Subspace Learning
Cross-view Correlation Alignment
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Abstract: Multi-view data usually suffer from partially missing views in open scenarios, which inevitably degrades clustering performance. The incomplete multi-view clustering (IMVC) has attracted increasing attention and achieved significant success. Although existing imputation-based IMVC methods perform well, they still face one crucial limitation, i.e., view recovery and subspace representation lack explicit alignment and collaborative interaction in exploring complementarity and consistency across multiple views. To this end, this study proposes a novel IMVC method to Align collaborative view Recovery and tensorial Subspace Learning via latent representation (ARSL-IMVC). Specifically, the ARSL-IMVC infers the complete view from view-shared latent representation and view-specific estimator with Hilbert-Schmidt Independence Criterion regularizer, reshaping the consistent and diverse information intrinsically embedded in original multi-view data. Then, the ARSL-IMVC learns the view-shared and view-specific subspace representations from latent feature and recovered views, and models high-order correlations at the global and local levels in the unified low-rank tensor space. Thus, leveraging the latent representation as a bridge in a unified framework, the ARSL-IMVC seamlessly aligns the complementarity and consistency exploration across view recovery and subspace representation learning, negotiating with each other to promote clustering. Extensive experimental results on seven datasets demonstrate the powerful capacity of ARSL-IMVC in complex incomplete multi-view clustering tasks under various view missing scenarios. The source code is publicly available at https://github.com/caoyu110/ARSL-IMVC.

Published as a conference paper at ICLR 2026
ALIGNING COLLABORATIVE VIEW RECOVERY AND TENSORIAL SUBSPACE LEARNING VIA LATENT REP- RESENTATION FOR INCOMPLETE MULTI-VIEW CLUS-
TERING
Youqing Wang!
Yu Cao!
Jinlu Wang? Xiang Xu
Jiapu Wang
Tengfei Liu?
Junbin Gao 4 Jipeng Guo
College of Information Science and Technology, Beijing University of Chemical Technology
2 Beijing University of Technology. Nanjing University of Science and Technology
4 The University of Sydney Business School, The University of Sydney
waag-youuqng,, 2024210615, 2024200756 guojipeng @buct edu, en
(jinluwang, ttwlilffelaalaeeeee 1egmaii com, www.iingaoeeedddeee.........ee adw.aaaeeeeeuaa.. edu.au
edu.
ABSTRACT
Multi-view data usually suffer from partially missing views in open scenarios, which inevitably degrades clustering performance. The incomplete multi-view clustering (IMVC) has attracted increasing attention and achieved significant suc- cess. Although existing imputation-based IMVC methods perform well, they still face one crucial limitation, i.e., view recovery and subspace representation lack explicit alignment and collaborative interaction in exploring complementarity and consistency across multiple views. To this end, this study proposes a novel IMVC method to Align collaborative view Recovery and tensorial Subspace Learning via latent representation (ARSL-IMVC) Specifically, the ARSL-IMVC infers the complete view from view-shared latent representation and view-specific estimator with Hilbert-Schmidt Independence Criterion regularizer, reshaping the consistent and diverse information intrinsically embedded in original multi-view data. Then, the ARSL-IMVC learns the view-shared and view-specific subspace representa- tions from latent feature and recovered views, and models high-order correlations at the global and local levels in the unified low-rank tensor space. Thus, leverag- ing the latent representation as a bridge in unified framework, the ARSL-IMVC seamlessly aligns the complementarity and consistency exploration across view recovery and subspace representation learning, negotiating with each other to pro- mote clustering. Extensive experimental results on seven datasets demonstrate the powerful capacity of ARSL-IMVC in complex incomplete multi- clustering tasks under various view missing scenarios. The source code is publicly available at
com/ com//aaoyll IMVC
INTRODUCTION
Recently, the rapid development of information technology promotes the complexity of data forms, including text, audio, images, etc. Extracting available information from multi-view data collected from different sources is challenging. especially in unsupervised scenarios (Xu et al.) 2013 Guo al. 2025a Zhao et al., 2026). As a key unsupervised learning technology, clustering is also ex- panded to multi-view case to better accommodate complex multi-view data (Chao et al. 2021 Chen (ct al. 2022 Lou et al.) 2025). Multi-view clustering (MVC) aims to divide unlabeled multi-view data into disjoint clusters by leveraging the consistency and complementarity across multi-view data (Wang et al. 2025a b). Among various MVC approaches, multi-view subspace clustering (Gao) let al., 20155 Cao et al. 2015; Shi et al. 2024 receives considerable attention due to its signifi- cant performance advantage and robustness. aims to learn optimal subspace representations in which the samples can be more clearly separated into distinct clusters, simultaneously preserving

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the complementary information and mitigating redundancy and noise across multiple views. When both inter-view consistency and view-specific diversity are fully explored and well balanced, the clustering performance can be significantly enhanced (Guo et al. 2023
However, in open scenarios, due to sensor failure, missing annotations, or data corruption. etc, is usually difficult to obtain complete data for all views. Reducing the negative impact of incom- pleteness of multiple views on clustering performance becomes a major challenge currently faced in the MVC filed (Wen et al., 2023b). And thus, the incomplete multi-view clustering (IMVC) meth- ods are widely proposed and divided into two categories, i.e., imputation-based and imputation-fiee methods (Liu et al., 2025 Wen et al. 2024b). The imputation based IMVC methods adhere the mechanism of first view recovery and then clustering structure exploration (Liu et al. 2024a Wang jt al., (021). The imputation-fres IMVC methods only focus on partial observable views to ex- plore clustering information, avoiding computational costs of missing view completion (Wen et al.) 2024b] Qin et al. [005]] Wen et al. 2026). Despite strong simplicity of imputation-free IMVC meth- ods, their discriminability to extract clustering information is restricted by limited available views, especially when the missing rate is high.
The imputation-based IMVC methods utilize heuristic or learnable strategies to impute the missing views, providing strong data foundation for clustering information exploration and enhancing the interpretability. Surprisingly, several methods jointly recover the missing views and Iearn clustering representations (subspace coefficient, graph similarity, cluster indicator, etc) in a unified framework, significantly improving clustering quality. Despite the success, most existing imputation-basee IMVC methods. First, the recovered or completed views often suf- fer from limited structural fidelity and insufficient diversity and consistency reshaping, which are both essential for effective multi-view clustering. More important, there is no explicit alignment and collaborative interaction in view recovery and subspace representation learning in exploring complementarity and consistency.
critical challenges remain in
To this end, this study unifies collaborative view completion and tensorial subspace learning, and breaks the gap between them in complementarity and consistency modeling by shared latent rep- resentation. Notably, the latent representation not only serves as fictitious transitional factor for view reconstruction but also directly contributes to the subspace learning with structural awareness. Along with view-specific diversity term, the proposed method provides more freedom in enriching feature description across views. Consequently, the shared and specific subspace representations derived from the latent space and imputed views are integrated into low- wawk tensor, enabling inter- actions across different levels of structural information. In summary, the primary contributions of this study are as follows:
The proposed novel ARSL-IMVC method facilitates the unified and explicit alignment of com- plementarity and consistency exploration across both missing feature reconstruction and subspace representation learning, fostering a coherent tross-view correlation modeling.
The complex high-order correlation among local specific and global shared subspace representa- tions is collaboratively explored. And the structural semantics embedded in subspace representa- tions are fed back to latent representation and recovered views, improving the imputation fidelity and clustering discriminability.
An effective iterative method is designed to solve the optimization problem. Extensive experi- ments verify the superiority of the proposed ARSL-IMVC method in incomplete clustering task.
2 RELATED WORK
Recently, numerous IMVC methods have been widely proposed (Wen et al. 2020a Shen et al. 2025 Jhang et al. 2025 Li et al. 2024, Wen et al. 2024a Hu et. 2025). which could be roughly grouped into two categories according to the way of handling missing samples. The first category crudely ignores missing samples and focuses on learning clustering representation from available views, i.e., imputation-free. Li et al. divided samples into view-complete parts and view-specific missing parts and learned low-dimensional representation by non-negative matrix factorization (Li et al. 2014). Hu et al. proposed doubly aligned incomplete multi-view clustering (DAIMC), align- ing the available views to learn a compact representation shared by all views and trying to weaken the influence of missing samples (Hu & Chen 2018). Due the powerful relationship representa-
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tion ability of graph, the incompleteness of data is transferred to the similarity domain (Wen al. 2020b 2023a). Wen et al. designed graph- IMVC method, Incomplete Multi-view Spectral Clustering with Adaptive Graph Learning (IMSC-AGC), where partial graph for each view is adap- tively constructed by only leveraging observable samples and expanded to complete graph, and then shared spectral embedding is learned (Wen al., 2020a). To weaken the impact of noisy view, Wen et al. further designed highly confident local structure induced consensus graph learning (HCLS-CGL) for IMVC (Wen al. 2023a). Some methods also tried maximize the utilization of available information by simultaneously considering feature and graph structure and establishing a connection between them (Bai et al.) [2024] Liu et al. 2024b).
Incomppcic Pats
Complete Pataa
Alignment
Tranria
pa
Alignment
E
pi
aetinattr
Projectss
mprommation
Vinw skard
Alignment
W
C-ds Friest ske
X²
Collaborative View Recovery (CVR)
Tensorial Subspace I Leurning (TSL)
Figure 1: The overall framework of proposed ARSL-IMVC method, which mainly consists of CVR and TSL modules and aligns them in cross-view consistency and complementarity exploration by latent representation.
Although achieving good progress, the imputation-free methods ignore the underlying connections between samples or views. which instinctively undermines the structural integrity and compromises the clustering performance. To address this issue, imputation-based based IMVC methods recover missing data and learn clustering representation on the filling data. Wen et al. proposed a unified embedding alignment framework (UEAF) to infer missing samples, fully leveraging the cross view correla- tions by common representation (Wen et al., (011).. Wang et al. leveraged both local view-specific and global view-shared similarity structures to guide the recovery (Wang al.) 2024). To utilize high-order relationships between samples, Chen et al. developed hypergraph induced missing re- construction strategy for IMVC (IMVC-HG) and further explored the complementarity embedded in inter-view label representations (Chen et al., 2025). Guo et al. proposed the robust mixed-order graph learning (RMoGL), utilizing the mixed-order structural information of recovered data from low-order to high-order (Guo et al. complex cross-view correlation and similarity relationships between samples by low-rank tensor learning (Li et al. 2022; Yao et al.
2025b). In addition, several methods focus on modeling both
2025 Chen et al. 2024 Li et al. 2025). Li et al. explored the high-order correlation of views and that of samples, utilizing hyper-Laplacios
regularizer in view recovery and low-rank tensor learning in subspace structure recovery (Li et al. 2022). Yao et al. focused on recovering the multi-view similarity graphs and utilized dual tensor constraint to explore complex correlations, which achieves the between/within view information completing for tensorial incomplete multi-view clustering (B (WWIC-IMMC) (Yao et al. 2025). In addition, to im- prove data separability, some kernel-based IMVC methods reconstruct the missing data in Hilbert kernel space (Liu et al. 22200] Wu et al.) 2024 Liu et al.) [021]] Wu et al. 2025). Although most existing IMVC methods unifying missing view recovery and clustering representation learning have achieved notable progress, they are only treated as weakly coupled strategies. Specifically, they fail to simultaneously exploit the inherent consistency and complementarity among multiple views dur- ing the view recovery and representation learning and achieve the semantic correlation exploration alignment through explicit bridge, resulting in shallow collaborative interaction between them and sub-optimal clustering structure. Thus. this study explicitly aligns the collaborative view recovery and tensorial subspace learning by a shared latent representation for IMVC (ARSL-IMVC), bridging the tight interaction between them.
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Table I: Main notations and descriptions in this study.
Notations
Descriptions
Notations
Descriptions
X E Rdoxa W E 10,1)
Data matrix of the v-th view Missing indicator matrix
Fi
View recovery estimator
Eg. Eu
Noise matrices
P" E Bdoxk
Projection matrix of the v-th view
2" E Rax
Specific and shared representations
H g Rkxa
Latent representation matrix
2 (Rx((++))X
Suhspace representation tensor
METHODOLOGY
In this section, the proposed ARSL-IMVC model is illustrated in detail from two main modules: Collaborative View Recovery (CVR) and Tensorial Subspace Learning (TSL), where the framework is presented in Figure[] Then, the iterative optimization procedure is provided. The basic notations conveniently summarized in the Table
3.1 COLLABORATIVE VIEW RECOVERY
Consider the incomplete multi-view data consisting of n samples from V views, i.e., {(x]]] [ where x E &d is the i-th sample in v-th view. The incomplete pattern symbolized with diagonal indicator matrix W {0, 1 such that W = if i-th sample exists in e-th view and 0 otherwise. The MVC adheres a convineing assumption that multi-view data is usually embedded in the shared latent space. With this inverse assumption, the ARSL-IMVC tries to linearly infer missing views from a "virtual" latent representation H R via reconstruction operator p" E Rd.xk which is beneficial for reshaping the consistency among multiple views. To improve the freedom view recovery, view-specific feature estimator E introduced thus the view reconstruction is formulated, i.e.,
1 V
p" H + ET
(1)
Further, to ensure that the various recovered views retain sufficient complementary information, the Hilbert-Schmidt Independence Criterion (HSIC) is introduced as diversity regularizer between any estimator pair Ej and E where the empirical HSIC term is defined (Gretton al. 2007):
HSIC(E), ET) = Tr K, K (n
(2)
where K2 and K v are inner product kernel matrices of Ey and EV" respectively, H I, 11 is the centralized matrix. The HSIC term penalizes the dependence between the various reconstruction views, thereby encouraging diversity and informativeness among them the feature level (Guo) et al. (022). To explore the consisteney-diversity and ensure the reconstruction quality, the CVR module is formulated as follows:
Σ HSIC(E,, ET) min H. H,P", BY
(3)
(P' X
s.t. X
(P")T""=
where X
[xf, .".......... ". W denotes the non-missing data, and the equality constraint is enforced to ensure reconstruction fidelity of observable samples.
3.2 TENSORIAL SUBSPACE LEARNING
Subspace representation learning is an effective method for exploring clustering semantics in low- dimensional embedding space, especially for self-representation learning methods. Leveraging the shared latent representation and recovered view-specific features, the global semantics and local clustering structures could be effectively characterized, i.c.,
= HZ + EH, H'
(P'
+
4)
where Z, Z" are shared and nie-sfecciii subspace representations, respectively, encoding the comprehensive structural semanties; and En and Eý noise terms.
4

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To explore the consistency and complementarity across views in subspace representation level, both shared and specific subspace representations into unified low-rank tensor. Thus, the TSL module is formulated as follows:
min 2.2 Eug Foy
| + +1I 2,, +
E 22,1
(5)
s.t. H = HZ EH, P H + E (P" E2
- =Z 22 z Z)
where (-)) is tensor construction function, which stacks the representations (12") Jo=1 Z) and rotates to form subspace representation tensor Z E [g*((++)xx In the low-rank tensor space, the high-order cross-view correlations at different levels be effectively captured, facilitating semantic alignment across diverse views and achieving collaborative interaction between local and global structural information.
3.3 FORMULATION OF THE PROPOSED ARSL-IMVC
By incorporating the CVR and TSL into unified framework, the final objective of ARSL-IMVC is formulated as:
min |21la + (1 +
E 2,1 + X2
Σ
HSIC E
E
V=1
w Lougleo
(6)
X WW (P" EV W P
(P' -
E E
H = HZ + Eu, -, 0
Z"
Z2,Z) Z)
where T= (H, P EÇ Z, Eg. z", Eÿ} is unknown variable set, A and X2 are haparepas that control the contribution of different regularization terms in the objective function. In Eq. the shared latent representation H not only facilitates the joint optimization and collaborative interac- tion between view recovery and subspace learning but also serves as a semantic anchor that aligns the reconstructed views with corresponding subspace representations in capturing cross-view comple- mentarity and consistency. The information flow propagation enables coherent cross-view semantic correlation exploration, promoting the clustering quality for complex IMVC task.
3.4
OPTIMIZATION
The objective function in Eq. with multiple variables is difficult to solve directly, the Alternating Direction Method of Multipliers (ADMM) (Lin et al.] (011) utilized iteratively optimize each variable. To make the objective function separable, auxiliary variables I and X are introduced, and then the augmented Lagrange function defined:
L(T, X c J.
2 3 Y.,Y,
1[TT + Blllla
Σ
E 22,1)
+ A2
Σ HSIC(EY, ET) + Σ 0 YY X H-H-FF
w w=1v
(Y XW X"W") Σ
db (Y, X x -
+ Y4, H HZ E.) (2,
where (Y,", Y Y Y, are Lagrangian multipliers, 6(A, B) = B + (A, B), is penalty factor. Then, each variable is alternately updated follows:
Update p"; Fixing other variables except P", the subproblem in Eq. w.r.t. P" is as follows:
min (Y X P" E PP=
min PP'
Tr((P") E + Y /
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The optimal closed-form solution could be obtained (Wang al. 2019), ie., P UVT where U and V are the left and right singular vector of (X: Ej + /
Update x Fixing other variables except X the subproblem in Eq. w.I.t X is follows:
min (YY x P H Ei) o x X X
O X X E
Taking the derivative w.r.t. X and setting it to zero, the optimal solution for X is as follows:
X = (A1 - A2(wa)² = - (4) W (W (1 Z²) (I - =ー)²)= (10)
where A P Ej Y/M,, A2 X 12//u and A3 E Y
Update H: Fixing other variables except H, the subproblem in Eq. w.r.t. H is as follows:
min Σ
-
P-H-
HZ -EH)
(11)
Taking the derivative w.r.t variable H and setting it to zero, the optimal solution could be obtained:
AH + μHB = C
(12)
where = -V EV=n M (P")T P B μ(1 E p (X:
z (."))
(
Ya/u) (1 2²
) +
Ei + /P/pp). It a Sylvester equation in Eq. (2 Bartels & Stewart 1972).
The matrix A is relaxed into À A + with strictly positive definiteness for the solution stability (e is small positive scalar).
Update z": Fixing other variables except Z", the subproblem in Eq. w.r.t Z" is as follows:
min 2
(Y3 X X z E + o(Y J")
(13)
where Y - T = Φ (2) and J (J). Taking the derivative w.r.t. z and setting it to zero, the optimal solution for variable Z could be obtained:
Z" ((X:) X + ( ((X:) x(") - (X:) E + (XX) -M"/ma) (14)
Update Z: Fixing other variables except Z, the subproblem in Eq w.r.t Z is as follows:
min oY,,, H HZ Eн) <( z J)
(15)
where Y = === 1741())))))))))))))))))))) ()), Z q (2) and J 1 Taking the derivative w.r.t. Z and
setting it to zero, the optimal solution for variable could be obtained:
z = (H H (H' (H En + Ya/u) + +J-Y
(16)
Update Ef: Fixing other variables except ET, the subproblem in Eq. w.r.t Ej is as follows:
min E
d Y X P"H ET) + X2
HSIC(EY, E
(17)
w=1wev
Here, the inner product kernel (i.e., K (E ET) is utilized for HSIC term. Taking the derivative w.r.t. Ej and setting it to zero, the optimal solution for variable E could be obtained:
E
X P' P''++YMM)
11/1) (I+
2
Σ
AK AKWA)*
(18)
p(n
Update E7: Fixing other variables except Ej, the subproblem in Eq. 7 w.r.t E is as follows:
min A E 22 + o (Y,
X
X
E min
A EV
+ 1/2 L (19)
E
where L - x X "
//. Its solution be obtained by 22,1 minimization thresholding Liu et al. 2010). i.e.,
operator column by column
(y.r)) =
1
A
L"(:.)
(20)
L'

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where (z)* max(22 0).
Update Eg: Fixing other variables except Eμ, the subproblem in Eq. w.r.t Eμ is as follows:
min A1 Eu 11,,1 + (Ya, H HZ Y//u)
(21)
EN
Similar to E2, the solution of Eн could be solved by 12,1 minimization thresholding operator col- umn by column, i.e.,
En(::)) (1 P pIM()))
A
) M(:5))
(22)
where M H H1/1
Update J: Fixing other variables except J, the subproblem in Eq. w.r.t variable J is as follows: min 11 o(), 2 - J) - min 1/ + 1/2 + 3/P J|'
(23)
J
It is classical tensor nuclear norm minimization problem, where the closed-form solution could be obtained via tensor singular value thresholding (t-SVT) (Zhang et al. 2014).
Update multipliers and penalty parameter: The (Y,', Y W 1- Y., V, μr updated by:
Y = Yi + x c H E Y == Y + + W W")
Yg ===Y= + -
-E)" Y. Y. p
HZ En),
(24)
y'= -= min (maz))
where p > is set accelerate the convergence. With all initial variables, each variable is iteratively
updated until stop conditions are satisfied. After obtaining comprehensive subspace representations
(Z, (Z") In 1), powerful affinity S is constructed for spectral clustering, i.e., S (Z + |
Σ
Z + Σ m 1 (Z))/))(( + 1).
EXPERIMENTS
4.1 EXPERIMENTAL. SETTING
Datasets:
To verify the effectiveness of ARSL-IMVC
method, seven benchmark datasets are uti-
lized, including BBCSport (Zhang et al.) 2024 HW (Asuncion al. 2007). BDGP (Cai et al,, 2012). Yale (Guo et al. 2025b). NGs (Hussain et al. 2010). 100leaves (Mallah et al.] 2013). and Scene-15 15 (Li Perona 2005). Competitors: Several representative methods are selected as com- petitors, including BSV (Ng et al.) 2001), Concat (Wen et al.) 2023b). IMSC-AGL (Wen et al.) 2020a), DAIMC (Hu & Chen 2018), CEAF (Wen et al., 2019). HCP-IMSC (Li et al. 2022), HCLS-CGL (Wen al. 2023a). BWIC-TIMC (Yao al. 2025 RMoGL (Guo al. 2025b).
Incomplete Data Construction: The incomplete multi-view data is constructed by randomly remov- ing samples from each view, with missing rates p (0.1, 0.3. 0.5) the BBCSport, HW, BDGP datasets, missing rates p E (0.1 : 0.1 0.8) on the Yale, NGs, 100leaves, and Scene-15 datasets. Following the experimental setting (Liu al. 2024b), each sample appears in at least one view. Parameters Settings: All compared methods are implemented with their public source codes and recommended parameter settings. For ARSL-IMVC, both A and X2 are searched within the range of {1, 10, 20, 30, 40, 50), and k is selected between 10 and 20. Chustering Metrics: To make compre- hensive comparison, all methods are repeated ten times and the average values of Accuracy (ACC), Normalized Mutual Information (NMI), and Purity metrics are reported.
4.2 EXPERIMENTAL RESULTS AND ANALYSIS
Sooleepreeentt quantitative clustering results on the BBCSport, HW, and BDGP datasets, where the best and sub-optimal results are marked in bold and underline. Figure illustrates the experimental results with broader missing rates on the Yale, NGs, 100leaves and Scene- 15 datasets. The following conclusions can be concluded:
The proposed ARSL-IMVC method consistently outperforms other IMVC existing methods on most cases. And, the ARSL-IMVC achieves significant performance improvements. For exapmle, in terms of ACC, it improves around 4.60%. 8.31%, and 5.41% over sub-optimal methods respec- tively BBCSport, HW, and BDGP datasets, when missing ratio is 0.1.

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Table Clustering results all methods on the BBCSport, HW, and BDGP datasets.
Dataset
Metrics
BSV
Concal
DAIMC
UEAF
IMSC-AGL
HCLS-COL
RCF-IMCC
BWIC-TIMC
RMoGL
Ours
ACC
35.85
58.07
75.39
71.32
84.30
72.00
91.91
90.75
89.19
96.51
0.1
NM1
1.98
34.96
60.76
63.27
72.63
68.90
79.84
82.10
83.18
89.77
RB-SSport
Purity
36.21
59.52
78.18
80.70
85.75
75.55
91.91
90.34
88.79
96.51
ACC
V4.85
0.3
NM1
1.22
17.69
58.29
58.19
74.34
71.33
75.47
70.12
68.86
84.95
Purity
36.21
47.81
79.78
88.62
83.45
89.15
94.85 85.85
ACC
30.51
45.44
57.74
67.22
81.99
78.49
86.05
77.53
76.47
88, 97
0.5
NMI
2.32
15.81
41.25
52.05
66.79
67.13
72.37
65.84
61.76
71.32
Purity
ACC
44.10
65.08
76.65
53.79
88.55 59
79.81
79.80
81.85
76.73
96.90
92.77
Parity
44.20
68.99
78.99
54.01
90.67
81.97
80.05
81.85
76.73
96.90
ACC
38.50
$7.05
44,48
84.28
81.45
75.35
92.44
HW
0.3
NMI
43.11
52.25
51.45
40.66
78.31
81.04
69.11
72.63
62.25
84.16
Puricy
38.90
58.97
60.16
45.35
85.64
84.00
76.50
74.75
65.03
92.46
0.5
NMI
33.78
39.15
51.01
30,85
73.36
81.39
60.47
59.70
54.74
77.97
Puricy
ACC
40.28
43.02
45.72
30.66
41.67
23.08
21.08
29.88
45.94
56.007
NMI
25.22
22.13
22.91
28.03
3.37
25.26
7.23
23.48
38,22
Purity
46.08
46.58
47.75
52.42
44.57
23.68
19.52
31.04
46.66
56.07
BDGP
ACC
39.22
39.20
41.85
16.82
38.97
23.34
23.93
20.32
41.66
50.58
0.3
NMI
23.31
16.55
17.03
22.58
3.36
29.06
20.30
31.59
Puricy
43.52
40.71
42.98
49.86
41.55
23.84
22.21
20.36
43.60
$2.07
49.21
0.5
NMI
20.99
11:78
20.22
24.14
15.81
3.57
24.84
2.43
6.77
32.16
Purity
40.60
35.43
47.78
39.42
24.32
19.00
25.61
32.68
50.21
10llonc
Scomo
170070
Vintng
044
0.1
Figure 2: Clustering results on Yale, NGs, 100leaves and Scene-15 with different missing rates.
Compared to imputation-free IMVC methods (DAIMC, IMSC-AGL, HCLS-CGL), the proposed ARSL-IMYC usually achieves superior clustering performance, illustrating the effectiveness of proposed collaborative view recovery strategy. And, it highlights that the reshaping cross-view consistency and diversity in feature-level indeed facilitates credible and strong view recovery.
The proposed ARSL-IMVC method also outperforms the imputation- baseed methods (i.e., UEAF, HCP-IMSC, B BWIC-TIMC, and RMoGL), owing to its learned latent representation that simulta- neously serves as a semantic foundation for both view recovery and subspace learning, thereby enabling their alignment in capturing cross-view consistency and complementarity. This explicit information flow transmission promotes deep interaction between CVR and TSL modules, im- proving the ability to accurately recover missing view and clustering semantic discriminability.
As illustrated in Figure 2 most IMVC methods exhibit significant performance degradation as the missing rate increases, while ARSL-IMVC maintains higher stability. It fully demonstrates the superiority of proposed ARSL-IMVC in complex IMVC tasks.
4.3 ABLATION STUDY
To verify effectiveness of aligning the view recovery and subspace learning by latent representation H, one ablation variant ARSL-IMVC-I is designed by removing the subspace learning H.
As shown the Table ARSL-IMVC consistently outperforms ablation variant ARSL-IMVC-1, achieving performance improvement of 12.48%, 26.75%, 9.51 %, 6.24%, and 10.63% BBC-
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Table The experimental results of ARSL-IMVC and its ablation variant with the 0.1 missing ratio.
Datasets
BBCSport
HW
Yale
NGS
100leaves
Metrics
ACC
NMI
ACC
NMI
ACC
NMI
ACC
NMI
ACC
NMI
ARSL-IMVC-I
84.03
71.52
70.15
61.77
76.55 78.88
89.96
76.65
91.09 89.24 96.65
78.61
ARSL-IMVC
96.51
89.77
96.90
92.77
86.06
87.96
96.20
89.27
Yale
(b) 100lcaves
(c) BBCSport
HW
Figure 3: Parameter sensitivity analysis of the a1 and X2 on Yale and 100leaves datasets with the missing rate 0. in Figures (3a) and (3b). The t-SNE visualization clustering representation on BBCSport and HW with the missing rate of 0.1 in Figures (3ch and (3d).
Sport, HW. Yale, NGs, and 100lcaves datasets regarding ACC metric. The result indicates that align- ing view recovery and subspace learning in complex correlation exploration promotes the semantic coherence between them, facilitating the fine-grained and clear clustering structure modeling.
4.4 PARAMETER SENSITIVITY AND VISUALIZATION ANALYSIS
To evaluate the sensitivity of ARSL-IMVC to parameter, with missing rate of 0.1, the ACC metric with different A1 and X2 is shown in Figures (3a and (3b). It can be observed that the performance of ARSL-IMVC is not significantly influenced by X2 when A is fixed, while it slightly affected by Å when A2 is fixed. Although, the ARSL-IMVC is relatively robust to parameter varying within a reasonable range.
To intuitively illustrate the clustering performance of ARSL-IMVC, the spectral embeddings on BBCSport and HW datasets are visualized by t-SNE (Maaten Hinton (0088) with a missing rate of 0.1. As shown in Figures (3c) and (3d). the spectral embedding oblained by ARSL-IMVC ex- hibits relatively clear clustering structure and samples from diverse clusters are obviously separated, verifying its discriminability in clustering semantics exploration.
Table 4: Clustering results of some methods on HDigit datasets with the missing rate of 0.1.
Methods
DAIMC
UEAF
IMSC-AGL
HCLS-IMSC
Ours HCP-IMSC
ACC
67.58
85.38
76.32
98.29
89.56
99.00
NMI
64.25
73.56
77.40
95.30
89.52
96.97
Purity
69.61
85,38
77.89
98.29
88.40
99.00
4.5 SCALABILITY ON LARGE-SCALE DATASET
To further validate the effectiveness and scalability of the proposed ARSL-IMYC on large-scale multi-view data, the Handwritten Digits (HDigit) dataset with 10000 samples is utilized, where two views are collected from various resources: MNIST and USPS. The experimental results of partial representative methods 0.1 missing ratio are shown Table Compared with the suboptimal HCLS-IMSC, improvements of approximately 0.7% in both ACC and Purity and approximately 1.7% in NMI are achieved by the proposed method. Compared to other baselines such as UEAF and IMSC-AGL, the performance gains reach 10% 25%. These results clearly demonstrate that ARSL-IMVC can effectively handle the representation learning challenges arising from substantial increases in sample size and feature dimensionality.

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Published as a conference paper at ICLR 2026
Burning (is aesord/lteiinnn
BSV
Cancat
DAIMC
HEAF
IMSC-AGL
HCLS-DGL
HCP-IMSC
BWIC-TIMC
RMoGL
OOurs
BBCS
BEGG
NGs
100leaves
Figure 4: The running time comparisons on the partial representative datasets with 0.1 missing rate.
INC
Bac
(a) Yale
(b) BBCSport
NGs
Figure 5: The convergence curves on Yale, BBCSport and NGs datsets with the missing rate of 0.1.
4.6 RUNNING TIME COMPARISON AND CONVERGENCE ANALYSIS
Figure reports the running time of all compared methods on the four benchmark datasets (BBC- Sport, BDGP. NGs and 100leaves). shown the Figure g the proposed ARSL-IMVC method generally requires comparable computational costs to other IMVC methods on the four datasets. Considering the superior clustering performance of proposed method, ARSL-IMVC demonstrates good balance between computational efficiency and clustering performance.
To empirically shown the stability the optimization algorithm, the convergence analysis results are verified on the Yale, BBCSport, and NGs datasets with the missing rate of 0.1, where the iterative residual errors are visualized. As shown in Figures (5a). (5b) and (5c). the residual curves of variable updating show that proposed optimization algorithm reach local minimum within finite number iterations, verifying the fast convergence and numerical stability of ARSL-IMVC.
5 CONCLUSION
In this study, novel ARSL-IMVC method was proposed for challenging incomplete multi-view clustering, which centers latent representation achieve unified alignment between view covery and tensor subspace learning in complex cross-view correlation exploration. The latent rep- resentation served as both view reconstruction basis and global semantics carrier, maintaining and aligning the cross-view consistency. And, global view-shared and local view-specifis subspace rep- resentations were organized into low-rank tensor, exploring the cross-view complementarity and multi-level structural correlations. Experimental results demonstrated that the ARSL-IMVC consis- tently achieves superior clustering performance under various missing rates.
ACKNOWLEDGMENT
This research was supported by the National Natural Science Foundation of China under Grant 62225303, 62403043, and 62433004; in part by the China Postdoctoral Science Foundation un- der Grant
in part by the Interdisciplinary Research Center Beijing University of Chemical Technology under Grant XK2025-06.
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ETHICS STATEMENT
Our research adheres strictly to ICLR ethical guidelines, emphasizing responsible AI development maximize societal benefits while mitigating potential harms. The proposed ARSL-IMVC method enhances incomplete multi-view clustering, offering advancements in data analysis that could ben- efit fields such as healthcare, environmental monitoring, and education by improving resilience to missing data. Our research is dedicated to the benefit of society and human well-being, and since does not involve human subjects, no ethical approval required. All datasets used in our experi- ments publicly available and comply with their respective licenses. The methodology and results are presented with full transparency to support reproducibility, including source code provided the supplementary materials, which will be open-sourced following the review process.
REPRODUCIBILITY STATEMENT
To ensure the reproducibility of our work, the complete source code of the ARSL-IMVC will be provided in the supplementary materials. The public datasets used in the experiments are all cited the paper and the construction of incomplete datasets can be carried out according to the specific methods mentioned in Section 4.1 of the main text.
REFERENCES
Arthur Asuncion, David Newman, al. Uci machine learning repository, 2007.
Shunshun Bai, Qinghai Zheng, Xiaojin Ren, and Jihua Zhu. plete multi-view clustering. Expert Systems with Applications, 1251155,,5, 2024.
imputation free incom-
Richard H Bartels and George W Stewart. Algorithm 432 [c2]: Solution of the matrix equation ax+ xb= [f4]. Communications the ACM, 15(9):820-82) 1972.
Xiao Cai, Hua Wang, Heng Huang, and Chris Ding. Joint stage recognition and anatomical annota- tion of drosophila gene expression patterns. Bioinformatics, 28(12):16-24 2012.
Xiaochun Cao, Changqing Zhang, Huazhu Fu, Liu, and Hua Zhang. Diversity-nnduced multi-view subspace clustering. In Proceedings of the IEEE Conference on Computer Vision and Patlern Recognition, pp. 586-594, 2015.
Guoqing Chao, Shiliang Sun, and Jinbo Bi. A survey multiview clustering. JEEE Transactions on Artificial Intelligence,
2021.
Jin Chen, Huafu Xu, Jingjing Xue, Quanxue Gao, Cheng Deng. and Ziyu Lv. Incomplete multi-view clustering based on hypergraph. Information Fusion, 117:102804, 2025.
Man-Sheng Chen, Jia-Qi Lin, Xiang-Long Li, Bao-Yu Liu, Chang-Don Bong Wang, Dong Huang, and Jian-Huang Lai. Representation learning in multi-view clustering: A literature review. Data Science and Engineering, 7(3):225-244 2022.
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, 35(11):15332-1558 2024.
Hongchang Gao, Feiping Nie, Xuelong Li, and Heng Huang. Multi-view subspace clustering, In Proceedings of the IEEE International Conference on Computer Vision, pp. 4238-4244 2015.
Arthur Gretton, Kenji Fukumizu, Choon Teo, Le Song. Bernhard Schölkopf, and Alex Smola. A kernel statistical test of independence. In Advances in Neural Information Processing Systems, pp. 585-592, 2007.
Jipeng Guo, Yanfeng Sun, Junbin Gao, Yongli Hu, and Baocai Yin. Multi-attribute subspace clus- tering via weig-weighted tensor nuclear norm minimization. IEEE Transactions on Image Pro- cessing, 31:7191-7205. 2022.
11

---

Published as a conference paper at ICLR 2026
Jipeng Guo, Yanfeng Sun, Junbin Gao, Yongli Hu, and Baocai Yin. Logarithmic schatten-p norm minimization for temsorial multi-view subspace clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(3):3396-3400 2023.
Jipeng Guo, Yanfeng Sun, Xin Ma, Junbin Gao, Yongli Hu, Youqing Wang. and Baocai Yin. Global- ity meets locality: An anchor graph collaborative learning framework for fast multiview subspace clustering. IEEE Transactions on Neural Networks and Learning Systems, 36(6):10213 - 10227, 2025a.
Wei Guo, Hangjun Che, Man-Fai Leung Long Jin, and Shiping Wen. Robust mixed graph learning for incomplete multi-view clustering. Information Fusion, 1 115:102776, 2025b.
Menglei Hu and Songcan Chen. Doubly aligned incomplete multi-view clustering. In Proceedings of the International Joint Conference Artificial Intelligence, pp. 2262-22002 2018.
Shizhe Hu, Chengkun Zhang, Guoliang Zou, Zhengzheng Lou, and Yangdong Ye. Deep multi- view clustering by pseudo-label guided contrastive learning and dual correlation learning. IEEE Transactions on Neural Networks and Learning Systems, 36(2):3646-363) 2025.
Syed Fawad Hussain, Gilles Bisson, and Clément Grimal. An improved co-similarity measure for document clustering. In International Conference on Machine Learning and Applications, pp- 190-197, 2010.
Bingbing Jiang, Chenglong Zhang, Xinyan Liang, Peng Zhou, Jie Yang, Xingyu Wu, Junyi Guan, Weiping Ding, and Weiguo Sheng. Collaborative similarity fusion and consistency recovery for incomplete multi-view clustering. In Proceedings of the AAAI Conference on Artificial Intelli- gence, pp. 17617-17625, 2025.
Fei Li and Pietro Perona. A bayesian hierarchical model for learning natural scene categories, In Proceedings of the IEEE Conference Computer Vision and Pattern Recognition, pp. 524-531, 2005.
Miaomiao Li, Siwei Wang, Xinwang Liu, and Suyuan Liu. Parameter-free and scalable incomplete multiview clustering with prototype graph. IEEE Transactions on Neural Networks and Learning Systems, 35(1):300-311) 2024.
Shao Yuan Li, Yuan Jiang, and ZhiHua Zhou. Partial multi-view clustering. In Proceedings of the AAAI Conference Artificial Intelligence, pp. 1968-1974, 2014.
Xingfeng Li, Yuangang Pan, Yuan Sun, Quansen Sun, Yinghui Sun, Ivor Tsang, and Zhenwen Ren. Incomplete multi-view clustering with paired and balanced dynamic anchor learning. IEEE Transactions on Multimedia, 27: 17:1486-1497, 2025.
Zhenglai Li, Chang Tang, Xiao Zheng, Xinwang Liu, Wei Zhang, and En Zhu. High-order correla- tion preserved incomplete multi-view subspace clustering. IEEE Transactions on Image Process- ing, 33:2067-20882 2022.
Zhouchen Lin, Risheng Liu, and Zhixun Su. Linearized alternating direction method with adaptive penalty for low-rank representation. In Advances in Neural Information Processing Systems, pp- 612-620, 2011.
Chengliang Liu, Jie Wen, Zhihao Wu, Xiaoling Luo, Chao Huang, and Yong Xu. Information drrovery-driven deep incomplete multiview clustering network. IEEE Transactions on Neural Networks and Learning Systems, 35(11)115442-1455 2024a.
Chengliang Liu, Jie Wen, Yong Xu, Bob Zhang, Liqiang Nie, and Min Zhang. Reliable representa- tion learning for incomplete multi-view missing multi-label classification. IEEE Transactions Pattern Analysis and Machine Intelligence, 47(6)-9440-496 2025.
Guangean Liu, Zhouchen Lin, and Yong Yu. Robust subspace segmentation by low-rank repre- sentation. In Proceedings of the International Conference on Machine Learning, pp. 663-670, 2010.
12

---

Published as a conference paper at ICLR 2026
Suyuan Liu, Junpu Zhang, Yi Wen, Xihong Yang, Siwei Wang. Yi Zhang, En Zhu, Chang Tang, Long Zhao, and Xinwang Liu. Sample-level cross-view similarity learning for incomplete multi- view clustering. In Proceedings of the AAAI Conference on Artificial Intelligence, pp. 14017- 14025, 2024b.
Xinwang Liu, Xinzhong Zhu, Miaomiao Li, Lei Wang, En Zhu, Tongliang Liu, Marius Kloft, Ding- gang Shen, Jianping Yin, and Wen Gao. Multiple kernel k-means with incomplete kernels. IEEE Transactions Pattern Analysis and Machine Intelligence, 42(5):1191-1204 2020.
Xinwang Liu, Miaomiao Li, Chang Tang, Jingyuan Xia, Jian Xiong, Li Liu, Marius Kloft, and En Zhu. Efficient and effective regularized incomplete muew clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence. 43(8):2634-2646, 2021.
Zhengzheng Lou, Hang Xue, Yanzheng Wang. Chaoyang Zhang, Xin Yang, and Shizhe Hu. Parameter-free free deep multi-modal clustering with reliable contrastive learning. IEEE Transactions on Image Processing, 34:2628-2644 2025.
Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of Machine Learning Research, 9:2579-2605, 2008.
Charles Mallah, James Cope, James Orwell, et al. Plant leaf classification using probabilistic inte- gration of shape, texture and margin features. Signal Processing, Puttern Recognition and Appli- cations, 5(1):45-54, 2013.
Andrew Ng, Michael Jordan, and Yair Weiss. On spectral clustering: Analysis and an algorithm. In Advances in Neural Information Processing Systems, pp. 849-856, 2001.
Yalan Qin, Guorui Feng, and Xinpeng Zhang, Scalable one-pass incomplete multi-view clustering by aligning anchors. In Proceedings the AAAI Conference on Artificial Intelligence, pp. 20042- 20050, 2025.
Qiangqiang Shen, Xuanqi Zhang, Shuqin Wang, Yuanman Li, Yongsheng Liang, and Yongyong Chen. Dual completion learning for incomplete multi-view clustering. JEEE Transactions on Emerging Topics Computational Intelligence, 91):455-467, 2025.
Long Shi, Lei Cao, Jun Wang, and Badong Chen. Enhanced latent multi-view subspace clustering.
IEEE Transactions Circuits and Systems for Video Technology, 34(12):12400- 2024.
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, 2021.
Siwei Wang, Xinwang Liu, En Zhu, Chang Tang. Jiyuan Liu, Jingtao Hu, Jingyuan Xia, and Jian- ping Yin. Multi-view clustering via late fusion alignment maximization. In Proceedings of the International Joint Conference Artificial Intelligence, pp. 3778-3788 2019.
Xinxin Wang. Yongshan Zhang, and Yicong Zhou. Pseudo-supervision affinity propagation for efficient and scalable multiview clustering. IEEE Transactions on Neural Networks and Learning Systems, 1282: 2025a.
Xinxin Wang, Yongshan Zhang, and Yicong Zhou. Bidirectional probabilistic multi-graph learning and decomposition for multi-view clustering. IEEE Transactions Image Processing, 34:3609 3621, 2025b.
Ziyu Wang, Lusi Li, Xin Ning, Wenkai Tan, Yongxin Liu, and Houbing Song. Incomplete multi- view clustering via structure exploration and missing-view inference. Information Fusion, 103: 102123, 2024.
Jie Wen, Zheng Zhang, Yong Xu, Bob Zhang, Lunke Fei, and Hong Liu. Unified embedding align- ment with missing views inferring for incomplete multi-view clustering. In Proceedings of the AAAI Conference on Artificial Intelligence, pp. 5393-5400, 2019.
Jie Wen, Yong Xu, and Hong Liu. Incomplete multiview spectral clustering with adaptive graph learning. IEEE Transactions on Cybernetics, 50(4):1418-1422 2020a.
13

---

Published as a conference paper at ICLR 2026
Jie Wen, Ke Yan, Zheng Zhang, Yong Xu, Junqian Wang. Lunke Fei, and Bob Zhang. Adaptive graph completion based incomplete multi-vien clustering. IEEE Transactions on Multimedia, 23:2493-2504, 2020b.
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 Conference on Computer Vision and Pattern Recognition, pp. 15712- 15721, 2023a.
Jie Wen, Zheng Zhang, Lunke Fei, Bob Zhang, Yong Xu, Zhao Zhang, and Jinxing Li. A survey on incomplete multiview clustering. IEEE Transactions on Systems, Man, and Cybernetics: Systems, (3(2):1136-144)) 2023b.
Jie Wen, Chengliang Liu, Shijie Deng, Yicheng Liu, Lunke Fei, Ke Yan, and Yong Xu. Deep double incomplete multi-view multi-label learning with incomplete labels and missing views. IEEE Transactions Neural Networks and Learning Systems, 35(8): 112111196-11111 1408, 2024a.
Jie Wen, Gehui Xu, Zhanyan Tang. Wei Wang. Lunke Fei, and Yong Xu. Graph regularized and feature aware matrix factorization for robust incomplete multi-view clustering. IEEE Transactions on Circuits and Systems for Video Technology, 34(5):3728-3741, 2024b.
Jie Wen, Jiang Long, Xiaohuan Lu, Chengliang Liu, Xiaozhao Fang, and Yong Xu. Partial multiview incomplete multilabel learning via uncertainty-drrive reliable dynamic fusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 48(1):233-22) -:200,2 2026.
Tingting Wu, Songhe Feng, and Jiazheng Yuan. Low-rank kernel tensor learning for incomplete multi-view clustering. In Proceedings of the AAAI Conference on Artificial Intelligence, pp. 15952-15960, 2024.
Tingting Wu, Zhendong Li, Zhibin Gu, Jiazheng Yuan, and Songhe Feng. Koala: Kernel coupling and element imputation induced multi-view clustering. In Proceedings of the AAAI Conference Artificial Intelligence, pp. 21581 1-21999, 2025.
Chang Xu, Dacheng Tao, and Chao Xu. A survey multi-view learning. arXiv preprint arXiv: 1304.5634, 2013.
Mingze Yao, Huibing Wang, Yawei Chen, and Xianping Fu. Between/within view information completing for tensorial incomplete multi-view clustering. IEEE Transactions on Multimedia, 27:1538-1550, 2025.
Chenglong Zhang, Yang Fang, Xinyan Liang, Han Zhang, Peng Zhou, Xingyu Wu, Jie Yang, Bing- bing Jiang, and Weiguo Sheng. Efficient multi view unsupervised feature selection with adaptive structure learning and inference. In Proceedings of the International Joint Conference Artificial Intelligence, pp. 5443-5452, 2024.
Zemin Zhang, Gregory Ely, Shuchin Aeron, Ning Hao, and Misha Kilmer. Novel methods for multilinear data completion and de-noising based on tensor-svd. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3842-3849, 2014.
Tianxiang Zhao, Youqing Wang, Shilong Xu, Tianchuan Yang, Junbin Gao, and Jipeng Guo. Dual- level noise augmentation for graph clustering with triplet-wise contrastive learning. Pattern Recognition, 172:1 12463, 2026.
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A APPENDIX
The Use of Large Language Models (LLMs)) In this research, large language models (LLMs) were employed exclusively to improve the clarity and grammatical accuracy of the manuscript. Their use was limited to refining sentence structure and correcting syntax to enhance readability and professionalism. At no stage did these tools influence the scientific content, methodology. or results. All core ideas and analyses presented are the original work of the authors, with no LLM-genen -eM--eeerrted content contributing the intellectual substance of the paper.
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Reviews:
[{"review_id": "0SqgJumCXY", "reviewer": "Reviewer_acAD", "summary": "This paper proposes a novel ARSL-IMVC method for the classic incomplete multi-view clustering task, which aligns the collaborative view recovery and tensorial subspace learning in cross-view complementarity and consistency exploration. It is interesting, which is the inverse idea of classical multi-view clustering. It uses an unknown latent shared representation to reverse infer missing multi-view data and act on the subspace representation learning. Latent representation as a bridge helps to explicitly realize cross-view correlation exploration. The extensive experimental results verify its effectiveness.", "questions": "(1) How sensitive is the model to the dimension of the latent representation? Could a too-small latent space limit the recovery ability? Please elaborate and explain further.\n(2) The low-rank tensor constraint may lead to over-smoothing of the subspace representations. How does the model maintain clustering discriminability under such constraint?\n(3) The proposed model seems to be complex; does it have an advantage in training time compared to existing methods? Please provide relevant comparative experiments.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "(1) This paper is clearly motivated and proposes to achieve the \"semantic alignment\" of view recovery and subspace learning through a shared latent representation in incomplete multi-view clustering, which is innovative.\n(2) The logic and writing of the paper are satisfactory.\n(3) Experiments on several datasets with multiple missing ratios provide convincing evidence of the clustering performance robustness.", "weaknesses": "(1) The choice of latent representation dimensions remains empirical, lacking selection guidance or systematic analysis. \n(2) For clustering tasks on large-scale datasets, runtime efficiency is crucial. But the paper does not provide an analysis of runtime, leaving its practical scalability unclear.", "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": "75FShOzH26", "reviewer": "Reviewer_seS7", "summary": "This work addresses incomplete multi-view clustering by introducing an aligned representation and subspace learning model. Unlike conventional imputation-based methods, ARSL-IMVC employs a shared latent representation to guide view recovery and tensor subspace construction simultaneously, thus promoting collaborative information exchange across views. The framework is novel and effective, enabling the model to capture both global coherence and view-level diversity. Comprehensive experiments across multiple datasets demonstrate the model's robustness and superior clustering performance under different missing view scenarios. The idea is novel, clear, and provides a meaningful advancement for incomplete multi-view clustering.", "questions": "Apart from the above weaknesses, I still have some questions:\n\n1. The semantic alignment between view recovery and subspace representation is new, its innovation needs further clarification, especially the difference from existing methods.\n\n2. Exploring the criteria of cross-view consistency and complementarity has been widely used in multi-view learning. What is the contribution of this study in this regard?\n\n3. If the latent representation has already been trained to capture shared semantics, does the introduction of a low-rank constraint on the subspace representation tensor result in redundant regularisation?\n\n4. The HSIC regularisation term can use different kernel functions. Why does ARSL-IMVC choose to use the inner product kernel?\n\n5. The latent representation H and the centralised matrix H use the same notation.\n\n6. The authors introduced a view-specific orthogonal matrix $P^{(v)}$ to recover the view-specific features. I have a concern about whether $(P^{(v)})^\\top P^{(v)} = I$ can still hold when the dimension of view-specific features is lower than $k$.\n\n7. The choice of HSIC: why this paper chooses HSIC as a diversity measurement here rather than some others, e.g., Gromov-Wasserstein distance.\n\n8. What are the global semantics and local cluster structures in Eq. (4) ?\n\n9. This paper utilises a rotation operator to transfer a $N\\times N\\times (V+1)$ tensor to a $ N\\times (V+1) \\times N$  tensor, making the results of the tensor low rank constraint sensitive to the orders of samples arranged in the input features. How does this paper address this issue?\n\n10. The datasets used in this paper are small-scale.\n\nThe scores of this paper will be raised after addressing the above weaknesses and questions.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper proposes a novel framework for joint view recovery and tensor subspace learning. It explicitly aligns the two modules through a shared latent representation, which is relatively uncommon in existing IMVC methods.\n\n2. The experimental design is comprehensive, covering various missing rates and including comparisons with multiple baseline methods. The results are superior and clearly demonstrate the effectiveness of each module.", "weaknesses": "1. Lack of introduction to datasets and baseline methods.\n\n2. While results are averaged over 10 runs, reporting the standard deviation would make the experimental conclusions more statistically convincing.\n\n3. Two main differences as induced in this paper need to be more detailed. And the authors are suggested to give more explanations related to some key words, e.g., \"limited structural fidelity\", \"insufficient diversity and consistency reshaping\", etc. This makes it easier for readers to understand these opinions. And some empirical or theoretical evidence is more favoured.\n\n4. Notations are not consistent. Please see my questions.\n\n5. The motivations of some equation formulations are not clear. Please see my questions.\n\n6. Complexity analysis is lacking.", "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": "C4Ojl4xwgg", "reviewer": "Reviewer_K2t4", "summary": "The IMVC is an important topic and relies on discriminative representation learning. Most of existing imputation-based IMVC methods perform well, but they still face one crucial limitation, i.e., view recovery and subspace representation lack explicit alignment and collaborative interaction in exploring complementarity and consistency across multiple views. These issues are crucial for IMVC. This study proposes a novel ARSL-IMVC that aligns collaborative view recovery and tensorial Subspace Learning via latent representation. It is a simple yet effective method, and this is interesting design for IMVC. Extensive experimental results on seven datasets demonstrate the\npowerful capacity of ARSL-IMVC in complex incomplete multi-view clustering tasks under various view missing scenarios. Overall, this paper has a clear and novel contribution to IMVC, and some concerns also need to be clarified.", "questions": "1.When stacking view-shared and view-specific subspace representations into a tensor, does the optimization enforce any independence between shared and specific subspaces, making the features tend to be the same?\n\n2.Besides the current averaging strategy, are there other fusion strategies explored to integrate shared and view-specific subspace representations? For example, learning an adaptive weight.\n\n3.There is a lack of detailed analysis of the severe performance degradation of certain datasets under high missing rates. Further explanation and improvement strategies are recommended.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.The paper is well-written and easy to follow，ARSL-IMVC provides a new and cohesive framework that aligns consistency and complementarity across views. \n\n2.The method analysis is relatively comprehensive, and the optimization steps are clearly explained. The experimental design is comprehensive, validating the performance of the method on seven datasets covering various missing rates, and comparing it with several representative baseline methods.The ablation and visualization analyses are well designed and strongly support the effectiveness of the proposed modules.", "weaknesses": "1.What is HW dataset? There is a lack of introduction to the statistical information of the used dataset. This is beneficial for readers.\nSome experimental settings need to be further provided.\n\n2. Some additional concerns can be found in **Questions**.", "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": "Cv0gkUKKbm", "reviewer": "Reviewer_WN4G", "summary": "This paper proposes a novel method, ARSL-IMVC, to tackle the task of incomplete multi-view clustering. This method combines collaborative view recovery (CVR) and tensor subspace learning (TSL) through a shared latent representation, aiming to enhance cross-view consistency and complementarity while strengthening the synergistic interaction between view recovery and subspace representation. Extensive experimental results on seven datasets validate the effectiveness and robustness of the method. Overall, the paper is well-structured, with clear motivations and promising results, and some concerns require further exploration.", "questions": "See Weaknesses section.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1).This paper proposes a method for aligning view recovery and tensor subspace learning using latent representations, which is well-structured.\n\n2).The paper's research motivation is clear, the model design logic is clear, and it is easy to understand.\n\n3).The experiments are detailed, and the method is compared with multiple baseline methods on multiple datasets at different missing rates and the experimental results show the method's good performance.", "weaknesses": "1).The background knowledge about tensors should be added with more details, which can help readers better understand the methods proposed in the paper.\n\n2).The model involves alternating optimization of multiple variables, and the computational cost of tensors is high, lacking analysis of computational complexity.\n\n3). The convergence of optimization process should be analyzed.\n\n4). Does the tensor low-rank regularization preserve local manifold structures within each view, or mainly capture global correlations? Would adding a local structural constraint improve the model?", "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 (Poster)