Debiased and Denoised Representation Learning for Incomplete Multi-view Clustering
Authors: Qianqian Wang
Xurui Liao
Wei Feng
Quanxue Gao
Venue: ICLR 2026 Poster (2026)
Keywords: Incomplete multi-view clustering
projection debiasing and denoising
robust contrastive learning.
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
TL;DR: We propose a consensus projection refinement strategy for deep incomplete multi-view clustering, aiming to mitigate cluster collapse risk induced by misalignment noise.

Abstract: Multi-view clustering integrates the consistency and complementarity of different views to achieve unsupervised data grouping. Existing multi-view clustering methods primarily confront two challenges: i) they generally perform feature extraction in the feature domain, which is sensitive to noise and may neglect cluster-specific information that is indistinguishable in the original space; ii) current dynamic fusion methods adopt static strategies to learn weights, lacking capability to adjust strategies adaptively under complex scenarios according to variations in data distribution and view quality. To address these issues, we propose a large language model assisted dynamic agent for multi-view clustering (LLM-DAMVC), a novel framework that recasts multi-view clustering as a dynamic decision-making problem orchestrated by a large language model. Specifically, each view is equipped with complementary agents dedicated to feature extraction. A dual-domain contrastive module is introduced to optimize feature consistency and enhance cluster separability in both the feature domain and frequency domain. Additionally, an LLM-assisted view fusion mechanism provides a flexible fusion weight learning strategy that can be adaptively applied to complex scenarios and significantly different views. Extensive experimental results validate the effectiveness and superiority of the proposed method.

Published as a conference paper at ICLR 2026
DEBIASED AND DENOISED REPRESENTATION LEARN- ING FOR INCOMPLETE MULTI-VIEW CLUSTERING
Qianqian Wang', Xurui Liao", Wei Feng", Quanxue Gao! Xidian University, Northwest A&F University
qqwangex an edu, en, 211591000248stu, xidian. edu. en weifeng. ft foxmail. com, qxgao@xidian.edu edu. on
ABSTRACT
Multi-view clustering achieves outstanding performance but relies on the assump- tion of complete multi-view samples. However, certain views may be partially unavailable due failures during acquisition or storage, resulting in distribution shifts across views. Although some incomplete multi-view clustering (IMVC) methods have been developed based on data imputation, these methods increase the unnecessary computational complexity. Therefore, some methods introduce consensus representation imputation and receives remarkable popularity. Nev- ertheless, they generally ignore the inter-view distribution bias due to missing views, which further leads semantic misunderstanding and representation noises. To tackle these issues, propose novel IMVC based Debiased and Denoised Representation (DDR-MMVC) learning. Specifically, it utilizes the unbiased repre- sentation learned from complete views to refine the biased representation learned from data with missing views. Additionally, we introduce a robust contrastive learning for consensus representation mitigate cluster collapse risk induced by misalignment noise. Comprehensive experiments demonstrate that DDR-IMVC achieves superior performance compared with state-of-the-an methods.
INTRODUCTION
Multi-view clustering (MVC) has achieved significant breakthroughs in unsupervised learning (Fng et al., 2023 Yan et al. 2024b; Zhang al.) 2024a). Unfortunately, the superior performance of existing MVC methods largely relies on the assumption of complete cross-view samples. However, due failures during data acquisition or storage, partial data some views may be unavailable. As result, existing MVC methods are inapplicable for incomplete multi-view data. Therefore, the problem of incomplete multi-view clustering (IMVC) has attracted increasing attention (Xu al.] 2024 Dong et al. 2024 Wan et al., 2024). The goal of IMVC is to uncover the common clustering patterns hidden in incomplete multi-viee view data and to group unlabeled instances into distinct clusters.
Existing IMVC methods can be categorized into two types: traditional methods and deep meth- ods. Traditional IMVC methods employ matrix completion to impute missing views for clustering, while some other methods utilize machine learning techniques to learn shared low-dimensional embedding. These methods can further divided into three subcategories: kernel-based methods (Liu et al., [219 2020). matrix factorization-Be based methods (Hu & Chen 2019 Chao et al., (022), and graph learning-basee of traditional IMVC methods largely depend the quality of features. Although they more interpretable than deep methods, their representational capacity is often limited.
methods (Wen et al.) 2019; Li et al. (022). However, the performance
Owing the powerful generalization and representation capabilities of deep neural networks, deep IMVC methods have achieved outstanding performance. Some deep methods address the view incomplete problem by imputing the miss-view data with neural network. For example, generative adversarial network (GAN)-based methods employ GAN to produce the missing data (Wang et al.) 2021
methods (Liu al. 2022 Jin of prototypes from the available data and then establish correspondences to recover missing data.
2023) learn certain number
"Corresponding Author

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Published as a conference paper at ICLR 2026
However, these methods may incur high computational complexity, and it is generally difficult to achieve accurate missing view recovery, which thus introduces noises to the data and degrade the clustering performance. Differently, some other methods attempt to perform miss-view imputation in the feature space rather than the data space by fusing the latent representation of other views (Wen) et al. 2019 Xu et al. 2024). Therefore, these methods effectively reduce the complexity and realize impressive performance. Nevertheless, they overlook inter-view distribution difference, resulting in the distribution shift of the shared representation between the complete views and incomplete ones, which further introduces substantial cross-view misalignment noise and lead to erroneous clustering structures (Lin al. 2022 Yin al. 2025).
To address the above issues, we propose a novel incomplete multi-view clustering method based on debiased and denoised representation learning, named DDR-IMVC. The proposed framework is illustrated in Figure [T] Notably, DDR-IMVC is not merely restricted to intra-view or inter-view interactions, but instead enables concurrent interactions across all instances. Specifically, to bridge the semantic gaps across views, DDR-IMVC derives the neighborhood relationships of samples with missing views from their available view information, and leverages these relationships to refine the corresponding missing- vvie features. In practice, we design adaptive weight matrices based on cluster separability to collaboratively integrate low-dimensional representation from all views and accommodate the influence of varying degrees of missing instances. In this space, it introduces an iitention-based complementarity refinement which utilizes the unbiased representation learned from complete views together with their neighboring relationship to refine the biased representation learned from data with missing views. Additionally, to enhance the consensus representation and eliminate the redundancy of all views, DDR-IMVC maximizes the mutual information between the consensus representation and the view-specific representations. Furthermore, to mitigate misalign- ment noises in shared representation and improve its discrininativeness, DDR-IMVE employs denoised contrastive strategy to learn clear clustering structure and reduce the risk of clustering collapse. Our main contributions can be summarized as follows:
We propose an innovative incomplete multi-view clustering framework, i.e., DDR-IMVC, which employs unbiased representation to correct and refine the distribution shifts of the biased representation.
To alleviate the cluster collapse problem induced by misalignment noise, we adopt a robust contrastive constraint based consensus representations, which facilitates diseriminative and robust consensus representation learning.
We analyze the performance of DDR-IMVC with extensive experiments, whose results demonstrate that DDR-IMVC outperforms state-of-the-art methods across four datasets under varying missing rates.
RELATED WORK
2.1
MULTI-VIEW CLUSTERING
MVC groups samples with similar feature patterns into the same cluster by integrating feature in- formation from different views Yang & Wang. 2018: Zhou et al.) 2024). Deep autoencoders, as powerful feature extraction tools, have been widely applied in MVC. To address the inconsistency between discrete clustering information and continuous visual information, Xu et al. (2021) employs a variational autoencoder to learn disentangled representations. MFLVC relies on an autoencoder to learn latent features at different levels to mine common semantics (Xu et al., 20226). However, these methods struggle eliminate the interference private information and noise during consistent formation extraction. Yan et (2024a) proposes a novel variational autoencoder under information bottleneck theory to preserve clustering information. Unlike the above approaches that optimize reconstruction loss to learn latent features, Xie et al.) (2020) constructs a multi-view joint cluster- ing network using stacked autoencoders, convolutional autoencoders, and variational autoencoders to capture precise multi-view features. Trosten et al. (2021) Tang & Liu (2022) employ encoding networks to extract view-specific features while maintaining cluster compactness through clustering constraints. Moreover, for real- world multi-view data with missing views, the above methods often struggle to uncover accurate data representations. Therefore, uncovering accurate clustering patterns in incomplete multi-view data has become important research direction.
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2.2 INCOMPLETE MULTI- VIEW CLUSTERING
In recent years, IMVC has achieved significant breakthroughs. Generally, deep IMVC methods can be divided into four categories: Autoencoder-based methods. [in et al. 2021 2022 predict the missing data with the autoencoders to leverage the available data across views, with the goal of minimizing the conditional entropy. 2) Adversarial Network-basse based methods. Wang et (2021) ex- plicitly generates missing view data through generative ad adversarial networks (GANs) and integrates multi-view information achieve efficient clustering. Wang et al. (2023) proposes self-supervised framework that combines GANs with dual contrastive learning, exploiting the hidden information in incomplete data. 3) Graph Convolutional Network-based methods. [Tang Liu (2022) dynami- cally updates neighbors based on learned semantic features, avoiding the interference of low-quality samples during data completion. Chao et al. (2024) constructs a neighbor-samp adjacency matrix and adopts graph convolutional networks (GCNs) to complete missing samples. Pu et al. (2024)
constructs a latent graph to preserve topological information for the dynamic imputation of missing embedded features. CCao al. (2025) adaptively completes missing representations by integrating intra-view local relationships and cross-view global relationships through GCNs. 4) Prototype-base methods. Dai consensus semantics without data completion or alignment. Yuan et al. (025) introduces a robust prototype contrastive strategy handle overfitting caused by prototype misalignment. Despite their effectiveness, most IMVC methods ignore the potential inter-view distribution bias due to missing views.
(2025) proposes an IMVC framework in a common semantic space based on
METHODOLOGY
3.1 NOTATIONS
Jo=1 consists of N samples, each represented by V views of dimensionality D... There are N₂ complete samples with all views and N₂ samples with missing views. Let the complete samples be denoted (X (Xclest Je=1 and the samples with missing views be denoted as {Xi]Vz> A complete view indicator matrix M E {0, 1 indicates the positions of missing views. Mi is set 1 if the i-th sample in the v-th view is observed; otherwise, it indicates a missing view. It is assumed that no sample is missing in all views simultaneously. i.e., vi [L, EV= M, 2 1. The task is to cluster these N samples with potentially missing views into K clusters.
A multi-view dataset X' = [X" E RND=a
3.2 "IEW-SPECIRE RECONSTRUCTION
Considering that the data across different views mostly heterogeneous and differently distributed, we provide independent autoencoders for each view to alleviate clustering instability on the man- ifold structure in high-dimn high-dimensional space (Hinton & Salakhutdinov 2006;
Guo et al. 2017). An
autoencoder (-) is used to learn the embedding of the sample:
Z Eg (X"),
(1)
where Z" R xd denotes the view-specific representation of the v-th view in the d-dimensional embedding space. 0 represents the learnable parameters of the autoencoder. Then, we reconstruct the embedding z" into X E Nx with the decoder (.).), as follows:
X (Z"),
where á denotes the Iearnable parameters of the decoder. The reconstruction loss across all views can be expressed as follows:
LREC
X
X
u=1
3.3 UNBIASED REFINEMENT FOR BIASED REPRESENTATION
Then, we fuse view-specific representations into a unified common representation via an adaptive weight matrix. In the common emhedding space, the common representations contain consistent
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View speciiiic Represenlation
View
Encoder
Unbiased Refinement for Biased Representation
Decoder
Reconstructed V Vie
FOOO
Shill-oorreian
Common Representation
C Consensus R Eppresentatoon
Dual Contrastive e Learning
Maximizing Mutual Information Coustraint
Rahustt Contrast
7:: Unblased
2": Biased
H(X)
1(X. V)
H(Y)
Representaiion Representation
Tellerviin VieW Contrest
View-specitic Representation
Reconstructed V View
View
Encader
Decader
GOOD
2"W,
BOOO
Ane'a
R
Figure 1: The architecture of proposed DDR-IMVC framework. (a) Independent autoencoders are employed for each view to extract deep features. (b) The deep features are adaptively projected in consensus embedding space to bridge the semantic gaps across views. (c) An attention-based
refinement strategy is employed to optimize the biased representations introduced by the incomplete
sample. (d) A denoised consensus representation contrastive strategy is adopted to alleviate the risk of clustering collapse.
and complementary information. Multi-view complementary information can enhance cluster sep- arability (Zhang et al. 2024b] Dai et al.) 2025). Since variance reflects sample deviation from the mean along a certain dimension, with well-separated clusters exhibiting high value (Xu al. 2023). we leverage the variance to assess the separability of clusters and compute an adaptive weight matrix NVV that preserves the clustering information of views with well-defined cluster structures:
Var (
W
ΣV=1 M Var(Zg)
where W,, denotes the weight the i-th sample in the v-th view. Var(.) represents the variance operator. The mask Ma allows the weight matrix adapt missing data. Z [Z]; Z&J denotes representations of the complete samples and incomplete samples in the v-th view. Based on the weight matrix W, the samples are mapped the view-shared common embeddings E Nxd
2;
W i
(5)
where E Z denotes the common representation of the i-th sample from all views.
The view-missing issue can cause distribution shifts the common representation To be specific, the distribution of the common representation fused from the complete views is different from that fused by incomplete views. Thus, we divide the common representation Z into unbiased represen- tation z and biased representation Z The unbiased representations are defined as the common representations of samples with complete views, while the biased representations correspond to samples with missing views:
z z =[[ II M., 1}:
(6)
V
z = z({
M, = 0}::]
(7)

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Published as a conference paper at ICLR 2026
The distribution shift will reduce clustering separability.. To address this problem, innovatively propose an attention-base complementarity refinement. The core idea is to compute the similarity between the biased representations z and unbiased representations z sample affinity attention weights A. Then, it extracts the unbiased representations most compatible with the representation with missing views correct the distribution shifts. Specifically, we first leverage multi-head attention network to compute the corresponding aflinity attention weights as follows:
Z'!!! (1)
A (1) Softmax
,1 11 L
Vd/L
where L denotes the number of attention heads, wilh and w denote learnable parameters of the 1-th head, d denotes the dimension of the common representations Z. Based on the affinity attention weights, the unbiased representations can be used to correct the distribution shifts present in the biased representation, and we can obtain the corrected biased representation B (3) of the 1-th head as follows:
n (1) (Z"Wl )
( denotes learnable parameters. Finally, the results from all attention heads are concate- R nated to obtain the corrective biased representation B in the common embedding space:
where
B [B(), ...., (()),
(10)
Then we incorporate corrective representation B into the biased representations to obtain shift- corrected consensus representations S E R xd.
= Z": Z31 +
(1I)
where 0 denotes all-zero matrix with the same dimensions as Z Obviously, the effectiveness of correcting the distribution shifts caused by missing views lies in the quality of the common repre- sentations, and learning accurate common representations from different views requires exploiting the correlation between the view-specific representations and the common representation. A natural idea to maximize the mutual information (Lin al. 202T) between unbiased common representa- tions and view-specific representations to enforce that the unbiased common representations retain as much consensus information. Specifically, we regard the unbiased representations as the anchor of the representations of each view, and sequentially introduce a maximizing mutual information constraint between the anchor and a specific view with the following loss function:
LMMI Σ (I(Se: Z a (H()c) + HZ))
(12)
where Se denotes the shift-corrected consensus projections S corresponding to the sample with complete views. a serves as the entropy regularization coefficient, I I(-) denotes mutual information, and (-)) denotes information entropy, which can be computed as follows:
(1(x= = Σ p(z) log p(x),
(13)
p(a,y)
(x: p(a, v) log
(14)
p(z)p(y)
where p(z) denotes the probability distribution of the random variable X, and p(x, y) denotes the joint distribution of the random variables X and Y.
Since the consensus representations capture both the inherent information of the incomplete-vis samples and the clustering information of its affiliated complete- view samples, restoring embed- ding with consensus representations can effectively ensure the integrity of the sample structure and the consistency of the distribution. Therefore, we complete the missing-view representations from consensus representations by:
(15) where denotes the dlement-wise multiplication. S denotes the representations after completion in the w-th view. We take the v-th column of matrix M E NXV as m" E Nx that indicates the missing samples in the w-th view and expand it into M N by replicating m" d times. Finally, we fuse the completed representations S" into via the weight matrix that constructed by leveraging the variance of the representation from each view.
="= + (1- M') (1-MM)) OS
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3.4 DUAL CONTRASTIVE LEARNING FOR DENOISED REPRESENTATION
3.4.1 INTER-VIEW CONTRASTIVE LEARNING
To overcome the heterogeneity in incomplete multi-view learning, we construct positive pairs from the same instance across views and negative pairs from different instances. Contrastive learning maximizes the positive-pair correlation while minimizing that of negative pairs. The contrastive learning loss across all views is:
V ΣΣΣ
N log
exp (sim (s), (/)ss))11)
L.
(16)
Lزz exp (sim (sh, /T)
where s and st denote the representations from v-th view and k-th view. sim(-) is cosine similarity. T represents the temperature coefficient.
3.4.2 ROBUST CONTRASTIVE LEARNING
To prevent cluster collapse after completing missing views with consensus representations, it is nec- essary to impose constraints between the consensus representations and the recovered representa- tions. A conventional approach is to apply contrastive learning between them. Although consensus representations capture the consistency of the data distribution, the completion process inevitably introduces potential noise. Conventional contrastive learning's strong focus on hard samples can exacerbate noise-induced overfitting. Inspired by Yuan et al. (2024), we employ a denoised con- trastive learning between consensus representation S and each view representation S to enhance the robustness of consensus representations against noise.
Set 85) = exp(sim(s,.8)))1 -n-1 exp(sim(e,....) and thus Σ (s;, 1. For the general form of InfoNCE, its power series expansion over the interval [0, 1] is:
exp (sim(si, s/)/T)
Linta =
log En=1 exp (sim(s:,
N
=1
1
(s., 8;)) (1- f(s s)
+... (1 (1- ((s,,
+...
c
N
1 H 2f,s, (()) + (1 f(s,, s²))
+... (1 f(s s7 +...
(17)
c
(1- s()
(1- (-=((sn)))) +...
ll
f1111 +
1
V
N
(1 - f(s
2N ΣΣ
le.
flll
N
c=2
where denotes the one-hot encoding whose i-th element is I; f, is a vector whose j-th element is (ss,,")) can be seen that, after expanding InfoNCE into an infinite series, the first term exactly the Mean Absolute Error (MAF) loss, which is proven to be robust to noise (Ghosh et al. 2015) 2017]. However, MAE loss treats each sample equally. The infinite terms can provide diffcrentiated attention to samples but are sensitive to noise. Therefore, we construct robust contrastive loss by truncating part of the infinite series to maintain a balance between MAE loss and InfoNCE loss, which is adjusted by truncation coefficient C. Specifically, take the first C terms of the infinite series and obtain the robust contrastive loss as follows:
1 1=12 ΣL (1 (1.(ssss s(s.
C
(18)
Its significance lies in that it transforms the unbounded amplification of log fs, s()) for hard sam- plcs into a bounded approximation, balancing positive sample discrimination and noise suppression. Adjusting the truncation coefficient C allows tuning between cluster collapse and noise robustness.

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Published as a conference paper at ICLR 2026
Algorithm DDP for Incomplete Multi-view Clustering
1: Input: Incomplete multi-view dataset X' (X") for all N samples, Training epoch E, Hyper-parameter λι λ2, a, and C.
2: Construct the complete view indicator matrix M RN
3: while Not reaching epochs E' do
4: Calculate the embedding representation (z)}² by Eq.(I).
5:
Calculate the common representations Z by Eq.(5).
6:
Correct the shifts to obtain consensus representations S by (q.(.
7:
Impute the each view embeddings S by (15()
8:
Compute the clustering-friende representation S' with the imputed embeddings.
9:
Optimize the total loss function Loll by Eq.(20).
10:
end while
Perform k-means clustering algorithm on S'.
12: Output: K clusters for N samples.
Finally, the dual contrastive loss is:
LDL Lo bre
(19)
3.5 THE OBJECTIVE FUNCTION
Overall, the total loss function of our method consists of three parts is formulated as:
fall LREC + Xı LMMi A2C
(20)
a and '2 are trade-off parameters. LREC is the autoencoder reconstruction loss. LMMI is the max- imum mutual information loss, used to enhance the common cluster information. LDCL is the dual contrastive loss that mitigates heterogeneity in incomplete multi-view learning and prevents cluster collapse. Finally, K-means is performed on S' E R NgNx xd to obtain K clusters.
4 EXPERIMENTS
4.1
DATASETS
We conducted experiments on four representative datasets. The datasets are: Haidtritten (LeCun ct al. 1989) comprises 2,100 samples belonging to 10 categories corresponding to digits from 0 to We employ three distinct features Pixel, Fourier and Profile for analysis. Scene-15 (Fei-Fei & Perona 2005 consists of 15 categories with a total of 4,485 samples. GIST, PHOG, and LBP are selected as three views in our experiments. ALOI-100 (Geusebroek et al. (005) contains 10,800 object images belonging to 100 categories. We extract HSB. RGB, Colorsim, and Haralick features to construct multi-view data. LandUse-21 (Yang & Newsam 2010) comprises 2,100 samples be- longing 21 categories corresponding to different land-use scene categories. GIST, PHOG, and LBP are used for analysis. To evaluate the performance our approach, we employ three standard metrics: Accuracy (ACC), Normalized Mutual Information (NMI), and Adjusted Rand Index (ART).
4.2 COMPARE METHOD
DDR-IMVC is compared with nine SOTA methods. Fusion-kmeans clusters the mean-fused fea- tures with k-means. Completer (Lin al. 202I) predicts missing views by minimizing conditional
entropy. DIMVC (Xu et al.) 2022aa) proposes no-imputation framework that maps data to reveal linear separability. DSIMVC (Tang Liu 2022) completes views by dynamically mining semantic features of neighbors. DCP (Lin et al. (022h learns consistent representations via dual contrastive learning under the information-theoree ing prototypes with dual attention layers. APADC (Xu et al. 2023) achieves imputation-free strat- egy through adaptive projection and distribution alignment. ICMV CChoo et al. (024) completes missing views with GCNs and aligns distributions through high confidence guidance. GHICMC (Chao et al. 2025) employs cascaded GCNs to enable global graph propagation and hierarchical information transfer.
framework. ProImp (Li et al. (023) recovers data by learn-

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Table 1: Clustering results of all methods on four datasets. The best and second-best results are highlighted with bold and underline, respectively.
Misssng.rates
0.3
0.7
Metrics
ACC
NMI
ART
ACC
NMT
ARI
ACC
NMI
ARI
ACC:
NMI
ART
Fusion-kmeans
20.45
25.42
8.62
16.41
17.48
5.51
12.86
12.58
2.77
11.45
9.81
1.38
(0mpleter(2021)
26.40
32.48
13.93
26.96
32.64
12.09
21.36
26.27
9.34
24.43
29.01
10.31
DIMVC(2022)
24.63
30.04
10.58
23.69
29.94
10.01
22.40
27.78
9.38
21.77
26.14
7.91
LandUse-21
DSIMVC12022)
18.47
19.34
5.58
18.47
5.16
18.13
5.26
17.97
5.11
DCP(2023)
26.78
30.87
13.80
27.08
30.69
13.80
23.07
27.00
11.31
25.18
28.04
12.00
Prulmp(202.3)
22.38
23.79
8.76
19.53
20.55
6,86
20.30
21.94
7.32
15.10
15.48
4.00
APADC(2023)
22.75
31.90
9.50
18.08
24.72
7.22
15.67
21.23
5.61
15.11
20.08
4.84
ICMVC(2024)
28.18
15.14
29.39
25.98
11.92
24.95
GHICMC(2025)
26.86
31.14
12.81
25.72
29.26
11.32
25.15
28.57
11.26
23.53
26.55
9.72
Ours
28.21
34.68
14.93
28.02
33.49
14.27
27.14
31.89
13.24
25.36
28.09
10.67
Fusion-kmeuns
34.20
34.84
20.93
22.39
23,60
12.80
17.54
17.31
7.88
14.90
13.54
4.29
C0mpleter(2021)
40.28
42.50
23.13
40.12
42.93
23.96
39.12
41.79
22.98
38.05
40.22
21.84
DIMVC(2022)
32.95
27.41
15.61
33.51
29.42
16.75
30.65
25.21
13.64
29.58
24.11
12.85
Scene-15
DSIMVC/2022)
27.65
29.74
14.11
26.73
29.36
13.94
26.40
28.03
13.04
25.31
27.04
12.43
DCP(2023)
38.54
42.39
23.33
40.49
43.10
24.14
39.50
42.35
23.51
38.55
40.57
21.72
Prolmp(2023)
40.74
42.14
24.00
41.69
43.03
25.28
40.28
41.80
23.89
39.96
40.35
22.92
APADC(2023)
43.70
44.20
26.00
43.10
24.30
39,90
23.80
38.50
41.10
22.80
ICMVC(2024)
38,78
36.62
21.84
37.40
34.94
20.60
31.35
27.91
14.98
25.31
23.88
11.33
GHICMC(2025)
41.26
43.21
24.95
40.98
43.13
25.05
40.91
42.29
24.64
38.79
40.94
22.92
Ours
46,16
47.62
28.69
45.53
45,99
28.05
44.35
43.67
26.79
42.12
41.20
24.73
Yusion-kmeans
41.70
47.59
34.22
36.28
38.76
28.51
11.54
25.69
22.14
200pleter(2021)
83.22
82.47
73.59
75.38
77.55
61.69
74.05
76.13
29.89
78.55
76.07
68.67
HandWritten
DIMVC(2022)
67.13
63.17
53.16
59.43
56.49
43.19
54.80
50.50
30.76
43.82
41.54
23.80
DSIMVC(2022)
84.35
80.32
74.38
85.64
80.71
75.94
84.73
78.82
74.13
82.71
75.35
69.85
DCP(2023)
53.35
65.72
35.60
51.96
63.88
31.49
59.06
65.07
36.51
60.97
60.53
29.90
Prolmp(2023)
83.20
80.29
74.17
84.24
77.75
72.60
78.16
70.79
63.96
68.85
62.92
APADC(2023)
67,43
65.34
47.18
68.95
67.28
45 98
68.85
68.61
56.43
61.77
61.97
48.26
(CMVC(2024)
83.16
81.33
74.78
82.01
79.62
72.22
75.13
71.99
63.19
72.47
70.01
59.71
GHICMC(2025)
96.19
92.14
92.89
96.11
91.32
90.83
94.88
89.16
89.10
92.73
85.85
84.71
Ours
96.38
92.23
91.99
96.15
91.49
91.21
94. 34
88.38
87.87
90.86
82.65
81.92
Fusion- kmeans
Fusion-kmeans
52.37
72.31
40.79
30.63
55.28
16.10
22.48
47.33
7.46
17.39
41.82
4,94
Completer(2021
48.19
77.96
44.25
43.03
72.43
36.73
36.16
66.89
26.52
34.55
64.06
24.97
DIMVC(2022)
71.86
84.99
61.79
68.52
82.15
58.31
64.80
78.53
51.36
61.64
75.33
47.25
ALOI-100
DSIMVC(20222)
38.76
29.71
66.00
39.32
28.53
61.28
25.16
DCP(2023)
51.85
74.88
42.73
47.38
70.55
38.38
42.37
66.30
32.36
36.02
60.75
25.40
Prolmp(2023)
68.39
83.47
62.08
45 98.98
73.01
38.53
32.71
65.74
24.76
29.23
62.08
19.46
APADC(2023)
47.40
68.92
35.02
38.95
62.27
26.10
32.78
58.16
20.10
26.02
53.91
14.11
ICMVC(2024)
68.02
56.64
68.14
80.40
67.68
53.92
70.50
GHICMC(2025)
0OM
0OM
OOM
0OM
Ours
76.02
88.35
67.82
73.18
85.82
64.36
69.87
82,34
58.09
66.94
78.60
53.20
Table 2: Ablation study results on LandUse21 and Scene- 15 datasets with missing rate 0.3.
Datasets
LandUse21
Scene- 15
LRFC LMMI Froul ACC
NMI
ARI
ACC
NMI
ARI
17.54
22.97
6.08
36.06
43.69
21.88
24.16
26.09
11.06
41.96
40.00
25.94
16.78
17.96
5.63
21.53
21.61
11.48
/
28.02
33.49
14.27
45.53
45.99
28.05
4.3 EXPERIMENTAL SETTINGS
We adopt Adam to optimize our framework DDR-IMVC and all the experiments are conducted in PyTorch 1.13.1 Windows with an NVIDIA 4070 SUPER GPU. The dimensions of encoders D.--102--124-1024--22 The decoder is symmetric to its corresponding encoder. The number of heads L in multi-head attention is set The entropy regularization coefficient is set to 10, and the truncation coefficient C' is set to 9.
4.4 INCOMPLETE MULTI- VIEW CLUSTERING PERFORMANCE
Table reports the incomplete multi-view clustering results of all methods under different missing rates. It shows that DDR-IMVC effectively handle high missing rates and large-scale issues in
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Published as a conference paper at ICLR 2026
ARI
20
6.1
As
ozea
oren
0.001
0.001
0.0001
(a) ACC
(b) NMI
(c) ARI
Figure Parameter sensitivity analysis on Scene-15 with the missing rate 0.3.
3 0.6
0.00
Motrics
0.4
210
100
100 1007
250
400
603
000
110
200
453
200
1007
Epoch
Epech
Epoch
Epoch
(a) LandUse-21
(b) Scene-15
(c) HandWritten
(d) ALOI-100
Figure 3: The convergence analysis all datasets with the missing 0.3.
Fusion kmeans
Completer
DIMVC
DSIMVC
DCP
ProImp
APADC
ICMVC
GHICMC
Ours
Figure 4: The visualization results of HandWritten dataset in all methods with missing rate of 0.5.
IMVC. From the perspective of effectiveness, our method significantly outperforms SOTA methods across four datasets. For example, the Scene-15 15 dataset, ACC, NMI, and ARI outperform the second-best method, APADC, by average of 3.56%, 1.92%, and 2.86%, respectively. We notice that when the missing rate is 0.5 or 0.7, DDDRIMVC performs slightly worse than GHICMC. We attribute this to the simplicity of the HandWritten dataset, where inter-class features singular. Under high missing rates, it is suitable use cascade graphs for data recovery. For other com- plex datasets, GHICMC shows significant performance drop. More critically, its high memory consumption prevents it from handling large-scale datasets. From the perspective robustness, DDR-IMVC can still maintain high level of performance under high missing rate. Moreover, unlike some methods whose performance drops sharply, DDR-IMVC remains stable even as the missing rate increases.
4.5 MODEL DISCUSSION
1) Ablation Study: To investigate the importance of each component, conducted ablation study on our DDR-IMVC framework using LandUse21 and Scene-15 datasets under a missing rate of 0.3. As shown in Table removing the attention correction mechanism for the learned consensus

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Published as a conference paper at ICLR 2026
140
6
-9
C-30
-15
0.9
f(s,,
(a)
(b)
Figure 5: The variation trend of the loss and its gradient.
representations (CMM)) or the robust contrastive learning (CDcL) leads to suboptimal performance. When all strategies are applied together, achieve the best results. The experimental findings demonstrate that the attention correction mechanism can refine the distribution of biased represen- tations, while the robust contrastive learning enhances the consistency of consensus representations and alleviates the risk of cluster collapse.
2) Parameter Analysis: Our objective loss mainly involves two trade-off parameters, A1 and X2. To verify their effectiveness, we conducted parameter analysis by setting both parameters in the range from 10-4 10. As shown in Figure excessively high low parameter values are unfavorable for clustering. Based on our parameter experiments, we recommend setting the parameter range between and 10.
3) Convergence Analysis: Meanwhile, to better verify the convergence and robustness of our model, we observed the convergence performance of all datasets under 0.3 missing rate. shown in the Figure 3 the total loss function involved in our training achieved excellent convergence. With the increase in training epochs, various metrics for evaluating clustering also tended to converge.
4) Visualization Analysis: As shown in Figure 4 with missing rate of 0.5, we visualized the distribution of common embedding all methods on the HandWritten dataset using t-SNE. Through the correction of the distribution shift of missing samples during the imputation process by DDR- IMVC, our method facilitated to discover the common clustering patterns of all views in the common embedding space.
5) Discussion of Robust Contrastive Loss: In Figure 5 we plot the InfoNCE loss and the loss function in Equation (18), as well as their gradients. As described in Section 4.5, the single-sample The function Equation (18)
InfoNCE function is Linfo - log f, with gradient 01
0Linfo
>E (1- When C = 1, the gradient of Equation (18) is 1,, indicating that treats all samples equally, equivalent to MAE. When C - oo, it degenerates to InfoNCE, giving excessively high attention to noisy samples. Our loss gradient is smaller than MAE, which indicates that our loss can assign different attention levels to different samples, improving training efficiency. is larger than InfoNCE and has upper bound, indicating that our loss prioritizes clean samples, thereby mitigating the issue of excessive attention to noisy samples and enhancing robustness.
C, = -E (1-1"_, with gradient off
CONCLUSION
In this work, we propose consensus representation refinement strategy for IMVC to address data shift and misalignment noise introduced by missing views. An adaptive representation fusion con- structs a common space. Within this space, unbiased representations correct the distribution of biased representations through an attention mechanism to form robust consensus representations. In addition, employ a denoising contrastive strategy to prevent cluster collapse that may occur when completing missing views in the consensus representations. The effective combination of these two strategies enables DDR-IMV to achieve superior performance across several IMVC tasks.
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6 ACKNOWLEDGMENTS
This work is supported by the National Natural Science Foundation of China under Grant 62176203, the Fundamental Research Funds for the Central Universities (ZYTS25267, QTZX25004), and the Science and Technology Project of Xi'an (Grant 2022JH-ISYF--000), Open Project of An- hui Provincial Key Laboratory of Multimodal Cognitive Computation, Anhui University (No. MMC202416), Selected Support Project for Scientific and Technological Activities of Returned Overseas Chinese Scholars in Shaanxi Province 2023-02.
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13


Reviews:
[{"review_id": "vBlDyD6i7O", "reviewer": "Reviewer_HWFR", "summary": "This paper addresses distribution shift in incomplete multi-view clustering caused by missing data. To mitigate cross-view semantic gaps, it optimizes projections into a shared embedding space from an information-theoretic perspective. The method leverages an unbiased projection together with an attention-based refinement strategy to build a robust consensus embedding, thereby alleviating heterogeneity and inconsistency issues commonly encountered in incomplete multi-view clustering.", "questions": "1. Dealing with data distribution drift is interesting in incomplete multi-view clustering, but how to prove the proposed method to handle the distribution drift better than the previous competitors?\n2. Abstract claim that \"Consensus representation imputation methods ignore the interview distribution bias due to missing views\", what is the interview distribution bias? This concept may require more detailed visualizations to help understanding.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "(1) Dealing with data distribution drift is interesting and valuable in incomplete multi-view clustering caused by missing data.\n(2) The paper proposes the novel idea of utilizing representations from complete views to refine those from missing views, guided by correlations between complete-view samples and missing-view samples.\n(3) The manuscript is clearly written and well organized, providing strong motivation, detailed methodology, and thorough analysis.\n(4) Experimental results across multiple datasets demonstrate strong performance.", "weaknesses": "1.\tSection 2.2 lacks sufficient coverage of recent incomplete multi-view clustering works, particularly those based on missing-view imputation.\n2.\tThe framework illustration (Figure 1) is relatively simple and does not fully reflect key methodological details.\n3.\tOne core contribution is using unbiased projections to correct biased ones; however, a more detailed explanation of its motivation and effectiveness is still expected.", "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": "RBsOtj0oUm", "reviewer": "Reviewer_qR7X", "summary": "The paper proposes a novel incomplete multi-view clustering framework. An adaptive projection matrix is constructed to integrate complementary information across views. Then, through an attention-based strategy, the framework utilizes unbiased projection to correct the distribution shift of biased projections, thereby obtaining a bias-corrected consensus projection. By maximizing the mutual information, it enhances cross-view semantic correlations. Finally, an innovative denoising contrastive learning strategy is introduced to alleviate the risk of clustering collapse caused by multi-view heterogeneity and misaligned noise.", "questions": "1.Can the model converge stably? It is recommended that the authors add convergence analysis experiments to demonstrate the stability and convergence of the proposed algorithm.\n\n2.What are the selection principles for the hyperparameters $\\alpha$ and $C$ in this paper? Please provide a detailed explanation.\n\n3.Please provide an explanation for the issue mentioned in weakness 3.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.This paper proposes a novel framework named PDD based on debiasing and denoising projection learning. By combining attention mechanisms with contrastive learning, it effectively addresses distribution shifts and clustering collapse caused by missing views in incomplete multi-view clustering.\n\n2.It introduces a denoising contrastive loss based on truncated power series approximation, which transforms the unbounded amplification of hard samples in the InfoNCE loss into a bounded constraint, balancing positive sample discriminability and noise suppression.", "weaknesses": "1. There lacks a convergence analysis.\n2. In addition to \\lambda_{1} and \\lambda_{2}, there are also hyperparameters $\\alpha$ and $C$, for which the authors do not provide detailed explanations regarding the principles behind their selection.\n3. This paper proposes a projection matrix based on prior separability, using variance to measure the projection weights of each view. More expanations should be provided on whether this could lead to imbalanced projections across views.", "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": "upr96Z4SEF", "reviewer": "Reviewer_knnk", "summary": "This paper introduces PDD (Projection Debiasing and Denoising), a framework for Incomplete Multi-View Clustering (IMVC). The framework addresses challenges such as distribution shifts caused by missing views and cluster collapse due to misalignment noise. By employing unbiased projection refinement and denoised contrastive learning, PDD achieves SOTA performance on multiple datasets under varying missing rates.", "questions": "(1) Is the proposed model suitable for large-scale datasets?\n(2) Does the proposed model perform stably across all missing rates?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.The use of unbiased projection refinement corrects distribution shifts in biased projections, enhancing consensus embeddings.\n2. The framework is robust under varying missing-view rates (10%–70%), outperforming nine strong baselines.", "weaknesses": "(1) It is not straightforward to learn the denoising effect of denoising contrastive loss, which should be explained.  \n(2) It is not clear why the model imputes the missing views in both the representation space and sample space.", "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)