Uncover Underlying Correspondence for Robust Multi-view Clustering
Authors: Haochen Zhou
Guofeng Ding
Mouxing Yang
Peng Hu
Yijie Lin
Xi Peng
Venue: ICLR 2026 Oral (2026)
Keywords: Multi-view clustering; Noisy Correspondence
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Abstract: Multi-view clustering (MVC) aims to group unlabeled data into semantically meaningful clusters by leveraging cross-view consistency. 
However, real-world datasets collected from the web often suffer from noisy correspondence (NC), which breaks the consistency prior and results in unreliable alignments.
In this paper, we identify two critical forms of NC that particularly harm clustering: i) category-level mismatch, where semantically consistent samples from the same class are mistakenly treated as negatives; and ii) sample-level mismatch, where collected cross-view pairs are misaligned and some samples may even lack any valid counterpart.
To address these challenges, we propose \textbf{CorreGen}, a generative framework that formulates noisy correspondence learning in MVC as maximum likelihood estimation over underlying cross-view correspondences. 
The objective is elegantly solved via an Expectation–Maximization algorithm: in the E-step, soft correspondence distributions are inferred across views, capturing class-level relations while adaptively down-weighting noisy or unalignable samples through GMM-guided marginals; in the M-step, the embedding network is updated to maximize the expected log-likelihood. Extensive experiments on both synthetic and real-world noisy datasets demonstrate that our method significantly improves clustering robustness. The code is available at [https://github.com/XLearning-SCU/2026-ICLR-CorreGen](https://github.com/XLearning-SCU/2026-ICLR-CorreGen).

UNCOVER UNDERLYING CORRESPONDENCE FOR ROBUST VIEW CLUSTERING
Haochen Zhou' Guofeng Ding' Mouxing Yang'
Peng Hu'
Yijie Lin
Xi Peng
College of Computer Science, Sichuan University, China.' National Key Laboratory of Fundamental Algorithms and Models for Engineering Numerical Simulation, Sichuan University, China.?
(haochenzhou.xl, guofengding haa.eediinnggg...mmnoooooo yangmouxing, penghu.ml, linyijie.gm, pengx.gm| @ @gmail.com
ABSTRACT
Multi-view clustering (MVC) aims to group unlabeled data into semantically meaningful clusters by leveraging cross-view consistency. However, real-world datasets collected from the web often suffer from noisy correspondence (NC), which breaks the consistency prior and results in unreliable alignments. this paper, identify two critical forms of NC that particularly harm clus- tering: i) category-level mismatch, where semantically consistent samples from the same class are mistakenly treated negatives; and ii) sample-level mis- match, where collected cross-view pairs are misaligned and some samples may even lack any valid counterpart. To address these challenges, propose Cor- reGen, generative framework that formulates noisy correspondence learning in MVC maximum likelihood estimation over underlying cross-view corre- spondences. The objective is elegantly solved via an Expectation MisitiinnnMaiizztatiionn algorithm: in the E-step, soft correspondence distributions are inferred across views, capturing class-level relations while adaptively down-weighting noisy or unalignable samples through GMM-guided marginals; the M-step, the embed- ding network is updated to maximize the expected log-likelihood. Extensive ex- periments on both synthetic and real-world noisy datasets demonstrate that our method significantly improves clustering robustness. The code is available at wwt.:/..........caa..eee.e.eeea
INTRODUCTION
Describing the same object from multiple perspectives (Yan et al. 2021 or modalities (Sharma al., 2018), multi-view data have become increasingly prevalent real-world applications. To exploit such data, contrastive multi-view clustering (MVC) has emerged as powerful unsupervised paradigm (Qin et al., 2025b Wang et al. 2025a).. Relying on the consistency prior that views from the same instance should be semantically aligned, contrastive MVC pulls positive pairs (i.., views of the same instance) closer while pushing negative pairs (i.e., views from different instances) apart in the embedding space. Through this process, could learn shared embedding space across views and group unlabeled samples into semantically meaningful clusters.
However, this prior is often difficult to satisfy. In practice, multi- view datasets are commonly structed by crawling paired data from the web, such as images with their associated alt text (Wang et al. 2015). This automatic process inevitably introduces the noisy correspondence (NC) prob- lem (Huang et al.) 2021), where cross-view pairs are incorrectly matched. Such noise undermines the cross-view consistency prior and severely distorts the semantic structure of the learned embed- ding space.
In this paper, we identify two major types of NC that are particularly harmful clustering: i) Category-level mismatch, where views from different modalities but belonging to the same class are mistakenly treated as negatives by contrastive MVC methods, despite their underlying semantic consistency; ii) Sample-level mismatch, which manifests in two scenarios: alignable mispairs, where
"Corresponding author.

---

A ripe red apple hanging branch.
Small rol-green apples hanging Iree.
A pet sitting inside on the green
bird 166 the gro brigh ür asp-!
1
L
(8) Painwise Reweighting
Painwise Realigmment
(c) Concependeoe Genention (Ours)
Figure 1: (Top) Examples of multi-view data, including noisy pairs L,-T,, (Bottom) Illustration of three paradigms for handling noisy correspondence, where green edges denote discovered corre- spondences and red edges indicate potential but undiscovered ones. (a) Pairwise reweighting, which applies robust contrastive losses to down-weight potentially noisy pairs during training but retains the original correspondences unchanged; (b) Pairwise realignment, which reassigns each sample to a more plausible cross-view counterpart; (c) Correspondence generation (Ours), which directly uncovers latent correspondences and filters out noise.
a sample is wrongly paired with a mismatched view despite having a correct counterpart elsewhere; and unalignable samples, where no valid counterpart exists due to corruption, noise, or poor data quality, Such issues are especially prevalent in web-collected data, where the pairwise noise ratio can exceed 20% (Sharma et al. 2018 Wang et al. 2015). Critically, manually verifying or cleaning these correspondences is prohibitively expensive, underscoring the need for robust multi-view clustering methods. To address NC, recent works (Qu et al. 2025) mainly adopt either pairwise reweighting or realignment strategies, as illustrated in Fig. However, both approaches overlook category-level semantics and unalignable samples, leading to suboptimal results in clustering.
Recognizing these limitations, we shift from the existing discriminative contrastive objective to generative one. Specifically, we formulate noisy correspondence learning in MVC as a maximum likelihood estimation objective of the underlying joint distribution, in which the counterparts across views are modeled as unobserved latent variables. Unlike previous methods (Wang et al. 20256 Qin et al. 2025a) that focus verifying whether given positive negative pairs correctly aligned, our formulation uncovers the underlying correspondences without heavily relying on pre- defined (potentially noisy) pairs. By maximizing the overall loeliike,,,od, capture the semantic structure in principled and probabilistic manner.
To effectively optimize the proposed objective, we develop an Expectation -aximmizaonniiiiiiiiiiinn (EM) based algorithm CorreGen. In the E-step, the goal is to infer a latent correspondence distribu- tion across views. We first estimate the marginal likelihood of each sample by fitting a Gaussian Mixture Model in the embedding space. Intuitively, this estimation assigns higher probabilities to samples that lie in large and coherent clusters, while noisy or unalignable samples receive lower probabilities. These marginals serve as constraints solve optimal transport formulation, yield- ing a soft many-to-many assignment that captures category-level relationships across views. In M-step, the estimated correspondences the embedding network such that semantically consistent pairs are assigned higher likelihoods. Iter- ating between the two steps gradually uncovers reliable correspondences and refines robust cluster representations. In summary, the contribution of our work can be summarized as follows:
used to maximize the expected likeliiei,oood, updating
We identify and formalize two types of noisy correspondence in MVC: category-level mismatch and sample-level mismatch, where both are prevalent in real-world multi-view datasets and harmful to clustering.
We propose CorreGen, a novel generative framework that models latent cross-vies view cor- respondences through maximum likelihood estimation, solved elegantly via EM algo- rithm. Furthermore, we prove that the standard InfoNCE a special case of our formulation under specific assumptions.
2

---

We introduce principled E-step solution that jointly models category-level correspon- dences and suppresses sample-level noise by leveraging GMM-guided marginals. Exten- sive experiments on both synthetic and real-world noisy datasets validate the effectiveness our approach. Notably, our method achieves 10% accuracy improvements on the chal- lenging UMPC-Food101 dataset (Wang al. 2015).
RELATED WORK
Robust Multi-view Clustering aims to handle imperfections that commonly occur in real-world datasets. These imperfections can be broadly categorized into two types: Incomplete Multi-view Problem (IMP) arises when some views are missing, resulting in incomplete cross-view informa- tion. To mitigate this issue, recent methods adopt various completion- based strategies such as an- chor learning (Liu et al. 2024). subspace learning (Zhang et al. [024), or diffusion models (Zhang jet al., 2025). These approaches aim to impute the missing views and recover complete multi-view representations; ii) Partially view-aligned Problem (PVP) occurs when the correspondences across views are misaligned. For example, in multi-camera surveillance, images of the same person from different cameras may be temporally asynchronous (Huang al. 2020). To address this, He et al. (2024) introduce a variational contrastive learning framework to realign unpaired data, while Yan al. 2025) design multi-stage strategy that iteratively updates cross-view correspondences for unpaired data.
Although both PVP and NC address erroneous cross-view correspondences, the NC problem stud- ied in this paper differs in two significant aspects. First, misalignments in NC are unobserved, with manually verified labels or alignment indicators available (Lee al., 2018). Second, NC encompasses not only instance-level mismatches, but also category-level misalignments and even unalignable samples that lack valid counterparts across views.
Noisy Correspondence Learning was first introduced in cross-modal retrieval (Huang et al. 2021) where mismatched image-text pairs are mistakenly treated as true positives. Recently, this problem has garnered increasing attention across a range of domains, including video reasoning (Lin et al.) 2024], graph matching (Lin et al. 2023), person re-identification (Yang al., 2022a) and multi- view clustering (Sun et al. 2024 2025). Existing solutions can be broadly categorized into two groups: i) Reweighting-
methods (Yang et al. 2024) aim to reduce the impact of mismatched pairs by assigning them lower weights during training. For example, Huang al. (2021) adjust the margins in triplet contrastive loss to account for false positives; ii) Realignment- based methods (Lin) plausible counterpart across views, thereby
et al. 2024 attempt to reassign each sample mitigating alignment errors.
Although existing methods achieve promising results, they mainly refine given positive pairs while overlooking potential category-level correspondences, leading to suboptimal clustering per- formance. Different from these discriminative approaches, we propose generative objective for noisy correspondence learning in MVC, which assigns higher likelihoods to semantically consistent samples and uncovers latent correspondences. Notably, our optimization does not rely heavily on off-the-shelf pairs, thereby mitigating the noisy correspondence problem from new perspective.
3 METHOD
In this section, we first introduce the problem setting and formalize correspondence learning in multi-view clustering (MVC) as a generative maximum likelihood estimation problem in Sec. 3.1 To optimize this objective, we propose CorreGen, an EM-based framework Sec. 3.2 and detail its two steps in Sec. 3.2.1 and Sec. 3.2.2
3.1 PROBLEM DEFINITION
with N instances observed from V views, the Given a multi-view dataset ((.,))...., 1
...... goal of MVC is to learn an encoder fo that maps each view x; (e) into a shared embedding space, (v)
ie., 2 (o)) Ideally, the distribution of these embeddings should form C well-separated
3

---

semantic clusters, such that traditional clustering algorithms (e.g., K-means McQueen 1967) ) can easily distinguish them.
To achieve this goal, recent contrastive MVC methods (Yang al. 2023 pull positive pairs (i.e., views of the same instance) closer while pushing negative pairs (I.e., views from different instances) apart in the embedding space. Formally, for any pair of views (v1; 02) with in # U2, the positive and negative sets are defined as
N
P P01.22
(01) (xg
(02) 12 1)}, 2
P P1102
U i=1 i=1j=1,j7
12 { (xx (0)) 2j .ij =)),
(I)
(22) belong to the same where 6) E {0, 1 is an indicator variable that equals 1 if x; (v5) and 2;
instance, and otherwise. Nevertheless, contrastive MVC essentially formulates an instance-level discriminative task et al. (018)), which overlooks the intrinsic cluster structure of data. As re- sult, real-worke multi-view datasets are particularly vulnerable to the noisy correspondence problem, where the assumed cross-view alignment fails to hold. For clarity, we formalize its two manifesta- tions, namely category-level mismatch and sample-level mismatch, as defined below.
Definition (Category-level mismatch). Consider a cross-view pair (xx _x(")), (1))), where Lij 10,1} denotes whether the pair treated as positive or negative. Let (01) and of be the oracle class labels of (()) and xx 2/)"), respectively. A category-leve mismatch occurs if
( if((")) = cj d(oz) but
$13 0, i.e., samples from the same semantic class are incorrectly assigned as a negative pair.
In other words, category-level mismatch occurs when semantically related instances are mistakenly treated negatives. Ideally, all cross-view pairs of samples from the same class should be regarded as positives with t/ 1, rather than only those from the same instance.
a. Definition 2 (Sample-level mismatch). Consider a cross-view pair (v1) (w2) ..!?), where (rs))
and 4 (12) denote the oracle class labels of x (v1) and a!! respectively. A sample-level mismatch occurs if either i) (01) + (w9) ii) at least one of c (21) or Ci
(wa) does not correspond any valid class. In both cases, the pair cannot be regarded as a valid positive correspondence.
Specifically, sample-level mismatch admits two scenarios: i) alignable mispaired: although the constructed pair is incorrect, the sample x; (1n) still has valid counterpart Ti This case often co-occurs with category-level mismatch; ii) unalignable mispaired: there is no valid counterpart, e.g., the sample x²")
(va) in the other view.
(v.) might be corrupted or purely noisy data.
These two types of complex noisy correspondence motivate a more fundamental question: can we reduce the reliance on pre-defined pairs and instead directly model the intrinsic relationships that couple different views? Building on this intuition, we adopt a generative formulation that maximizes the marginal log- likelliod of the observed multi-view data (Bengio et al. 2013):
0" arg max
M
log p( (")
In multi-view clustering, each sample in one view may be associated with multiple counterparts in another view. Since these associations are unknown a priori, we treat them as latent variables. By aggregating over all unordered view pairs (v,, 12), the objective can be reformulated as:
N
V
N
0" = arg max
log Σ
p(a
(01)
(22)
Maximizing this marginal likelihood implicitly encourages the model learn a meaningful joint distribution p( (e1) 2 (ez). 0). In particular, to maximize the inner summation over j. the param- eters must assign higher joint probability to semantically consistent pairs, thereby revealing the underlying cross-view correspondences in probabilistic sense.
4

---

Compared with discriminative objectives, this generative formulation offers two key advantages: i) alleviates the heavy reliance on pre-defined positive and negative pairs, making it naturally ro- bust to sample-level unmatchable cases; ii) it captures many-to-many probabilistic correspondences across views, which better reflects the complex coupling of real-world multi-view data and mitigates category-level mismatch. However, the nested summation in Eq. (3) makes direct optimization in- tractable. To address this, we cast the objective into the Expectation (EM) framework and present the theoretical derivation in the next section.
3.2 CORRESPONDENGE GENERATION VIA EXPECIATION--MNIMAZAATI
3 we first consider subset of To simplify the derivation of the joint log-likelihood defined in Eq. the objective involving only two views:
N
0 arg maax
log
p (vi)
()) 0))
(12)
(4)
Directly optimizing Eq. is intractable due to the nested log-sum over latent variables. To address
this, we introduce an auxiliary distribution (ax, ((2)) over ar (*2) such that Σ5= Q(x)) allows us derive a lower bound:
(12))
(02)) = This
Q(af p(ar)) (11) ,
(12)
p (01)
(02). 2
log
log
(5)
Q10)) (02))
N (2a) log
pla (11) (v1) xx (12);
Q(x)
(6)
(1))))
where the inequality follows from Jensen's inequality. The bound becomes tight when ((a))aa)
(12), p(a))-)) xz :=("1)), 0), i... when the auxiliary distribution matches the posterior under the current pa- rameters f). Substituting this choice of Q into the bound gives:
N
N
0+ arg max
(aa
logp(o, (11) 1
Q(0) (22) ((x) log ((a))0))
(7)
0
i=
==
N
N
arg max
Σ
p(z))
x p(
( ((0) (lg)))llgppl p(x) (v.) 2 ) 0):
(12),
(8)
where the entropy term
Σ. Σ Q(ar)a)) log Q(x)) omitted since it independent of In
the E-step, we estimate the posterior distribution p(x) (02), xx ((1) _,((),, which provides a soft assign- ment of correspondences between samples across views. In the M-step, maximize the weighted log-likelihood in Eq. (8). updating the parameters 0 guided by the correspondences inferred in the E-step. By aggregating over all views, the above derivation naturally generalizes multiple views. Fig. shswws an overview of the above EM process and the details of the two steps will be discussed in the next section.
3.2.1 E-STEP: ESTIMATING UNDERLYING CORRESPONDENCES
In the E-step, we estimate the posterior distribution of latent correspondences p(a) (ra), x (or)) .00)) under the current parameters g(t):
p(z) (m) 20) (m)) p(a: (01) B())
(2z) p( p(z/f0) x (21) g(t))
which naturally decomposes the estimation into two parts, namely, the marginal distribution of indi- vidual views and the joint distribution across views.
5

---

E-step
M-step
Virmall Sample
LIMM Guide
Guide
Underlying Currespondence Estimation
Robust Correspondence Learning
Figure 2: Overview of the CorreGen framework which operates via an EM procedure: the E-step in- fers the underlying correspondence distribution using GMM-guided marginals and virtual sample mechanism to handle noise; the M-step subsequently utilizes these estimated soft correspondences guide the robust representation learning.
First, we estimate the joint distribution between views ei and U2, represented as a matrix P R
where each entry P.j p(a; (+1) (")) 3 (uz), ((t)), A good estimate of P should not only satisfy the marginal constraints but also capture the semantic dependency between the two views. Inspired by recent works that utilize Optimal Transport (OT) model complex cross-view relationships for clustering (Deng et al. 2025; Fu et al. 2025). we formulate the estimation of the optimal joint
distribution an OT problem. We introduce correlation function s(z, (01) ((x)) (e.g. cosine similarity) to measure the semantic correlations of a sample pair under the current parameters ((t),
with x! feco (z.")). Then the expected correlation is defined as
Ep(s] ΣΣ
(m)) Pij s(2 22, (12)).
(10)
We then seek the optimal joint distribution by maximizing this expectation:
p = arg max
Ep(s]
Pell(p ((12))
(11)
s.t 11 (1))
(2))
= p PER NxN Piy Piy=p ((1) PT 1N (12))
where p(e.) is the marginal distribution vector for view u. i.e,, ((()) (. 0(0). This formula- tion ensures that the estimated joint distribution preserves the marginal constraints while assigning higher probability mass semantically correlated pairs. However, due to the sample-level un- alignable problem, there may exist outliers whose joint probabilities with all other samples should ideally be close zero.
Virtual Sample for Partial Alignment. To handle the outliers and obtain more realistic joint distribution, we first introduce a virtual sample for each view to represent the outliers. Let p denote the potential noise ratio, which corresponds to the marginal probability mass of the virtual sample. We then augment the joint distribution P Re (N++)))()++) ensuring that the total probability mass assigned to outliers equals Formally, satisfies
PIN+1 = p]), PT P11N41 = = (p<)))
(12)
which enables the model absorb unalignable or noisy samples into the virtual probability mass.
Recall from Eq. 99 that estimating the posterior probabilities requires both the joint distribution
p(æ (v1) (12). ((()) and the marginal distribution p(æ; (e1), ((1)). In the expectation formulation Eq. these marginals act as constraints on the feasible set of couplings (e1) (e()),,(())) (r2)),, which es- sentially determines how many valid counterparts each sample can align with. Under category-level mismatch, the number of valid counterparts is not uniform but depends on the size and structure of the sample's semantic class. Therefore, the marginal distribution should naturally reflect this variability: samples from larger clusters or closer to cluster centers are assigned higher alignment mass, while outliers receive lower probabilities.

---

GMM-guided Marginal Estimation. We assume that each sample is generated from latent semantic cluster, which can be approximated by an anisotropic Gaussian distribution x!") (Hee E.). Accordingly, we fit the embedding space of each view with Gaussian Mixture Model (GMM) and compute the posterior responsibility of each cluster for every sample. The marginal probability is then estimated as
pla:""; ((()) md 1
No
(13)
m
1 N
= exp (-eV exp
(z) (0)
1e) E3 (z (0)
[t)
(14)
where N₂ is the number of samples assigned to cluster e by GMM, E and m are shaping parame- ters. Concretely, first compute the Mahalanobis distance in Eq. (14) between each sample and its cluster center, and map the result through an exponential kernel to obtain an assignment confidence
d,. This confidence is further passed through curve-shaping function -=-- which amplifies the contrast between high- and low-confidence samples: samples closer to the cluster center receive disproportionately higher weights, while distant ones are smoothly down-weighted rather than sup- pressed abruptly. Finally, the re-scaled confidence is combined with the cluster proportion N./N to yield the final probability to fill the marginal distribution in Eq. (II). In practice, we set c = 0.1 and 10, and apply momentum update to stabilize training.
Proposition 1. Eq. 77 with virtual sample can be solved by an efficient scaling algorithm if adding an entropy regularization XH(P), where X is a regularization factor. Specifically, we derive the optimal augmented joint distribution Pa through the following iterations:
p Diag(u) exp( ($ (xp(S/X)Diag(') ()))g(())
(15)
with iteration update + (()) /(xpp(//////))) (/))))) - p(vx)) (exx)((exx()))))) /A))u)
where B UE BRN are scaling vectors, p(m)) [p(t)); The extended correlation
matrix S E ((N+1))(N+3) constructed as:
S ON A
$ $ 01xN
(16)
where Sij = s(2,))) ,2 (00)) and A is constant. The optimal joint distribution estimation P is obtained by discarding the last row and column of P i.e. P = Pi.N.:N- The proof is provided in Appendix
3.2.2 M-STEP: ROBUST CORRESPONDENCE LEARNING
In the M-step, we maximize the overall log-likelihood of the observed data based the esti- mated posterior distribution. make Eq. tractable, we approximate the joint distribution
p(a) (v1) (=(")) () by normalizing the similarity scores of embeddings in the latent space
exp(s(z) (m)) (12))//T)
(w1) p(x) 2
(02),
(17)
ΣN cxp(s(z!1)
(1)) 2h 1/T)
where z (0) fo (e)) denotes the embedding of a!!" and is temperature parameter. According to Eq. we compute the posterior using the optimal joint distribution p and marginals (v:)
obtained the E-step, defined as Qij /.t/p!"u)
(e1)) Substituting this parameterization into Eq. (8)
the M-step objective becomes
N EΣO,
Oi log exp(s(2( (1L) , = (12))
0" arg max
(18)
EN EN exp(s(x!1)) (11) zz 1/7))
where -(.,)) denotes correlation function. Unlike contrastive objectives that rely manually defined positive/negative pairs, this formulation leverages the soft correspondences p inferred in the E-step, thereby mitigating the negative effects of noisy correspondence and enabling robust representation learning. Importantly, we find that the widely used InfoNCE loss can be unified into our framework special stated below.
7

---

(a) Warmup (10 epoch)
(b) 100 epoch
(c) 200 cpoch
(d) Ground Truth
Figure 3: Estimated posterior distributions over the course of training on the Caltech101 dataset.
Proposition 2. the marginal distribution ( 0) is uniform and the posterior probability degen-
erates to plar (w2), (w1)) .0) 1 (i.e., only paired cross-view samples are treated as valid positives),
then Eq. 8 reduces the standard InfoNCE contrastive objective:
cxp(s(z, (v1) 1.2,-2) (/22))/T)
0 = arg max
log
(19)
n= exp(s(z) (v1) (22) )/T))
0
2m
The proof is in Appendix B
EXPERIMENTS
In this section, we conduct extensive experiments to evaluate the effectiveness of our method in ad- dressing both category-level and sample-level noisy correspondence. Our study is guided by the fol- lowing research questions: Q1: Does our method outperform existing robust MVC approaches under
noisy correspondence (Section 4.2 ? Q2: Can our method reliably uncover underlying category-
level correspondences across views (Section 4.3 ? Q3: How does performance vary under different
levels of mismatch (Appendix ? Q4: How sensitive is method to hyperparameter choices
(Appendix D QS: Are the proposed components crucial for the improvements (Appendix F??
4.1 EXPERIMENTAL SETUP
Datasets. We evaluate our method on four widely used datasets: Scene (Fei-Feii & Perona 2005). Caltech101 (Li et al. 2015), LandUse21 (Yang & Newsam] 2010)), and UMPC-FoodI01 (Wang al. 2015). Notably, UMPC-Food101 contains images from 101 food categories paired with recipes crawled from the web, which inevitably introduces substantial irrelevant or noisy informa- tion. Representative examples of such noisy image-ter text pairs are provided in Appendix
Baselines. We compare CorreGen against seven state-of thefthhe-rrt MVC methods, including DCP
et al. 2022), SURE (Yang et al. (022b), GCFAgg Yan et al.) 2023 CGCN (Wang et al. 2024). DIVIDE (Lu et al. 2024). CANDY (Guo et al.) 2024), and ROLL (Sun et (025).. For fair comparison,
apply view realignment strategy the learned representations following prior studies (Guo et al, 2024] Sun et al. 2025), where realignment is consistently performed within batches of 512 ensure fair evaluation.
Implementation Details. CorreGen introduces a generative objective for MVC that can be seam- lessly integrated into existing contrastive frameworks. We implement on top of DIVIDE (Lu al. 2024 as the base model. More details are provided in Appendix
4.2 PERFORMANCE COMPARISON (Q1)
Since MVC is unsupervised task, category-level correspondences depend the underlying class sizes and distributions, making category-level mismatch an intrinsic challenge rather than one that be explicitly specified. Therefore, in this section, focus evaluating model performance under different sample-level mismatch settings, which include two cases: i) alignable mispairs, caused by instance-level permutations across views; and ii) unalignable mispairs, caused by noisy
8

---

The clustering performance with different mismatch ratios (MR). The best results and second best results are marked in bold and underline. All the results are the mean of five individual runs with different random seeds.
Table 1:
Scene 15
LandUse21
Caltech101
UMPC-Food101
MR Ratio Method
ACC
NM1
ARI
ACC
NM1
ARI
ACC
NM1
ARI
ACC
NMI
ARI
DCP
40.16
42.71
24.20
30.88
11.70
51.91
74.91
47.57
16.33
36.56
7.50
SURE
43.41
44.33
25.71
23.14
29.20
10.62
38.94
65.64
27.28
29.86
46.37
19.22
GCEAgE
33.58
32.91
16.76
23.48
26.75
10.80
34.27
55.57
19.98
16.12
30.03
6.55
41.34
23.57
26.88
36.40
66.72
24.72
29.58
39.57
0%
DIVIDE
44.57
45.9%
28. 43
32.50
39.44
18.16
62. 20
83.30
50.50
36.20
$7.92
27.72
CANDY
42.55
41.67
25.41
30.92
36.33
16.20
$4.06
60.02
35.10
53.06
22.39
17.83
Ours
50.25
48.92
32.87
32.87
39.52
18.54
68.52
84,45
63.45
49.77
58.36
35.73
DCP
35.88
37.63
16.51
24.20
28.46
10.10
43.99
70.83
35.43
17.83
35.63
8.45
SURE
37.26
35.56
19.94
24.67
27.45
10.91
35.91
60.06
24.56
20.30
32.89
8.99
GCFAgg
33.11
COCN
35.96
35.73
20.10
24.52
26.38
10.36
33.01
64.17
24.41
28.01
38.36
13.63
20%
DIVIDE
41.91
40.16
24.84
30.89
35.93
16.21
55.66
70.72
50.92
31.41
51.21
22.70
CANDY
41.05
30.34
33.43
65.
82.29
30.41
50.36
20.36
ROLL
44.86
46.96
28.71
24.33
33.11
15.16
20.39
46.44
15.03
21.26
43.05
13.73
Ours
48.04
47.36
30.75
32.26
38.76
17.83
68.01
84.23
62.78
46.76
S5.22
32,46
DCP
25.28
25.24
5.78
24.01
26.95
8.37
41.5 11.52
69.35
29.59
13.36
24.
4,60
SURE
28.16
26.52
13.16
22.67
24.91
9.94
26.89
$2.55
18.73
11.06
21.51
3.20
GCFAgE
5.14
CGCN
35.99
33.07
19.47
20.62
23.35
7.83
37.74
65 666
28.20
20.71
31.44
8.51
50%
DIVIDE
39.67
36.47
22.69
29.75
33.17
15.23
38.81
59.18
33.03
25.21
44.47
16.00
ROLL
42.41
44.49
26.43
28: 28.65
32.81
15.01
18:57
43.50
13.68
20.97
38.54
11.89
Ours
45.07
44.977
27.87
32.03
37.98
17.84
66.60
83.61
62.38
42.57
$1.79
27.29
DCP
21.46
21.11
2.87
21.17
22.59
7.17
32.13
58. 16
20,78
12.31
20.48
4,05
GCEAgE Pg
11.53
3.08
0.90
17.38
15.17
4.44
16.61
32.57
5.78
3.58
6,90
0.14
CGCN
28.81
25.42
12.89
20.29
20.70
7.32
35.32
63.83
25,77
18.13
29.48
6.92
80%
DIVIDE
35.90
32.95
19.63
28.56
31.74
14.32
27.42
53.68
21.56
24.78
42.98
15.63
CANDY
38.27
20.74
28.44
31.39
14.01
54
77.30
$3.79
27.59
48. 10
17.62
ROLL
37.62
38.27
21.19
25.67
28.42
11.96
20.83
45.58
13.97
T9.39
39.68
13.52
40.96
41.74
24.74
31,52
37,21
17.75
64.74
82.77
61.78
43.00
53.03
27.12
or corrupted samples. We control these two factors using the Mismatch Ratio (MR) and Corruption Ratio (CR), with detailed construction described in Appendix C
Our method consistently achieves the best performance, benefiting from its generative objective and robust correspondence discovery, which remain effec- tive even with a few aligned pairs. Table 2 further evaluates scenarios with both alignable and unalignable mismatches. While all baselines degrade severely MR and CR increase, our method maintains strong performance by jointly leveraging GMM-based marginals to down-weight noisy samples and virtual samples absorb unalignable ones, mitigating the influence of low-quality pairs.
Table Teports results under different MR.
4.3 POSTERIOR DISTRIBUTION VISUALIZATION (Q2)
We next investigate whether CorreGen can uncover the latent correspondences across views. On Caltech with MR=0.2 and CR=0.0, we sample mini-batch and estimate their posterior distri- butions at different training stages, comparing them with the true category-level ground truth.
As shown Fig. 3 the category-level correlations are weak in the early training phase. By mid- training, the estimated posterior distributions already resemble the ground truth, and the gap further narrows in the later stages. These results demonstrate that CorreGen progressively uncovers the latent class-level correspondences, thereby effectively alleviating category-level mismatches.
5 CONCLUSION
In this paper, propose novel generative framework for multi-view clustering under the noisy correspondence challenge. Unlike existing discriminative approaches that rely heavily on off-the- shelf pairwise alignments,
method models cross-view dependencies by maximizing the joint likelihood of observed data, thereby uncovering latent correspondences in a principled manner. Ex- tensive experiments across multiple datasets demonstrate that approach not only achieves supe-

---

Table 2: The clustering performance on four multi-view datasets with different Mismatch Ratios (MR) and Corruption Ratios (CR).
Scenel5
LandUse21
Caltech101
HMPC-FFodd01
Setting
Method
ACC
NM1
ARI
ACC
NMI
ARI
ACC
NM1
ARI
ACC
NMI
ARI
DCP
36.50
40.52
21.55
24.62
29.19
11.37
41.03
69.34
37.81
12.97
28.
4.71
SURE
37.93
38.53
21.23
24.48
28.32
33.71
58.99
20.69
13.14
25.06
4.95
GCHAge
29.59
26.33
14.22
24.29
25.13
10.70
28.57
43.65
14.21
8.89
17.07
2.11
MR 0.2
CGCN
27.78
26.95
12.92
23,52
23.96
8.81
35.61
64.81
30.16
28.02
39.04
13.57
DIVIDE
36.05
36.18
20.22
29.30
34.69
15.13
73.31
53.82 82
29.01
49.00
20.92
CANDY
35.57
37.00
20.71
29.13
33.70
14.87
82.23
62.52
30.13
49.77
20.06
ROLL
36.13
36.76
17.99
23.15
24.28
5.39
16.50
40.44
12.16
18.51
39.78
11.63
Ours
41.23
41.43
25.05
31,13
37.36
17.00
67.12
84.45
64.13
45.97
54.66
31.36
DCP
34.31
37.70
19.55
17.95
22.13
5.96
36.98
63.14
32.46
7.36
17.71
1.58
SURE
18.37
20.05
7.40
11.19
GCHAgg
27.85
24.05
12.73
23.24
24.19
9.92
27.57
45.00
14.43
7.77
15.68
1.67
MR 0.2
CGCN
28.36
31,46
16.32
22.24
25.04
9.61
35.83
76.99
41.69
24.07
35,01
10.17
CR
CANDY
31.24
34.08
19.00
24.72
28.03
11:27
62.57
81 81.52
55.76
25.00
47.27
17.36
ROLL
27.03
25.83
9.42
16,40
15.49
3,20
12.97
36.57
9.80
T6.12
36,52
9. 9,66
DCP
33.62
35.05
14,48
24.48
27.57
10.35
38.03
64.81
9.30
19.71
SURE
25.37
26.07
11.48
21.38
24.14
8.08
27.52
53.57
15.64
6.86
15.83
1.58
GCBAgE
24.26
13.31
6.45
22,00
19.02
7.77
23.83
38.62
10.43
5.24
9.64
0.57
MR 0.5
CGCN
29.65
29.89
15.37
23.57
24.86
29.22
58.
25 .8
35,71
11.60
CR
DIVIDE
32.88
32.87
18.08
29.00
12.49
14.37
43.918
61.51
37.87
23.04
43.28
14.71
CANDY
34,60
35.31
19.84
27.77
11.46
13.63
58.35
78
56.14
27.97
48, 24
18.81
ROLL
35.23
35.79
18.54
23.34
23.99
8.83
14.78
38.46
11.07
17.54
35.48
9.67
Ours 39.54
39.55
23.12
31.20
36.25
16.92
66.87
84.15
67.31
38.84
50.09
24.98
5.19
SURE
26.91
28.73
12.06
19.57
21.18
6.60
25.90
54.83
18.07
7.00
17.28
1.77
GCFAgE
22.27
14.13
6.68
20.57
17.30
6.72
21.56
37.88
9.61
4.61
8.88
0.42
MR CR 0.5
CGCN
DIVIDE
30.27
31.25
16.31
26.13
29.12
12.30
48.07
68.23
44.69
20.67
42.07
12.52
CANDY
29.44
32.67
17.09
24.08
27.21
11.01
51 28
75.16
41.70
24.70
46.58
17.19
32.84
Ours
36.19
36.84
20.83
28.72
32.54
14.50
$7.06
80.34
45.37
37.26
49.30
23.25
rior clustering performance but also exhibits strong robustness to sample-level and category-level mismatches. In the future, we plan to extend this framework to unpaired multi-modal learning and apply it to cross-modal retrieval tasks with large-scale noisy data.
AUTHOR CONTRIBUTIONS
All authors contributed significantly to this work. Xi Peng and Yijie Lin conceived the study, de- signed the CorreGen algorithm, and refined the manuscript. Haochen Zhou co-designed and imple- mented the CorreGen algorithm, conducted the experiments, and drafted the manuscript. Guofeng Ding supplemented the baseline evaluations and contributed to the content of the manuscript. Peng Hu and Mouxing Yang provided suggestions for the algorithm's is design and contributed to the for- mulation of the manuscript. All authors reviewed and approved the final version.
ACKNOWLEDGMENTS
This work supported in part by the Fundamental Research Funds for the Central Universities un- der Grant CJ202303, CJ202403; in part by NSFC under Grant 624B2099, U25A201523, 62472295; in part by Sichuan Science and Technology Planning Project under Grant 24NSFTD0130 in part by Fundamental and Interdisciplinary Disciplines Breakthrough Plan the Ministry of Education of China under Grant JYB2025XDXM6 in part by System of Systems and Artificial Intelligence Laboratory pioneer fund grant under Grant HLJJGGG20220225517-55
REFERENCES
Yoshua Bengio, Aaron Courville, and Pascal Vincent. Representation learning: A review and new perspectives. IEEE transactions on pattern analysis and machine intelligence, 35(8):1798-1833 2013.
10

---

Laetitia Chapel, Mokhtar Z Alaya, and Gilles Gasso. Partial optimal tranport with applications positive-unde positive-unlabeled unlabeled learning. Advances in Neural Information Processing Systems, 33:2903-222 2913, 2020.
Marco Cuturi. Sinkhorn distances: Lightspeed computation of optimal transport. Advances in neural information processing systems, 26, 2013.
Bowen Deng, Tong Wang, Lele Fu, Sheng Huang, Chuan Chen, and Tao Zhang. THESAURUS: contrastive graph clustering by swapping fused gromoy-wassersten couplings. In Proceedings of the AAAI Conference on Artificial Intelligence, pp. 16199-16207, 2025.
Jacob Devlin, Ming- Beig-Weiilee Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint arXiv:1810. 04800, 2018.
Li Fei-Fei and Pietro Perona. A bayesian hierarchical model for learning natural scene categories. In 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR'0S) 005), volume 2, pp. 524-531. IEEE, 2005.
Lele Fu, Bowen Deng, Sheng Huang, Tianchi Liao, Chuanfu Zhang, and Chuan Chen, Learn from global rather than local: Consistent context-aware representation learning for multi-view graph clustering. In Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intel- ligence, IJCAI 2025, Montreal, Canada, August 16-22, 2025, pp. 5145-5153, 2025.
Ruiming Guo, Mouxing Yang. Yijie Lin, Xi Peng, and Peng Hu. Robust contrastive multi-view clustering against dual noisy correspondence. 37, 2024.
Zongho Han, Changqing Zhang, Huazhu Fu, and Joey Tianyi Zhou. Trusted multi-view clas-
sification. In International Conference on Learning Representations, 2021. URL. https:
//openzeview. http://rrrmmm1-000ooo1oc111ee1
Changhao He, Hongyuan Zhu, Peng Hu, and Xi Peng. Robust variational contrastive learning for partially view-unaligned clustering. In Proceedings of the 32nd ACM International Conference Multimedia, pp. 4167-4176, 2024.
Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick. Momentum contrast for unsupervised visual representation learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 9729-9738, 2020.
Zhenyu Huang, Peng Hu, Joey Tianyi Zhou, Jiancheng Lv, and Xi Peng. Partially view-aligned clustering. In Proceedings of the 34th Conference Neural Information Processing Systems, NeurlPS 2020.
Zhenyu Huang, Guocheng Niu, Xiao Liu, Wenbiao Ding, Xinyan Xiao, Hua Wu, and Xi Peng- Learning with noisy correspondence for cross-modal matching. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P.S. Liang, and J. Wortman Vaughan (eds.), Advances in Neural Information Pro- cessing Systems, volume 34, pp. 29406-29419. Curran Associates, Inc., 2021.
Diederik Kingma and Jimmy Ba. Adam: method for stochastic optimization, arXiv preprint 1412 2014.
Kuang-Huei Lee, Xiaodong He, Lei Zhang, and Linjun Yang. Cleannet: Transfer learning for scalable image classifier training with label noise. In Proceedings of the IEEE conference computer vision and pattern recognition, pp. 5447-5456, 2018
Yeqing Li, Feiping Nie, Heng Huang, and Junzhou Huang. Large-sear scale multi-view spectral clus- tering via bipartite graph. In Proceedings of the AAAI conference on artificial intelligence, vol- ume 29, 2015.
Yijie Lin, Yuanbiao Gou, Xiaotian Liu, Jinfeng Bai, Jiancheng Lv, and Xi Peng. Dual contrastive prediction for incomplete multi-view representation learning. IEEE Transactions on Pattern Anal- ysis and Machine Intelligence, 4544)14447-4411, 2022. 2022.

---

Yijie Lin, Mouxing Yang. Jun Yu, Peng Hu, Changqing Zhang, and Xi Peng. Graph matching with bi-level noisy correspondence. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 22662-2377,,- 2023.
Yijie Lin, Jie Zhang, Zhenyu Huang, Jia Liu, Zujie Wen, and Xi Peng. Multi-granulaen granularity correspon- dence learning from long- long-term noisy videos. arXiv preprint arXlv:2401.16702, 2024.
Suyuan Liu, Siwei Wang, Liang, Junpu Zhang, Zhibin Dong, Tianrui Liu, En Zhu, Kunlun He, and Xinwang Liu. Alleviate anchor-shift: Explore blind spots with cross-view reconstruction for incomplete multi-view clustering. Advances in Neural Information Processing Systems, 37: $7509-87531. 2024.
Yiding Lu, Yijie Lin, Mouxing Yang, Dezhong Peng, Peng Hu, and Xi Peng. Decoupled contrastive multi-view clustering with high-order random walks. In Proceedings the AAAI conference artificial intelligence, volume 38, pp. 14193-14201, 2024. 2024.
James B McQueen. Some methods of classification and analysis of multivariate observations. In Proc. of 5th Berkeley Symposium on Math. Stat. and Prob., pp. 281-297, 1967.
Yalan Qin, Nan Pu, Hanzhou Wu, and Nicu Sebe. Margin-aware noise-robust contrastive learning for partially viewealigned problem. ACM Transactions on Knowledge Discovery from Data, 19 (1):1-20, 2025a.
Yalan Qin, Xinpeng Zhang, Shui Yu, and Guorui Feng. A survey on representation learning for multi-view data. Neural Networks, 181:106842, 2025b.
Qian Qu, Xinhang Wan, Jiyuan Liu, Xinwang Liu, and En Zhu. Enchor-guided sample-and anauuue incremental alignment framework for multi-view clustering, IEEE Transactions on Circuits and Systems for Video Technology, 2025.
Piyush Sharma, Nan Ding, Sebastian Goodman, and Radu Soricut. Conceptual captions: A cleaned, hypernymed, image alt-text dataset for automatic image captioning. In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume I: Longg Papers), pp- 2018
Yuan Sun, Yang Qin, Yongxiang Li, Dezhong Peng, Xi Peng, and Peng Hu. Robust multi-view clustering with noisy correspondence. IEEE Transactions on Knowledge and Data Engineering, 2024.
Yuan Sun, Yongxiang Li, Zhenwen Ren, Guiduo Duan, Dezhong Peng, and Peng Hu. Roll: Robust noisy pseudo-label learning for multi-view clustering with noisy correspondence. In Proceedings of the Computer Vision and Pattern Recognition Conference, pp. 10732-30741 2025.
Qianqian Wang, Zihao Zhang, Wei Feng, Zhiqiang Tao, and Quanxue Gao. Contrastive multi-view subspace clustering via tensor transformers autoencoder. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pp. 21207-2123 21215, 2025a.
Xin Wang, Devinder Kumar, Nicolas Thome, Matthieu Cord, and Frédéric Precioso. Recipe recog- nition with large multimodal food dataset. In 2015 IEEE International Conference Multimedia & Expo Workshops (ICMEW), pp. 1-6, 2015. doi: 10.1 21100//CME..21...
Yiming Wang, Dongxia Chang, Zhiqiang Fu, Jie Wen, and Yao Zhao. Partially view-aligned repre- sentation learning via cross-view view graph contrastive network. IEEE Transactions on Circuits and Systems for Video Technology. 34(8):7272-7283, 2024.
Yunbo Wang. YuJie Wu, Zhien Dai, Can Tian, Jun Long, and Jianhai Chen. Noisy correspondence rectification via asymmetric similarity learning. In Proceedings of the AAAI Conference on Arti- ficial Intelligence, volume 39, pp. 21384-21392. 2025b.
Bichen Wu, Chenfeng Xu, Xiaoliang Dai, Alvin Wan, Peizhao Zhang, Zhicheng Yan, Masayoshi Tomizuka, Joseph Gonzalez, Kurt Keutzer, and Peter Vajda. Visual transformers: Token-based image representation and processing for computer vision, 2020.
12

---

Zhirong Wu, Yuanjun Xiong, Stella X Yu, and Dahua Lin. Unsupervised feature learning via non- parametric instance discrimination. Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 3733-3742, 2018.
Weiqing Yan, Yuanyang Zhang, Chenlei Lv, Chang Tang, Guanghui Yue, Liang Liao, and Weisi Lin. Gcfagg: Global and cross-view feature aggregation for multi-view clustering. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 19862-19872, 2023.
Wenbiao Yan, Jihua Zhu, Jinqian Chen, Haozhe Cheng, Shunshun Bai, Liang Duan, and Qinghai Zheng. Partially multi-view clustering via re-alignment. Neural Networks, 182: 106884, 2025.
Xiaoqiang Yan, Shizhe Hu, Yiqiao Mao, Yangdong Ye, and Hui Yu. Deep multi-view learning methods: A review. Neurocomputing, 448: 106-119991 2021. ISSN 0925-2312. doi: https://oiioo org/ 10.1016fj.eucc0m22211.....000 URL https: /tt:://wwwwww. www.ssciencedireet.... wwwpsccioe//e.eeeeee....cc..eeee
atticle//111/9222211210000
Mouxing Yang, Yunfan Li, Zhenyu Huang, Zitao Liu, Peng Hu, and Xi Peng. Partially view-aligned representation learning with noise-robust contrastive loss. In Proceedings of the IEEE/CVF Con- ference on Computer Vision and Pattern Recognition (CVPR), pp. 1134 1143, June 2021.
Mouxing Yang, Zhenyu Huang, Peng Hu, Taihao Li, Jiancheng Lv, and Xi Peng. Learning with twin noisy labels for visible-infrared person re-identification. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 14308-14311 2022a.
Mouxing Yang. Yunfan Li, Peng Hu, Jinfeng Bai, Jian Cheng Lv, and Xi Peng. Robust multi-view clustering with incomplete information. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022b.
Mouxing Yang, Zhenyu Huang, and Xi Peng. Robust object re-identification with coupled noisy labels. International Journal of Computer Vision, 132(7):2511-252) 2024.
Xihong Yang, Yue Liu, Sihang Zhou, Siwei Wang, Wenxuan Tu, Qun Zheng, Xinwang Liu, Liming Fang, and En Zhu. Cluster-guided contrastive graph clustering network. In Proceedings of the AAAI conference on artificial intelligence, volume 37, pp. 10842- 2023.
Yi Yang and Shawn Newsam. Bog-of-visual-words and spatial extensions for land-use classification. In Proceedings of the 18th SIGSPATIAL international conference on advances in geographic information systems, pp. 270-279. 2010.
Guang-Yu Yu Zhang, Dong Huang, and Chang-Dong Wang. Unified and tensorized incomplete multi- view kernel subspace clustering. IEEE Transactions on Emerging Topics in Computational Intel- ligence, 8(2):1550- 1566, 2024. doi: 10.100/TETC12204.33336
Yuanyang Zhang, Yijie Lin, Weiqing Yan, Li Yao, Xinhang Wan, Guangyuan Li, Chao Zhang, Guanzhou Ke, and Jie Xu. Incomplete multi-view clustering via diffusion contrastive generation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pp. 22650-22658, 2025.
13

---

APPENDIX
A EFFICIENT SOLVER FOR JOINT DISTRIBUTION ESTIMATION (PROOF OF PROPOSITION I
In this section, we derive the efficient solver for Eq. (IT) under the sarule formulation, where the marginals augmented with virtual probability mass p following Eq. (12):
p (v) Ip (wx); p].
(20)
To incorporate virtual samples in the optimal transport problem, we construct an extended correla- tion matrix S following Chapel et al. (020))
$=
S
O ONx1
(21)
0IXn
A
where S E R with S.y s( (01) (12)). and A < min( Since the objective is to
maximize the expected correlation, assigning the smallest correlation value A to the virtual-virtual interaction and setting all data-virtual correlation as 0, ensures the virtual samples do not introduce a constant bias into the overall correlation score.
By adding an entropy regularization term H(P) = - -Ei Psj log P.j. the optimization objective can be formulated as:
arg max (P, + XH(P) s.t. P1 = p(m,, p_1=)((0) P20
(22)
where À > 0 is regularization factor. The augmented objective function is strictly convex and smooth. To derive the solution, we introduce the Lagrangian with dual multipliers a, B E RN+1 enforcing the row and column constraints, respectively:
- P. log P.j + a (p(lo)) P1) (p((z) 1
(23)
1.j
Taking the first-order optimality condition with respect to P.j. for any j. ,. we have:
dc S.j - A(1 + log P.y) - a, - -B =
(24)
OP.
Rearranging the terms yields:
log P.j S.j a2 G3 1.
(25)
By absorbing the constant terms into the scaling vectors, we obtain a multiplicative form of the solution:
P. = ü, exp( exp( /A)oj,
(26)
where ū; : exp(-oi/A- 1/2) and úy =- exp(- 1/2) are strictly positive scaling factors. In matrix form, this is expressed as:
p Diag 2 exp( Diag)
(27)
Imposing the marginal constraints P1 = (()) and PT = 111ppt0 (v2) leads to the following system:
Diag(ū) (exee(/(/)))) A)Ø) ((1) Diag(o) exp(S /A)ū) (
(28)
Solving these equations via fixed-point iteration results the alternating Sinkhorn updates (Cuturi 2013
- (- @ (exp($/A)6).
8 i- @ (oxp(STA)jū))
(29)
where @ denotes element-wise division. By the Sinkhorn updates, the alternating scaling converges to unique positive vectors (ü, ö) that satisfy the predefined marginals. Consequently, the resulting p* is the unique global maximizer of the entropy-regularizee problem.
Finally, the optimal joint distribution pa is obtained by discarding the last row and column of the augmented matrix P ie., P P P.N.I:N-
14

---

B CONTRASTIVE LEARNING AS A SPECIAL CASE OF CORRGEN (PROOF OF PROPOSITION 2
Starting from our generative objective in Eq. (8)
N
(m1) a (000 log (Mr) [x) p(a) (12) xz
0r
arg max
(30)
(12) x (vi) .0) 1, the summation over Under the assumption that the posterior collapses to p(ar p(ax reduces to
0r arg max
log p(x (01)
" (.(")))))
(31)
Further decomposing the joint probability gives
p(a (11)
(22), =. (22) (()=(")) (11) 0) p( (2)
(32)
If the marginal p(a; 0) is uniform, i.e, p(a; (01); 0) +. it contributes only a constant indepen- dent of 0, which can be omitted. Thus, the objective simplifies
(0x)
0* arg log (22), ar
(01) 00)
(33)
After parameterizing the conditional probability with similarity in the embedding space, it yields exactly the InfoNCE objective (He et al. 2020):
exp(s(z, (v1) 2, (/2) n= cxp(s(z)) (11) 3/T)
g arg max
log
(34)
C IMPLEMENTATION DETAILS
Implementation of CorreGen. CorreGen is implemented on top of DIVIDE (Lu et al. 2024). Specifically, we replace the original contrastive objective in DIVIDE with our generative objective, while retaining its feature extraction structure as the mapping function fe. For the within-viens con- trastive module (i.e., between features and their momentum counterparts), posterior matrix Q with the identity matrix at a ratio of 3 = 0.5. For the cross-view learning module, directly use the estimated posterior matrix without modification. To ensure stable train- ing, we initialize the EM algorithm with the identity matrix I as the posterior estimate in the first few iterations, which serves as a warm start to avoid poor local optima. After this warmup phase, we switch to the adaptive posterior estimation strategy described in our method, thereby uncovering latent correspondences across views.
fuse the estimated
Training Setup. We implement CorreGen with PyTorch 2.1.2 and optimize it using the Adam optimizer (Kingma Ba. 2014)) with the learning rate of 0.002. The batch size set to $12 for smaller datasets (e.g., Scene15, LandUse21) and 1024 for larger ones (e.g- Caltech101, UMPC- Food101). All experiments are conducted on Ubuntu 20.04 with NVIDIA 3090 GPUs. We set the maximum warmup phase to 50 epochs and train for total of 200 epochs. The regularization parameter À = 0.03, and the noise ratio for the virtual sample in Eq. [2) is set to = 0.2 across all experiments.
Datasets. We evaluate our method on four widely used multi-view benchmarks:
Scene15 (Fei-Feii & Perona 2005) contains 4,485 natural images spanning 15 scene cate- gories, covering both indoor and outdoor scenarios. We extract two types of hand-crafted features for each image, namely, PHOG and GIST descriptors.
Caltech101 eLi al. 2015) includes 8,677 images from 101 object categories. To form two distinct views, we adopt deep representations obtained from DECAF and VGG19 networks, consistent with Han al. (202))
15

---

LsndUse21 Yang & Newsam 2010) contains 2,100 satellite imagery samples in 21 cate- gories. We follow Lin et al. (2022) to construct two views by extracting PHOG and LBP descriptors.
UMPC-Food101 (Wang al. 2013) consists of paired food images and textual recipes, with 60,000 samples for training and 20,000 samples for testing across 101 categories. We the test split for clustering evaluation. Visual features are extracted using a ViT (Wul et al. 2020) pretrained on ImageNet, while textual features are obtained with BERT (Devlin et 2018). Notably, the recipe descriptions often contain irrelevant noisy information, making UMPC-Food101 realistic benchmark for studying noisy correspondence.
Simulation of sample-level mismatch. To evaluate robustness under different conditions, sim- ulate two types of sample-level mismatches: i) Alignable mismatch: a fraction of instances (each with multiple views) randomly permuted across views. The fraction is controlled by the Mis- match Ratio (MR). ii) Unalignable mismatch: fraction of view samples are corrupted with random Gaussian noise, with the fraction defined as the Corruption Ratio (CR).
D PERFORMANCE VISUALIZATION WITH VARYING MR AND CR VALUE (Q3)
Previous comparisons in Section focused specific MR and CR values, which do not fully reveal robustness across different mismatch levels. Here, we fix MR at two representative values and vary CR continuously, visualizing clustering performance of CorreGen and four state-of-the-ar baselines to examine their robustness.
For evaluation, we re-align samples across views using a nearest-neighhor principle following Guo et al. 2024);; Sun et al. (223). To quantify category-level consistency, we report the Category-level Alignment Ratio (CAR) (angg et al. 2021). defined as
CAR 1 N
Σ ò (C(a)")) (((())) ==1
(35)
where C(-) is the oracle category label, T(i) is the re-aligned counterpart of (01) and 8(-) is the indicator function. As shown in Fig. 4 on UMPC-Food101, CorreGen demonstrates substantially lower performance degradation as CR increases, consistently outperforming all baselines. Even under severe mismatches (e.g., MR=0.5), CorreGen maintains a stable CAR score, highlighting its ability to recover reliable category-level correspondences despite high noise.
E PARAMETERS ANALYSIS (Q4)
In this section, we provide detailed sensitivity analysis of CorreGen using the Scene15 (Fei-Feil & Peronal 2005) dataset under the setting (MR = 0.2, CR = 0.2). We focus on three critical hyperparameters in the E-step: the pre-defined noise ratio p. the number of Sinkhorn iterations t, and the curve-shaping parameter m. To study potential interactions, we examine them in two pairwise groups.
Pre-defined Noise Ratio p and Curve-Shaping Parameter m. As shown in Fig. the performance remains stable across wide range p values. For m, the performance consistently strong when m < 10, where the marginal probabilities remain moderately discriminative. As m grows larger, the probability distribution becomes overly smoothed, leading to a slight decline in performance.
Pre-defined Noise Ratio and Sinkhorn Iterations f. Fig. Tig. iillustrates the clustering performance of our method across wide range of Sinkhorn iterations ( [10, 1000)) and pre-defined noise ratio (p 0.5)). We observe that while increasing the number of iterations leads to modest performance gain, the method remains comparable even with a small number iterations. This stability is particularly advantageous as it preserves high computational efficiency without compro- mising accuracy. Furthermore, when p is close to the underlying noise ratio (e.g., 0.1-0.2), selecting appropriate number of iterations enables the model to achieve optimal performance.
16

---

20
Maw 40-
<g saw
Compption Rasa (0R)
Corspliis (allo
(a) ACC
(b) NMI
-Q-
Coroplas
(c) ARI
(d) CAR
Figure 4: The clustering performance under varying CR value. Solid lines indicate results with
MR 0.2, while dashed lines correspond MR 0.5. The CR values varies from 0.0 to 0.8.
43
43
50
63
-2.
22g
(a) ACC
(b) NMI
(c) ART
Figure 5: Parameters Analysis Pre-defined noisy ratio P and the curve-shaping parameter m.
F ABLATION STUDIES (Q5)
In this section, we conduct ablation studies on Scene15 and 10 evaluate the ef- fectiveness of each component. We also compare our method CorreGin with the standard In- foNCE objective. Experiments are performed under two settings: (MR 0.0, CR 0.0) and (MR 0.2, CR = 0.2).
As shown in Table 3 the results lead to three key observations: i) On relatively clean datasets, the effect of the Virtual Sample module is not significant, and using smaller p may yield better results; ii) The GMM-guided marginal estimation consistently enhances clustering accuracy by assigning higher probabilities informative samples. thereby improving joint distribution estimation. iii) Training with vanilla InfoNCE fails to capture latent sample- and category- correspondences, resulting in significant performance degradation under noisy conditions.
17

---

64
200
230
(a) ACC
(b) NMI
(c) ARI
Figure 6: Parameters Analysis of pre-defined noise ratio p and Sinkhorn iterations t.
Table 3: Ablation study CorreGen on Scene15 and UMPC-Food101, where who denotes the component is not adopted. "Virtual" refers to the Virtual Sample module, "Guide" refers to the GMM-guided marginal estimation, and "Vanilla InfoNCE" denotes training with the standard con- trastive objective.
MR=00,, CR=0.0
MR=022, CR=0.2
Setting
1cene
UMPC-Food101
Scene
UMPC-Food101
ACC
NMI
ARI
ACC
NMI
ARI
ACC
NMI
ARI
ACC
NMI
ARI
CorreGen
50.25
48.92
49.77
58.36
41.78
45.97
54.66
31.36
w/o Virtual
49.44
48.38
49.45
59,22
36.65
41.10
44.01
$3.92
30.36
w/o Guide
49.06
48.01
31.98
49. .4
57.95
35.37
40.98
41.21
24.77
44.59
54,03
30.67
w/o Virtual & Guide
49.00
48.33
31.83
48.92
58.42
35.61
40.52
40.95
24.66
43.68
53.41
29.78
Vanilla InfoNCE
47.83
47.81
31,37
48.47
57.82
34.73
38.36
37.60
21.96
43.84
52.76
29.15
G CONVERGENCE ANALYSIS
In this section, we analyze the convergence behavior of CorreGin from both theoretical and empiri- cal perspectives to demonstrate the training stability of our proposed framework.
Theoretical Analysis. the two-view case, our optimization objective is the likelihood function:
N
N
L()) = log
Σ
p(x (1r) (vr) (12) (x2) 0).
(36)
1=1
j=1
(v1) , we derive lower bound By introducing an auxiliary distribution (1) for each sample x. via Jensen's ' inequality:
(a (02)) log p(a (01)
(1x)
x
(())
& B(Q.0).
(37)
(1)
which holds with equality when (ax) (02)) = p(a, (12) (v1) Qit+)) (z
0). In the E-step, we estimate
x B(0) to make the bound tight such that (0z)) p(x) (v2), (01),
c()())) B(Q
(38)
Subsequently, the M-step updates 0 to maximize this expected log-likelihood, ensuring ((Q(++)) g(++1)) > B(Q(++1) ((())))))))))......)..)))))))))) Combining these steps yields the following inequality chain, proving that the likelihood monotonically non-decreasing:
((0(++1)) 2 ((Q(++1),(t**)))))) gl++1) 2 B(Q ((0)) (()(t)).
(39)
Given that the likelihood function is bounded, this monotonicity guarantees the convergence of our algorithm to stationary point.
18

---

2005
1002
1001
Reforminne
4.000
2.00
100
352
Epoch
Figure 7: Convergence analysis CorreGen on the 1cene dataset. The red dashed line indicates the transition from the warmup phase the EM optimization phase.
Empirical Verification. To empirically verify this stability, we tracked the training loss and clus- tering performance the Scene15 dataset over the training process. As our optimization performs gradient descent on the negative expected log-likelln log-likelihood, the loss naturally decreases as training progresses. illustrated in Fig. 7 the training process exhibits a clear and stable convergence pat- tern. During the initial warm-up phase (epochs 0-20), the loss decreases rapidly while performance metries show a sharp increase. After the EM procedure is activated (marked by the red dashed line), the loss continues to decline steadily. After approximately 150 epochs, both the objective function and all evaluation metrics stabilize and reach a plateau, confirming that our objective has converged.
H ANALYSIS OF CATEGORY-LEVEL. MISMATCH RATIO
In this section, we first provide the mathematical formulation of the Category-level Mismatch Ratio (CMR). For a category с containing Ne samples, the total space of possible cross-view pairwise interactions in this category is N2. According to Definition | the mismatch ratio % for category is calculated as:
Te = ExjeCooooocy I[tr, = 1)
N N
1
(40)
N2
N
where ti denotes whether the pair (i,J) is an observed correspondence as defined in Definition 1 and [(4..j 1) N₂ because each sample has exactly one observed correspondence in existing datasets.
Specifically, for dataset with C categories, CMR is defined the average across categories:
CMR
Σ
n
1 N.
(41)
According to the above formulation, Table reports the CMR of datasets used our experiments. The results indicate that category-level mismatches pervasive across datasets (consistently ex- ceeding 98%), highlighting the necessity of uncovering latent correspondences beyond the limited off-the-shelf pairs.
Furthermore, analyze the behavior of this metric under fixed data size N, i.e., Ee N N. As Eq. (40) is strictly concave on (0, oc), applying Jensen's 's Inequality for concave functions yields:
N = C N
(42)
C
N₂
The equality holds if and only if N1 N2 This inequality implies that balanced datasets will inherently exhibit a higher average category-level mismatch ratio compared to imbalanced or long-tailed datasets of the same size.
Nc, when the dataset is perfectly balanced.
19

---

Table 4: The Category-Ieve levell Mismatch Ratio (CMR) for the datasets used in our experiments.
Dataset
CMR ( (%)
Scene15
99.65
LandUse21
99.
Caltech101
98.25
UMPC-Food101
99.53
Text
Image
Label
The enpoopperdd New Mexico
lhe applyyec. [0
aks
( crudel Aseran pielitc made with dougs Applecakee
Apple Pic
appleple
Why wly del hos thick of aleee Lave Chicken Put Ps. but have sove over made Word, Iieey den' wdy haven.
Reflowereeee
Americas
Thonkghiig
Fere in Creade oddivrr Thokkggiing in Outike fores...
Blubbery Maplo Mulfia
buby back ribs
Sou've mony the
They auk cay
Watmmnk templaz. Powered Blazed
exis PM
Cocpetticn Kandeuok, Expren Digizl Premart Cooka
Kensooo EMds Food Preensor
Saeoomettar Eley
beef carpaccio
Wis vip
2
Wis tr Chomia
Maganme
Seal Flana 'apens
Sabecrth
AMAM Good Food Gooe Tinne Series
sprica Barr Lovia fivm Youllabe chanal My Vagie Kicianakowo you. trrdly inchiling was
how make cone goue me pos
pirza, quicy haggre phoopple
heignets
Add You May Like
nww Cook Tencinioee
Linke
Filyko
Burn
Checson Crder Stal mede oi bemomik dosing forr Cil Femands Solad Clay Sendecch fun Narla Fiz
caprese_salad
with Staies TradsokTnatit
Pofest Purtey
andd Chedee Corlle Roruran lerver Salal ask Neor riso recpe! (dzalla)
Figure 8: Examples of noisy image-text pair in the UMPC-Food101 dataset.
I IMAGE-TEXT PAIR EXAMPLE OF UMPC-FOOD101
UMPC-Food101 (Wagg et al. 2015) constructed by crawling food images with textual recipes col- lected from the web. As shown in Fig. [ the texts often contain irrelevant descriptions, hyperlinks, or noisy information unrelated the visual content, making realistic benchmark for studying noisy correspondence in multi-view clustering.
J THE USE OF LARGE LANGUAGE MODELS
In this paper, LLMs were used to refine the writing in the Introduction, Related Work, and Experi- ments sections, as well as verify the clarity of mathematical derivations.
20


Reviews:
[{"review_id": "msmBxnE2cT", "reviewer": "Reviewer_eYLV", "summary": "This paper tackles noisy correspondence in multi-view clustering, arguing that real-world, web-crawled pairs contain (i) category-level mismatches (same class but treated as negatives) and (ii) sample-level mismatches including both alignable mispairs and truly unalignable samples. It proposes a generative objective that maximizes the (marginal) joint likelihood over latent cross-view correspondences and optimizes it with an EM procedure: the E-step estimates a soft, many-to-many coupling via entropy-regularized optimal transport subject to GMM-guided marginals and augmented with a virtual node to absorb outliers; the M-step maximizes a weighted log-likelihood implemented with similarity-normalized scores, unifying InfoNCE as a special case.", "questions": "1.Please provide a sensitivity analysis for $\\rho$ and the number of Sinkhorn iterations?\n\n2.Please report the original category-level mismatch rate in the used datasets.\n\n3.What is the computational cost of the EM procedure? Specifically, how do the training time and GPU memory usage compare with those of DIVIDE?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "The paper treats cross-view links as latent variables and optimizing a likelihood bound provides a clean alternative to ad-hoc pair reweighting strategy. The design explicitly handles category-level relations (many-to-many couplings) and unalignable samples (virtual node), which prior methods largely ignore. \n\nExperiments on Scene15, LandUse21, Caltech101, and UMPC-Food101 show consistent gains under varying mismatch and corruption rates; visualizations indicate the learned posteriors approach class-level ground truth during training.", "weaknesses": "1.The proposed method depends on several manually tuned hyperparameters, such as the virtual mass $\\rho$ and the number of Sinkhorn iterations. The paper lacks a sensitivity analysis showing how performance varies with these values.\n\n2.While the paper qualitatively visualizes the estimated correspondences in Figure 3, it does not provide any statistics about the intrinsic mismatch level of the datasets used. Without knowing the original category- or sample-level mismatch rate, it is difficult to judge how challenging the benchmark setting is. \n\n3.The introduced EM-style framework, particularly the Sinkhorn-based E-step with virtual-node augmentation, likely incurs non-trivial computational overhead. The paper does not report training time or GPU memory consumption.", "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": "4DnwVF4fAP", "reviewer": "Reviewer_jwwK", "summary": "Multi-view clustering (MVC) leverages cross-view consistency but suffers from noisy correspondence (NC), including category-level mismatch and sample-level mismatch. This paper proposes a generative framework, CorreGen, which formulates NC learning as maximum likelihood estimation of underlying cross-view correspondences, solved via an Expectation-Maximization (EM) algorithm. In the E-step, soft correspondence distributions are inferred using GMM-guided marginals to down-weight noisy samples; in the M-step, the embedding network is updated to maximize expected log-likelihood. Extensive experiments on synthetic and real-world datasets demonstrate superior robustness.", "questions": "Please refer to the Weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.\tThis paper introduces a generative framework that reduces reliance on noisy predefined pairs by modeling latent correspondences, enabling more robust semantic structure learning.\n2.\tThis method effectively handles both category-level and sample-level mismatch via GMM-guided marginals and virtual samples, outperforming baselines on complex datasets.\n3.\tAblation studies show stable performance across varying curve-shaping parameters and noise rates, reducing hyperparameter tuning burden.", "weaknesses": "1.\tThis method may incur higher computational cost due to EM iterations, GMM fitting, and optimal transport computations, potentially limiting scalability to very large datasets.\n2.\tThis method relies on GMM assumptions, which may fail to model non-Gaussian embedding distributions, leading to suboptimal marginal estimates in complex data.\n3.\tThe experiments focus on two-view settings, limiting generalization to multi-view scenarios where correspondence inference becomes more complex.", "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": "seWqd0yXR1", "reviewer": "Reviewer_iE2N", "summary": "The paper addresses the challenge of noisy correspondence (NC) in multi-view clustering (MVC), which arises when data collected from the web contains misaligned or unmatchable samples. The authors distinguish two harmful types of NC: 1) Category-level mismatch: samples from the same class treated as negative; 2) Sample-level mismatch: mispaired or unalignable samples. To tackle this, they propose CorreGen, a generative EM-based framework that formulates correspondence discovery as maximum likelihood estimation. In the E-step, they estimate soft correspondence distributions using optimal transport constrained by GMM-guided marginals and augmented with virtual samples to absorb outliers. In the M-step, they update embeddings to maximize expected log-likelihood using these inferred correspondences. Extensive experiments on synthetic and real datasets show strong robustness with substantial improvements under both category- and sample-level mismatches.", "questions": "Please refers to the weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper shifts from discriminative pairwise reweighting/realignment to a principled maximum likelihood framework, reducing reliance on noisy pre-defined pairs.\n2. The proposed method consistently outperforms state-of-the-art baselines under varying mismatch and corruption rates, especially on the noisy UMPC-Food101 dataset.", "weaknesses": "1. While the EM-based optimal transport is elegant, they may introduce computational overhead when applied to very large-scale or high-dimensional datasets. The paper would benefit from a more detailed runtime analysis.\n2. The paper should clarify why the posterior weight $Q_{ij}$ is defined as $\\frac{\\boldsymbol{P}_{ij}^*}{\\boldsymbol{p}_i^{(v_1)}}$ in Equation (17).\n3. In Equation (17), the matrix ${Q}$ appears to serve as a re-alignment signal that guides the model's learning. It would be informative to analyze what happens if ${Q}$ is replaced with an identity matrix, and how would performance change if ${Q}$ were substituted with the ground-truth correspondence matrix?\n4. A minor presentation issue: on page 2, the text refers to Figure 2, but it seems this should be Figure 1.", "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": "JRrAfJXW35", "reviewer": "Reviewer_YFa9", "summary": "This paper addresses noisy correspondence in real-world multi-view clustering. The authors identify category-level mismatch and sample-level mismatch. The paper proposes a generative framework based on maximum likelihood estimation and optimized via an Expectation-Maximization algorithm. The framework infers a soft correspondence distribution in the E-step (guided by GMM-based marginals and optimal transport) and refines embeddings in the M-step. Experiments on four benchmark datasets demonstrate superior robustness under various noisy settings, including up to 80% mismatch rates.", "questions": "1）Could the authors provide a more comprehensive comparison with recent advances on incomplete multi-view and PVP problems, especially those published post 2022?\n2）Can the authors provide quantitative or visual evidence (e.g., convergence plots) to support the stability and convergence behavior of CorreGen’s EM algorithm?\n3）How does CorreGen compare with other OT-based multi-view methods in terms of robustness?", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "1）The paper presents a thoughtful formulation by explicitly distinguishing two realistic types of noisy correspondence in multi-view data, namely, category-level mismatch and sample-level mismatch, providing a solid rationale for why existing contrastive MVC methods fall short under such conditions.\n2）Instead of relying on pairwise contrastive learning, the authors shift to a generative modeling perspective, leveraging an Expectation-Maximization algorithm to uncover latent correspondences. This allows them to model complex many-to-many, probabilistic associations between samples across views.\t\n3）The method demonstrates consistently strong performance across diverse datasets and under various levels of noise and corruption.", "weaknesses": "1）The related work section does not adequately cover more recent progress, especially in areas concerning missing modalities and partially view-aligned representation learning.\n2）Although warm-start and momentum updates are mentioned as strategies to stabilize training, the paper does not provide convergence curve analyses.\n3）The paper does not include comparisons with recent methods that also employ optimal transport for multi-view clustering. Incorporating an experimental comparison with approaches such as “PROTOCOL: Partial Optimal Transport-enhanced Contrastive Learning for Imbalanced Multi-view Clustering” would strengthen the work.", "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 (Oral)