Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
Authors: Xihong Yang
Siwei Wang
Fangdi Wang
Jiaqi Jin
Suyuan Liu
Yue Liu
En Zhu
Xinwang Liu
Yueming Jin
Venue: ICML 2025 spotlightposter (2025)
Keywords: Multi-view Clustering; Contrastive Learning; Noisy Scenarios
Primary area: general_machine_learning->clustering

Abstract: Leveraging the powerful representation learning capabilities, deep multi-view clustering methods have demonstrated reliable performance by effectively integrating multi-source information from diverse views in recent years. Most existing methods rely on the assumption of clean views. However, noise is pervasive in real-world scenarios, leading to a significant degradation in performance. To tackle this problem, we propose a novel multi-view clustering framework for the automatic identification and rectification of noisy data, termed AIRMVC. Specifically, we reformulate noisy identification as an anomaly identification problem using GMM. We then design a hybrid rectification strategy to mitigate the adverse effects of noisy data based on the identification results. Furthermore, we introduce a noise-robust contrastive mechanism to generate reliable representations. Additionally, we provide a theoretical proof demonstrating that these representations can discard noisy information, thereby improving the performance of downstream tasks. Extensive experiments on six benchmark datasets demonstrate that AIRMVC outperforms state-of-the-art algorithms in terms of robustness in noisy scenarios. The code of AIRMVC are available at https://github.com/xihongyang1999/AIRMVC on Github.

Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
Xihong Yang" 12 Siwei Wang
Fangdi Wang' Xinwang Liu
Jiaqi Jin
Suyuan Liu Yue Liu En Zhu
Yueming Jin
Abstract
View
Infrared Scrsut
Leveraging the powerful representation learning capabilities, deep multi-view clustering methods have demonstrated reliable performance by effec- tively integrating multi-source information from diverse views in recent years. Most existing methods rely on the assumption of clean views. However, noise pervasive real-world scenar- ios, leading to a significant degradation per- formance. To tackle this problem, we propose novel multi-view clustering framework for the automatic identification and rectification of noisy data, termed AIRMVC. Specifically, we reformu- late noisy identification as an anomaly identifica- tion problem using GMM. We then design a hy- brid rectification strategy to mitigate the adverse effects of noisy data based on the identification results. Furthermore, introduce noise-robust contrastive mechanism generate reliable repre- sentations. Additionally, we provide theoreti- cal proof demonstrating that these representations can discard noisy information, thereby improving the performance of downstream tasks. Extensive experiments on six benchmark datasets demon- strate that AIRMVC outperforms state-of-the-art algorithms in terms of robustness in noisy narios. The code of AIRMVC are available at on
View2:
Video Sensor
View 3:
Sound Sansor
Figure I. An illustrative diagram of noise in multi-view scenario. In the diagram, the areas marked with red exclamation points indicate instances where sensor failures malfunctions specific moments lead to data corruption. Compared to other views, these instances are considered noisy data.
1. Introduction
In real-world scenarios, multi-soure information data is prevalent. To effectively handle such data, Multi-Viss Clustering (MVC) has emerged as a powerful unsupervised method. In recent years, MVC has gained significant atten- tion and has become a prominent focus of research. Existing MVC methods can broadly categorized into two main groups. The first group comprises traditional approaches, including Multiple Kernel Clustering (MKC) (Liu al., 2021), Non-negative Matrix Factorization (NMF) (Wen et al., 2018), subspace clustering(Zhou et al., 2019), and graph-based clustering (Liu et al., 2022a). With the advance- ment of deep neural networks, deep multi-view clustering algorithms (Yang et al., 2023b: Sun al., 2024), represent- ing the second category MVC methods, have garnered significant attention from researchers.
Github.
'Scoool of Computer, National University of Defense Technol- ogy, Changsha, Hunan. China "National University of Singapore, Singapore. IIttelligent Game and Decision Lab, Beijing, China, sihong_edus cdu@ co.. Correspondence Xinwang Liu <xin- wangliu@ nudt.edu.co edu.en>.
While existing MVC algorithms have demonstrated notable clustering performance, they predominantly rely on the as- sumption that the features from all views are clean. These approaches generally adopt a standard workflow: represen- tations are first extracted via an encoder, followed by
Proceedings of the 4nnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
feature fusion strategy, and then utilized for downstream clustering tasks. The integration of clean views enables the exploitation of complementary information from different perspectives of the same sample, resulting in enhanced per- formance compared to single-view clustering methods. This complementary information across views is instrumental in revealing the underlying cluster structures within the data. How can the complementary information across multiple views be effectively captured? Contrastive learning presents a paradigm that utilizes self-supervise techniques to learn cross- view consistency, ensuring coherent predictions across diverse views (Lu et al., 2024; Yang et al., 2023b; Xu et al., 2022b). Alternatively, self-training explores consistency by generating a unified cluster partition, thereby facilitating the discovery of complementary information (Xu et al.. 2022a: Wang et al., 2021).
verse effects of noisy data, thereby enhancing the robustness of the correction process. In this way, the adverse effects of noisy data could be mitigated. Furthermore, by carefully refining the soft predicted distributions, we design noise- robust contrastive mechanism to enhance the discriminative capacity of the learned representations. Furthermore, we conduct theoretical investigation of the contrastive mecha- nism to validate the stability and robustness of the learned representations. Extensive experiments conducted on six benchmark datasets demonstrate the effectiveness and ro- bustness of our proposed method. The key contributions of our paper are summarized as follows:
We reformulate the noise identification as an anomaly identification problem, solving it by GMM. Based on the results, we propose a hybrid rectification strategy to automatically correct the noisy data.
Although the aforementioned methods have demonstrated promising results, we identified notable limitations when applied to real-world scenarios involving noisy data. Fig. illustrates an example of noisy data in a multi-view setting, where three views are presented, and random noise exists within some of them. Moreover, we observed a significant performance degradation in existing methods under such noisy conditions (Tab, 4). The noisy data not only fail to contribute positively during multi-view feature fusion but also disrupt the underlying cluster structures. Moreover, the erroneous influence of noisy data introduces consid- erable bias in the optimization process, thereby diminish- ing the advantages of complementary information across views. Consequently, the performance of these methods may even fall below that of single-view models. Detailed experimental evidence supporting this claim is presented in Section. 5.3. Recently, some noisy-based deep nulti-view clustering methods have been proposed to alleviate the prob- lem. RMCNC (Sun et al., 2024) designed a noise-tolerance contrastive loss mitigate the impact for noisy correspon- dence. MVCAN (Xu al., 2024) employed un-shared network structure and designed two-level optimization for multi-view clustering. Although large improvement has been made, the exploration of noisy data in those methods remains focused on enhancing feature robustness. How- ever, they have yet to develop dedicated frameworks for the identification and rectification of noisy data.
A noise-robust contrastive mechanism is proposed to generate more reliable representations. Besides, we theoretically prove that the generated representations could discard noisy information to benefit the down- stream task.
We conduct extensive experiments on six benchmark datasets to verify the effectiveness and robustness of AIRMVC.
2. Preliminary & Problem Definition
In this paper, we focus on the multi-view clustering task with noisy inputs, as noise is a common occurrence in multi- source information inputs in real-world scenarios. To ad- dress this challenge, we aim to enhance the robustness of the network by automatically identifying and rectifying noisy data in an unsupervised multi-view setting. For simplicity, we provide the following symbolic definitions. Given a dataset (a*) J with V views and N samples, we define E and y as the extracted representations and the soft pre- dictions of class probabilities for each sample, respectively. The encoder network and decoder network are denoted as J (xx: O") and G'(E" 3"; oD), respectively. Additional nota- tions are summarized in Tab. 5 in the Appendix.
Most existing multi-view clustering (MVC) methods oper- ate under the assumption that the input multi-view data is both complete and consistent. In such idealized scenarios, the primary learning paradigm in MVC involves learning representations for V independent views, followed by the application of various fusion strategies to effectively extract and utilize shared information across the views. Although these models demonstrate strong performance under ideal conditions, we observe a significant decline in robustness when low-quality, noisy views are introduced, leading to substantial performance degradation. However, noise is a
To automatically identify and rectify the noisy data in multi- view scenario, we propose novel deep contrastive multi- view clustering framework, termed AIRMVC. Specifically, we reformulate noise identification as an anomaly identi- fication problem and introduce Gaussian Mixture Model (GMM) to address this problem. By substituting the la- tent variable of GMM with the soft prediction, we enable dynamic update of GMM parameters. Based on the identifi- cation results, introduce hybrid rectification strategy that employs an interpolation mechanism to alleviate the ad-
2

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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
View
View 2 (noise)
Mix Prediction
Clean
Hybrid Rectify
GMM
Classifier
Projector
View (Noise))
Identification & Rectification
View |
Noise-Rober Robust
Encoder
Decoder
True
8
Fabse
U2
Latent Space
Figure 2. Illustration of the overall framework of the proposed AIRMVC. Specifically, we first encode the input multi-view data to generate representations. Next, automatic noise identification and rectification strategy is introduced to mitigate the adverse impact of noisy data. Simultaneously, we propose a noise-robust contrastive mechanism to generate more reliable and discriminative representations for the downstream clustering task.
pervasive issue real-world scenarios. To further illustrate this problem, we conduct toy experiments involving cluster- ing tasks on BBCSport and WebKB datasets under different scenarios, including noisy multi-view, clean single-view, and clean multi-view conditions. From the experimental results are presented in Fig. 3 and Tab. 4, it can be observed that when confronted with noisy data, the model's perfor- mance degrades drastically, even performing worse than sing clustering. Therefore, it is critical to mitigate the adverse effects noisy data in multi-view clustering tasks. In the following sections, we detail our proposed strategies for the automatic identification and rectification of noise.
3.1. Noisy Identification
For a given multi-view dataset (="]== we utilize an en- coder network to generate the representations, expressed as E" FF ; O"). For each representation, it using a multi-layer perceptron (MIP) layer as the projector. Subsequently, we model its distribution using Gaussian Mixture Model (GMM). This process can be described as follows:
first pro-
K
((E)
q(Eqq=M
k=1
(I)
K
p(g k)N pk σk),
3. Methodology
where q E (1.2....... K} represents the discrete latent vari- ables. P4 and a denote the mean and variance, respectively. Assuming that q follows uniform distribution, the proba- bility of q k could be expressed as p(q k) 7- Based this, the posterior probability of assigning 2; to the k-th cluster can be calculated as:
To mitigate the negative impact of noisy data, we propose robust Automatic [dentification and Rectification deep contrastive Multi-View Clustering framework with noisy view, which termed AIRMVC. The overall framework of AIRMVC is presented in Fig. 2. Specifically, we begin with providing the detailed deseriptions of our AIRMVC, including three components, i.c., noisy identification, bybrid rectification, and the noise-robust contrastive mechanism. Then, we define the objective functions to optimize the whole model. Finally, we present the theoretical analysis of our designed noise-robust contrastive component.
Xak p(g: k|z,) x N(zzllue ox).
(2)
The discrete variables can correspond directly to the la- bels an ideal condition. The entire process can be op- timized and solved using the Aopectation-Maximiiine (EM) algorithm. However, real-world scenarios, noisy
3

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In this way, we obtain the soft prediction of a sample belong- ing to the k-th cluster (ux). Furthermore, we combine the model's predictions with the representation distribution in Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
data inputs are pervasive and unavoidable, leading biases in the optimization process. Thus, the identification and rectification of noisy data are critically important. In unsu- pervised scenarios, identifying noise remains a challenging task. To address this issue, we establish a connection be- tween the latent variable q and the model prediction y in an unsupervised manner. Specifically, we replace the assign- ment p(q: k|zz) with the soft prediction of the network p(y: k- The parameters of the GMM can then be computed as follows:
where represents the cluster of clean samples with higher mean value, while with lower mean value. Consequently, (p; can be inter- preted as the probability of a sample x; being clean, whereas ii denotes the probability of s; being noisy. Using Eq. (6), we can calculate the posterior probability that deter- mines whether a sample æi is clean, which is presented in Fig. 2(a).
corresponds to the cluster
3.2. Hybrid Rectification Strategy Design
E, Eiplyi = k. kl,;)
In Section 3.1, we estimate the probability &i of each sam- ple being classified as clean in v-th view. Following this, we propose hybrid rectification strategy to address noisy sam- ples. The details of the strategy are illustrated in Fig. 2(b), Specifically, we utilize a combination of predicted soft dis- tributions to perform noise rectification:
[4 = Norm
Eipiv: = k((z4)
(3)
ok Eip(v: (F, - (R, P&)TT
E,P(y- k12z))
where Norm means the lg normalization. Based on Eq. (3), we reformulate Eq. (2) by considering the intra-cluster dis- tance. Since we implement lg normalization, we have (E / (E - ) = 2 2E pa. the process of Eq. (2)
y = (2..-. v).
(7)
m = o x of +1
could be expressed by:
where m. represents the mixed soft prediction, and h(-) denotes the classifier head. We utilize multilayer percep- tron (MLP) with a softmax function as the backbone for h(-). In this paper, we focus on the unsupervised clustering task, where obtaining reliable supervisory information particularly challenging. Following previous noise-robust MVC methods (Huang et al., 2020; Yang al., 2023a; Sun et al., 2024; Yang et al., 2021), we assume the first view to be the clean view. Therefore, in Eq. (6), the mixed soft prediction is predominantly influenced by the clean samples. Conversely, as s approaches 0, the mixed soft prediction is adjusted based on the prediction of the first view.
Xik p(g: = k((x,)
- (E, - ) (E, - -mx) 12
exp
Σx exp - -EE -kh) (E, Max k2
(4)
exp (E) pn//ww)
Ex exp (E, pu px/0
an unsupervised manner and update them using the GMM. By formulating the GMM to model the distribution of rep- resentations and soft predictions, we transform the noisy identification problem into anomaly identification prob- lem. In a multi-view setting, if sample is clean, its soft predictions and cluster assignments should remain consis- tent across the different views. For a given sample x;, it is classified as either clean (normal data) or noisy (anoma- lous data). Based on the above analysis, we provide the conditional probability to determine the likelihood of x; containing clean information, which can be calculated as:
With the mixed soft prediction, we could provide the follow- ing rectification loss:
Lrs
m log (ui))
(8)
V
V=2
where y" represents the w-th soft prediction and v e [2....,V] VV. this manner, the noisy data could be rectified by the cross-entropy loss. A more detailed experimental analysis of the hybrid rectification strategy is presented in Section 5.3.
exp (E. Mgs/ Xy=gli = p(u- = qi x.) Es exp (E, pk/OR)
(5)
3.3. Moise-Robuss Contrastive Mechanism
Contrastive learning (Yang et al., 2024b) has been proven to be an effective technique for enhancing representation robustness. In this subsection, we propose noise-robust contrastive mechanism to further mitigate the impact of noisy data in multi-view clustering tasks. In unsupervised multi-view noisy scenarios, constructing positive and neg- ative sample pairs based solely on indices may result in
After that, we introduce a two-component GMM to auto- matically identify the clean probability of a given sample, presented as:
p(xy=ali) = a= + p(Xy=olis 0)
(6)
41
1-pi

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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
incorrect pairings (Sun al., 2024). Ensuring the reliability of sample pair construction is significant challenge. To im-
Table I. Statistics summary of six henchmark datasets.
Dataset
#Views
#Samples
#Clusters
prove the accuracy of pair construction, incorporate soft
BBCSport
2
544
5
predictions as an additional validation criterion. Similar to previous methods, the first step is to calculate the similarity between samples across views:
WebKB
1051
2
Reuters
5
1200
6
UCI-digit
3
2000
10
Caltech101
9144
102
sim E E2I2
s " ET)
(9)
STL10
4 13000
10
where sim(-) denotes the similarity function, e.g., cosine similarity. Next, present the noise-robust contrastive loss for i-th and j-th sample in m-th and n-th view as:
4. Theoretical Analysis
In this subsection, we examine the rationale behind our proposed noise-robust contrastive mechanism from a the- oretical perspective. For clarity, we provide the following definitions of symbols. Let and xx denote the input sam- ple and its positive sample in our noise-robust contrastive mechanism. and y/ represent the clean and noisy soft prediction, respectively. We consider E* as the represen- tations by maximizing the mutual information between and x+, i.e., E* I x-). ). Besides, we define I (1; yla+)) S 0 and [ y (x+) ) > n,. For input sample x. the clean soft prediction y, and the noisy soft prediction y'. we have:
gT = ) )(,)) 2 7}
(10)
(log(1- [ (E." EE)) + log(1 - (EE (.))),
where T is the confidence threshold used to control the construction of sample pairs for contrastive learning by se- lecting similar samples. As illustrated in Fig. green denotes correctly constructed sample pairs, while red indi- cates incorrect ones. Our proposed strategy significantly improves the accuracy of sample pair construction, thereby enhancing the overall reliability of the contrastive learning process. Then, the robust contrastive loss for all cross-view defined by:
Theorem 4.1. The representations E' retain clean informa- fion and discard noisy information, which can be presented
I(x;y) - S ((E":)) ((;;)), T(E::1/) s T(x;'') - +
1 Lcon V(V
(14)
gnn #
(11)
1=
For the input samples z, the corresponding pos- itive samples xt and prediction yı. could be interpreted as the relatively small information gain contributed by the positive samples x.. For the fixed and its positive samples x+, the information gain for the class prediction y is limited. In contrast, x+ contributes greater information gain to the noisy prediction 3/', which we regard as 7). By calculating the mutual information / (x,;; y:). Theorem. 14 demonstrates that the representations E" learned by the contrastive mech- anism could discard the noisy information while preserving the clean information. The proof is provided in Section A.2.
Remark:
3.4. Objective Function
Our proposed AIRMVC primarily optimized using three objective functions: reconstruction loss Cree. rectification loss Lys, and robust-noisy contrastive loss Lcon. To be specific. Free denotes the reconstruction procedure with autoencoder network to learn the representations E in latent space. The process could be formulated as:
V
N
Crea
| - (");
(12)
5. Experiments
where G" and F are the decoder and encoder network for w-th view, respectively. In summary, the overall objective function of AIRMVC is:
In this section, we perform a series of experiments to evalu- ate the effectiveness and advantages of our proposed method. Specifically, we aim address the following research ques- tions (RQs): RQ1: How does AIRMVC compare with other leading deep multi-vien clustering techniques in terms of performance? RQ2: What art the impacts of the compo- nents of AIRMVC to enhance multi view clustering results? RQ3: What clustering structures are identified by AIR- MVC? RQ4: What is the effect of parammtersseterss on the efficacy of AIRMVC?
L= Cree + a Crs + 3- Loons
(13)
where and 3 are the trade-off hyper-parameters. By op- timizing the overall objective function, AIRMVC could automatically identify and rectify the noisy data unsuper- vised multi-view clustering task. Due to the space limited, we present the training algorithm in Alg. in Appendix.
5

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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
Table Multi-view clustering performance on six henchmark datasets (Part 1/4).
The highest performance metrics are emphasized in red,
while the runner-up results are marked in blue.
Noisy Rate
10%
30%
50%
70%
Metric
ACCT
NMIT
PURT
ACCT
NMIF
PURT
ACCT
NMI
PURT
ACC1
NMI
PURT
CANDY
NeurIPS 2024
23.16
05.60
40.62
19.49
03.93
38.79
17.10
03.72
38.42
16.36
02.68
36.58
RMCNC
TKDE 2024
35.48
15.80
35.48
30.57
12.87
30.57
28.56
10.67
28.05
24.26
04.57
24.26
BBCSport
TGM-MVC
ACM MM 2024
37.28
08.39
40.84
36.37
06.33
38.82
30.19
05.81
30.40
25.13
04.16
25.13
SCE-MVC
NeurIPS 2024
47.06
15.96
47.98
45,40
15.67
45.96
43.57
12.72
45.22
39.73
12.95
39.46
MVCAN
CVPR 2024
44.85
18.99
44.85
39.15
15.81
39.15
26.65
1
25.97
24.26
06.57
23.76
DIVIDE
AAAI 2024
31.25
04.57
38.60
30.15
03.28
36.76
28.68
02.65
35,66
27.02
02.22
36.03
AIRMVC
Ours
49.45
28.63
49.44
45.59
20.11
47.24
45.04
23.34
53.13
40,99
16.52
45.59
CANDY
NeurIPS 2024
19.03
12.41
19.03
18.08
10.85
18.10
16.56
07.84
16.56
15.60
04.87
15.60
RMCNC
TKDE 2024
78.12
10.77
78.10
66.98
08.78
66.98
60.04
06.24
60.00
52.71
04.35
52.16
WebKB
TGM-MVC
ACM MM 2024
76.86
13.81
76.86
71.87
11.65
71.87
62.86
08.04
62.86
55,51
06.87
55.50
MVCAN
CVPR 2024
77.83
12.39
78.12
67.46
06.20
67.46
64,22
05.94
64.22
55.66
05.74
55.65
SCE-MVC
NeurIPS 2024
76.78
18.78
69.65
74.12
13.22
68.19
65.75
08.17
62.18
60.08
03.52
60.77
DIVIDE
AAAI 2024
66.41
15.14
69.28
53.66
10.91
57.65
52.24
07.70
56.26
51.38
05.60
55.34
AIRMVC
Ours
83.73
27.15
83.73
77.93
13.48
78.12
74.98
08.42
74.98
62.89
06.69
62.32
CANDY
NeurIPS 2024
24.58
08.50
33.75
22.17
08.09
33.08
20.83
05.57
29.25
18.83
04.44
26.75
RMCNC
TKDE 2024
39.42
24.21
41.83
35.83
16.96
37.83
30.17
10.92
31.67
26.83
09.07
28.75
Reuters
TGM-MVC
ACM MM 2024
31.28
09.05
31.53
30.30
08.51
30.30
26.44
06.78
27.59
23,90
04.58
25.42
SCE-MVC
NeurlPS 2024
43.25
22.89
43.23
41.25
20.00
41.92
39.92
22.42
39.09
39.33
19.87
39.08
MVCAN
CVPR 2024
45.25
23.50
45.50
37.67
14.53
38.75
29.67
14.04
30.25
23.25
18.47
25.08
DIVIDE
AAAI 2024
41.08
16.82
42,50
33.42
13.42
34.42
30,50
10.03
33.25
27.92
09.39
28.61
AIRMVC
Ours
48.25
26.34
48.25
46.67
23.54
46.67
44.83
21.72
45.58
41.75
20.91
42.33
5.1. Experimental Settings
ducted the PyTTrch (Imambi et al., 2021) platform using an NVIDIA A6000 GPU. For fair comparison, reproduce the results of all baselines using the original source codes and configurations provided by their authors. Our proposed AIRMVC is trained using the Adam optimizer (Kingma & Ba, 2014) with its default settings. To enhance the discrim- inative power of the network and obtain reliable soft pre- dictions in an unsupervised setting, we pre-train the model with an auto-encoder module for 100 epochs. The trade-off hyperparameters a and / are consistently set to 1.0. The maximal training epoch is set to 400 for all datasets. A de- tailed overview of the hyperparameter settings is provided in Tab. 7 in the Appendix.
To evaluate the effectiveness of the proposed AIRMVC framework, we implement comprchensive exper- iments on six widely used datasets: BBCSport, Reuters, Caltech101, UCI-digit, WebKB, SUNRGB-D, and STL10. Tab. provides detailed statistical information for all datasets. To simulate a noisy input environment, we ran- domly introduce noise into the multi-view input data x at varying proportions of (10% 30%, 50%, 70%, 90%}.
Datasets:
Evaluation Metrics: To provide a thorough evaluation of the model's clustering performance, we utilize three widely recognized metrics: Accuracy (ACC), Normalized Mutual Information (NMI), and Purity (PUR). To ensure a fair com- parison, all methods are assessed across 10 independent runs, and the average results are reported.
5.2. Comparison Experiments (RQ1)
In this subsection, we conduct comprehensive experiments to demonstrate the superior and effectiveness of our de- signed AIRMVC. To be specific, we compare with 11 state- of-the-art baselines with different noise ratio. The experi- mental results are presented in Tab. 2, 3, 6, 8, 9. We highlight the optimal results in bold red, and the sub-optimal results with blue. Due to the space limited, we present Tab. 6, 8, 9 in Section. A.3 of Appendix. From the results, we could observe the following observations:
Comparison algorithms: To showcase the broad applica- bility and superior performance of the proposed AIRMVC, we compare it against 11 state-of-the-art deep multi-view clustering methods. These baselines are categorized into two groups: classical deep multi-view clustering methods (CoMVC (Trosten et al., 2021), SiMVC (Trosten et al., 2021), MFLVC (Xu al., 2022b), DealMVC (Yang al., 2023b), SURE (Yang et al., 2023a), CANDY (Guo al.), DIVIDE (Lu et al., 2024). TGM-MVC (Wang et al., 2024a), and SCE-MVC (Wang et al., 2024b)) and noise-resilient deep multi-view clustering methods (RMCNC (Sun et al., 2024) and MVCAN (Xu et al., 2024)). Detailed informa- tion on these baselines is provided in Section. A.5 of the Appendix.
1) AIRMVC significaay outperforms state-of-the base- lines across most metrics and datasets. To be specific, com- pared to the best multi- clustering algorithm, AIRMVC achieves remarkable improvements by 2.39%, 9.64%, and 1. 1.46% w.r.t. ACC, NMI and PUR in BBCSport dataset with 10% noise. We analyze the reason is that AIRMVC could
Implement Details: In this study, all experiments are con-
6

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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
Table Multi-view clustering performance on six henchmark datasets (Part 2/4).
The highest performance metrics are emphasized in red,
while the runner-up results are marked in blue.
Noisy Rate
10%
30%
50%
70%
Metric
ACCT
NMI1
PURT
ACCT
NMIF
PURT
ACCT
NMI
PUR
ACC1
NMI
PURT
CANDY
NeurIPS 2024
80,90
67.70
80.90
72.30
61.19
72.30
67.10
54.94
67.10
63.10
52.50
65.20
RMCNC
TKDE 2024
27.40
14.74
29.50
25.20
12.17
26.80
23.65
11.22
25.30
22.20
10.10
24.05
UCI-digit
TGM-MVC
ACM MM 2024
60.23
65.08
64.89
59.52
64.03
63.60
56.31
60.23
60.25
$2.01
56.88
58.28
SCE-MVC
NeurIPS 2024
72.60
71.70
72.55
68.30
67.49
70.00
66.55
67.10
68.80
64.45
55.58
66.30
MVCAN
CVPR 2024
86.50
79.00
86.50
74.35
72.78
76.90
64.15
66.54
67.65
63.10
54.21
63.24
DIVIDE
AAAI 2024
88.20
80.28
88.20
76.00
71.56
78.45
71.00
62.80
74.20
66.25
54.72
68.25
AIRMVC
Ours
93.95
89.08
93.95
77.60
76.65
80.75
76.05
68.17
76.05
69.20
60.38
69.20
CANDY
NeurIPS 2024
16.67
16.93
19.67
15.87
16.62
19.19
10.64
10.91
10.94
10,98
15.14
17.35
RMCNC
TKDE 2024
08.75
16.57
08.71
07.20
16.02
07.21
06.94
12.87
06.87
06.71
11,58
06.71
Caltech101
TGM-MVC
ACM MM 2024
12.81
31.50
28.95
10.58
26.57
26.25
07.16
21.84
19.54
06.66
20.46
18.57
MVCAN
CVPR 2024
20.53
35.81
24.60
14.30
26.02
14.14
10.28
23.19
10.99
10,34
20.43
10:44
SCE-MVC
NeurIPS 2024
20.33
35,28
17.62
14.25
25.74
14.01
10.78
20.51
10.44
10.77
19.46
08 54
DIVIDE
AAAI 2024
18.03
35.40
20.41
15.10
25.80
20.08
11.10
23.33
16.33
10.16
18.88
14.87
AIRMVC
Ours
21.45
37.16
34.69
15.89
29.39
27.60
11.80
23,66
23.33
11.89
21.14
20.14
CANDY
NeurIPS 2024
27.08
21.03
27.33
20.56
19.23
20.21
18.19
18.48
18.77
17.49
16.79
17.80
RMCNC
TKDE 2024
16.51
03,56
16.92
15.85
02,94
16.22
14.78
02.33
15.12
14.12
01.70
14.95
STLIO
TGM-MVC
ACM MM 2024
27.50
19.51
28.10
21.80
21.62
21.65
20.01
20.02
20.78
19.87
14.05
19.77
SCE-MVC
NeurlPS 2024
27.58
23.97
27.05
20.77
19.34
20.92
18.45
14.51
20.10
15.85
12.60
16.93
MVCAN
CVPR 2024
26.64
24.05
26.57
21.62
20.17
20.52
19.36
20.01
19.09
17.25
17.96
17.37
DIVIDE
AAAI 2024
27.58
24.54
27.08
22.03
20.55
22.17
20.78
20.25
20.61
16.86
20.25
20.28
AIRMVC
Ours
28.81
25.04
29.01
22.46
23.64
22.46
21.95
23.09
22.02
20.14
22.66
20.14
Table 4. Performance variation of multi-view clustering on WebKB
dataset in noisy scenario with 10% noisy ratio.
Methods
TGM-MVC
SCE-MVC
Metries
ACC
NMI
PUR
ACC
NMI
PUR
Clean
81.45
15.70
81.45
83.43
20.64
83.43
Noise
76.86
13.814
76.86L
76.784
18,78
69.65]
Dan
Bonniyy Bestly Sinll
Saao Dara
Own
Dincct Rords Segle Narw
Neo Para
ACC
NMI
In summary, AIRMVC enables robust training under vary- ing levels of noise. Moreover, the above observations and experimental results further validate the effectiveness and generalization capability of AIRMVC.
Figure 3. Ablation studies for our proposed noisy-identification and rectification strategy on BBCSport dataset.
automatically identify and rectify the noisy data, leading to robust learning procedure.
5.3. Ablation Study (RQ2)
2) When noise is present in multi-view data, the perfor- mance of deep multi-view clustering models tends to be- come unstable. The clustering performance of the model cxhibits a downward trend as the noise proportion increases. We attribute this decline to the distortion of the underlying clustering structure caused by the presence of noisy data.
In this subsection, we conduct experiments to investigate the effectiveness of the components in AIRMVC. Due to the space limited, we present the experimental results with 30% noise ratio in Section. A.3.2 of Appendix.
Effectiveness of design modules: Here, we implement ablation studies verify the designed modules, including the noisy identification and rectification strategy and noise- robust contrastive mechanism. In this subsection, we denote "(w/o) D&R", "(w/o) Con", and "(w/o) D&R&Con" repre- sent the model to remove noisy identification and rectifica- tion strategy, noise-robust contrastive mechanism, and both modules combined, respectively. Besides, we leverage an autoencoder network as the backbone for "(w/o) D&R&Con" to derive representations for the downstream clustering task. We conduct experiments with three metrics on six datasets. The experimental results are demonstrated in Fig. 4. From those results, we could conclude the following observations:
3) Compared with the classical deep multi-view clustering methods, e.g., TGM-MVC (Wang et al., 2024a), our AIR- MVC could achieve better performance. These methods lack specifically designed strategies to mitigate the adverse effects of noise, which consequently leads to a decline in performance.
4) Although noise deep multi-view clustering methods could obtain promising performance, e.g., MVCAN (Xu et al., 2024), the impact of noise has not been fully eliminated in complex noisy scenario. The noisy identification and rectifi- cation strategies and noise-robust contrastive mechanism in AIRMVC could identify and rectify the noisy data. Thus, achieving better performance.
1) When any component of our designed model is removed, the performance of the model degrades. This indicates that
7

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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
SinviDait &Cm Tevoo Ca #0am
ACC
XMI BBCS
PER
10
STLI0
Reuters
Figure 4. Ablation studies on BBCSport, Caltech101, STLIO, and Reuters datasets with 10% noisy ratio.
20 Epoch
80 Epoch
1 140 Epoch
200 Epoch
Figure 5. Visualization of the representations during the training process UCI-digit dataset.
each part of our design contributes to the overall clustering performance.
the noisy views to mutually amplify their adverse effects. Furthermore, the fusion process exacerbates the impact of noise. Without rectification, the clustering performance of multi-view view data is even worse than that a single view.
2) The removal of noisy identification and rectification strat- egy ("(w/o) D&R") results in more substantial perfor- mance degradation compared the removal noise-robust contrastive mechanism ("(w/o) Con"), highlighting the rel- ative importance of noisy identification and rectification strategy to the model's 's performance.
2) Compared the directly rectification with the first view, our proposed AIRMVC could achieve better performance, This phenomenon be attributed to the tendency of di- rectly using the correction results from the first view to homogenize features across different views. In contrast, our noisy identification and rectification strategy effectively filters out noisy data from each view while retaining com- plementary information that is beneficial for downstream tasks.
Effectiveness of rectification strategy:
In AIRMVC, we rectify the noisy data with two steps. Specifically, we first employ two-component GMM to iden- tify the noisy data. Then, we rectify the noisy data based on identification result. To illustrate the adverse effects of noise, present experimental evidence in Tab. 4 using the WebKB dataset, demonstrating a significant performance degradation in noisy scenarios. This underscores the ne- cessity of designing strategy specifically targeted at noise identification and rectification. further validate the effec- tiveness of our noise identification and rectification strategy, conduct experiments the BBCSport dataset with 10% noise ratio. For comprehensive evaluation, define four different experimental setups. For simplicity, we use "Noisy Data" to represent the direct fusion noisy multi- view features, "Single View" to represent the results from a single noisy view, "Directly Rectify" to represent directly using cross-entropy with the first view rectify, and "Ours" represent our proposed strategy. The experimental results derive
5.4. Visualization Analysis (RQ3)
To visualize the latent representation space and assess the ef- fectiveness of AIRMVC, we employ t-SNE (Van der Maaten & Hinton, 2008) the visualization tool in experiments, Specifically, we extract representations from the UCI-digit dataset. The results, as shown in Fig. 5, reveal the following observations. As training progresses, the cluster structures within the UCI-digit dataset become increasingly distinct. By the 200th epoch, well-defined and distinguishable clus- structures have emerged. This observation demonstrates the capability of AIRMVC effectively uncover the latent cluster structures within feature representations.
presented in Fig. 3. From these results, the following observations:
5.5. Hapee--prrameter Analysis (RQ4)
In this subsection, conduct experiments to analysis the sensitivity of the hyper- ppeamerrraeeters in this paper.
1) Directly fusing noisy multi-view data results in the worst clustering performance. We attribute this phenomenon to the lack of any noisy rectification mechanism, allowing
Sensitive analysis of trade-off hyper-parameter a and (3:
8

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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
00
50
BDC3port
Web
Reuters
UC-dggt
60
50
40
10
20
20
02
64
3.5
58
68
0.
0.4
6.6
0.
ACC
NMI
PUR
Figure 6. Sensitive analysis on hyper- on six datasets with 10% noisy ratio.
60
50.
101
0.1
6.1
01
10
10
031
BBCSport-ACC
WebKB-ACK
Reuters-NMI
STLI0-PUR
50
40.
130
20
23
20.
10
10.
10
122
10
E01
BBCS
WebKB-NMI
Caltech101-N2
UCI-digit-NMI
Figure Sensitivity Analysis a and with ACC, NMI, and PUR on BBCSport, WebKB, Reuters, UCI-digits, Caltech101 and STL10 datasets with 10% noisy ratio.
To further examine the impact of the parameters and 3
Fig. 6. We have the following observation. As the threshold increases, the clustering performance of the model improves progressively. We attribute this to the fact that higher thresh- olds reduce the number of incorrect contrastive learning sample pairs.
on our model, we performed sensitive experiments on six datasets with 10% noise ratio. Specifically, we analyze pa- rameter values within the range of {0.01, 0.1, 1.0, 10}. Ac- cording to the results presented in Fig. 7. We could find the following observations. When a and 9 approach extreme values, the model's clustering performance deteriorates sig- nificantly. This decline can be attributed to the disruption of the balance in the loss function. We observe that the model achieves optimal clustering performance when the values of a and 3 are set to 1.0. Thus, we set the parameters to 1.0. 2) Compared to changes 33, variations a result more pronounced changes the model's performance. This indi- cates that the noisy identification and rectification module contributes more significantly to enhancing performance.
6. Conclusion
In this work, we present novel deep contrastive multi-view clustering network to automatically identify and rectify the noisy data (AIRMVC). In AIRMVC, we first consider the noisy identification as an anomaly identification problem. Then, based on the identification results, we introduce hy- brid rectification strategy alleviate the adverse impact of noisy data. After that. design noise-robust contrastive mechanism to obtain more discriminative representations. Moreover, we theoretical proof that the learned representa- tions could discard the noisy information. Comprehensive experiments conducted on six benchmark datasets validate the effectiveness and robustness of AIRMVC.
Sensitive analysis of threshold т:
We conduct experiments to evaluate the influence of the threshold parameter т. We varied the value of within the range of (0.2, 0.4, 0.6, 0.8). The results demonstrated in

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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
Acknowledgments
He, K., Fan, H., Wu, Y., Xie, S., and Girshick, R. Mo- mentum contrast for unsupervised visual representation learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 9729- 9738, 2020.
This work was supported by the National Science and Tech- nology Innovation 2030 Major Project under Grant No. 20222D0209103, the National Natural Science Foundation of China (project No. 62325604, 62441618, 62476281, U24A20323 and 62276271), and the Program of China Scholarship Council (No. 2024061 10009).
Hinton, G. E. Training products of experts by minimizing contrastive divergence. Neural computation, 14(8):1771- 1800, 2002.
Impact Statement
Hjelm, R. D., Fedorov, A., Lavoie S., Grewal, K., Bachman, P., Trischler, A., and Bengio, Y. Learning deep representations by mutual information estimation and maximization. arXiv preprint arXiv:1808.000 2018.
This paper presents work whose goal advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
Huang, J., Mo, Y., Hu, P., Shi, X., Yuan, S., Zhang, Z., and Zhu, X. Exploring the role of node diversity in directed graph representation learning. In Proceedings of the Thirty-Thine International Joint Conference on Artificial Intelligence, pp. 2072-2080, 2024a.
References
Chen, T., Kornblith, S., Norouzi, M., and Hinton, G. A simple framework for contrastive learning of visual rep- resentations. In International conference on machine learning, pp. 1597-1607. PMLR, 2020.
Huang, J., Shen, J., Shi. X., and Zhu, X. On which nodes does gen fail? enhancing gen from the node perspec- tive. In Forty-first International Conference on Machine Learning, 2024b.
Cover, T. M. Elements of information theory. John Wiley & Sons, 1999.
Dang, Y., Liu, Y., Yang, E., Guo, G., Jiang, L., Zhao, J., and Wang, X. Efficient and adaptive recommendation learning: A guided filtering framework to erase outdated preferences. ACM Transactions on Information Systems, 43(2):1-25, 2025a.
Huang, Z., Hu, P., Zhou, J. T., Lv, J., and Peng, X. Partially view-aligned clustering. Advances in Neural Information Processing Systems, 33:2892-2902, 2020.
Hyvärinen, A. and Dayan. P. Estimation of non-normalized statistical models by score matching. Journal of Machine Learning Research, 6(4), 2005.
Dang, Y., Liu, Y., Yang, E., Huang, M., Guo, G., Zhao, J., and Wang, X. Data augmentation as free lunch: Exploring the test-time augmentation for sequential recommenda- tion. arXiv preprint arXiv:2504.0m 0000:444440044,, 2025b.
Imambi, S., Prakash, K. B., and Kanagachidaambaresan G. Pytorch. Programming with TensorFlow: solution for edge computing applications, pp. 87-104, 2021.
Dong, Z., Jin, J., Xiao, Y., Wang, S., Zhu, X., Liu, X., and Zhu, E. Iterative deep structural graph contrast clustering for multiview raw data. IEEE Transactions Neural Networks and Learning Systems, pp. 1-13, 2023a. doi: 1.11009NNNSS220233.33
Kingma, D. P. and Ba, J. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 2014.
Li, X., Sun, Y., Sun, Q., Ren, Z., and Sun, Y. Cross-view graph matching guided anchor alignment for incomplete multi-view clustering, Information Fusion, 100:101941, 2023.
Dong. Z. Wang, S., Jin, J., Liu, X., and Zhu, E. Cross-view topology based consistent and complementary informa- tion for deep multi-view clustering. Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pp. 19440-19451, October 2023b.
Li, X., Pan, P. Sun, Y., Sun, Q., Sun, Y., W. Tsang, I., and Ren, Z. Incomplete multi-view clustering with paired and balanced dynamic anchor learning. IEEE Transactions on Multimedia, pp. 7087-7098, 2025.
Guo, R., Yang, M., Lin, Y., Peng, X., and Hu, P. Robust contrastive multi-view clustering against dual noisy cor- respondence. In The Thirty-iigtth Annual Conference on Neural Information Processing Systems.
Li, Z., Tang, C.,, Liu, X., Zheng, X., Zhang, W., and Zhu, E. Consensus graph learning for multi-view clustering. IEEE Transuctions on Multimedia, 24:2461-2472, 2021.
Hassani, K. and Khasahmadi, A. H. Contrastive multi-view representation learning on graphs. In International Con- ference on Machine Learning, pp. 4116-4126 PMLR, 2020.
Liu, S., Wang, S., Zhang, P., Xu, K., Liu, X., Zhang, C., and Gao, F. Efficient one-pass multi-view subspace clus- tering with consensus anchors. In Proceedings of the
10

---

Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
AAAI Conference on Artificial Intelligence, volume 36, pp. 7576-7584, 2022a.
Wan, X., Liu, J., Liang, W., Liu, X., Wen, Y., and Zhu, E. Continual multi-view clustering. In Proceedings of the 30th ACM International Conference on Multimedia, pp. 3676-3684, 2022.
Liu, x., Liu, I.., Liao, Q. Wang, S., Zhang, Y. Tu, W., Tang, C., Liu, J., and Zhu, E. One pass late fusion multi- view clustering. In International Conference on Machine Learning, pp. 6850-6859. PMLR, 2021.
Wan, X., Xiao, B., Liu, X., Liu, J., Liang, W., and Zhu, E. Fast continual multi-view clustering with incomplete views. IEEE Transactions on Image Processing, 33:2995- 3008, 2024. doi: 10.1 10.110997TP222243338877
Liu, Y., Tu, W., Zhou, S., Liu, X., Song, L., Yang, X., and Zhu, E. Deep graph clustering via dual correlation reduction. In AAAI Conference on Artificial Intelligence, 2022b.
Wang, F., Jin, J., Dong, Z., Yang. X., Feng, Y., Liu, X.,
Zhu, X., Wang, S., Liu, T., and Zhu, E. View gap mat- ters: Cross-view topology and information decoupling for multi-view clustering. In Proceedings of the 32nd ACM International Conference Multimedia, pp. 8431-8440, 2024a
Liu, Y., Yang, X., Zhou, S., Liu, X., Wang, S., Liang, K., Tu, W., and Li, L. Simple contrastive graph clustering. IEEE Transactions on Neural Networks and Learning Systems, 2023.
Wang. F., Jin. J., Hu, J., Liu, S., Yang, X., Wang, S., Liu, X., and Zhu, E. Evaluate then cooperate: Shapley-based view cooperation enhancement for multi-view cluster- ing. In The ehirty-eighth Annual Conference on Neural Information Processing Systems, 2024b.
Lu, Y., Lin, Y., Yang, M., Peng, D., Hu, P., and Peng, X. De- coupled contrastive multi-view clustering with high-order random walks. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 14193-14201, 2024.
Wang. Q., Ding, Z., Tao, Z., Gao, Q., and Fu, Y. Generative partial multi-view clustering with adaptive fusion and cy- cle consistency. IEEE Transactions on Image Processing. 30:1771-1783, 2021.
Mo, Y., Lu, Z., Yu, R., Zhu, X., and Wang. X. Revisiting self- supervised heterogeneous graph learning from spectral clustering perspective. In NewrlPS, 2024.
Mo, Y., Yu, R., Zhu, X., and Wang, X. Hg-adapter: Im- proving pre-trained heterogeneous graph neural networks with dual adapters. In ICLR, 2025.
Wen, J., Zhang, Z., Xu, Y., and Zhong, Z. Incomplete multi- view clustering via graph regularized matrix factorization. Proceedings of the European conference on computer vision (ECCV) workshops, pp. 0-0, 2018.
Sun, Y., Qin, Y., Li, Y., Peng, D., Peng, X., and Hu, P. Robust multi-view clustering with noisy correspondence. IEEE Transactions on Knowledge and Data Engineering, 2024.
Xu, J., Ren, Y., Tang, H., Yang. 7.,, Pan, I.., Yang. Y., Pu, X., Philip, S. Y., and He, L. Self-supervised discriminative feature learning for deep multi-view clustering. IEEE Transactions on Knowledge and Data Engineering, 35 (7)74770-742,, 2022a.
Tian, Y.. Krishnan, D., and Isola, P. Contrastive multiview coding. In Computer Vision-ECCC 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceed- ings, Part XI 16. pp. 776-794. Springer, 2020.
Xu, J.. Tang. H., Ren, Y., Peng, L., Zhu, X., and He, L. Multi-level feature learning for contrastive multi-view clustering. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 16051- 16060, 2022b.
Trosten, D. J., Lokse, S., Jenssen, R., and Kampffmeyer, M. Reconsidering representation alignment for multi-view clustering. In Proceedings of the IEEE/VF conference on computer vision and pattern recognition, pp. 1255- 1265, 2021.
Xu, J., Ren, Y., Wang. X., Feng, L., Zhang, Z. Niu, G., and Zhu, X. Investigating and mitigating the side effects of noisy views for self self-supervised clustering algorithms in practical multi-view scenarios. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 22957-22966. 2024.
Tsai, Y.-H. H., Wu, Y., Salakhutdinov, R., and Morency, L.- P. Self-supervised learning from multi-view perspective. arXiv preprint arXiv2006.005777 05576, 2020.
Van den Oord, A., Li, Y., Vinyals, O., et al. Representa- tion learning with contrastive predictive coding. arXiv preprint Xrviv: 0877003748 2(3):4, 2018
Yang, M., Li, Y., Huang, 7., Liu, Z., Hu, P., and Peng, X. Partially view view-aligned representation learning with noise- robust contrastive loss. In Proceedings of the IEFF/CVF conference on computer vision and pattern recognition, pp. 1134-1143, 2021.
Van der Maaten, L. and Hinton, G. Visualizing data using t-se.. Journal of machine learning research, 9(11), 2008.

---

Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
Yang, M., Li, Y., Hu, P., Bai, J., Lv, J., and Peng, X. Robust multi-view clustering with incomplete information. IEEE transactions pattern analysis and machine intelligence, ((LI):1055-169) 2023a.
Yin, M., Wang, H., Xu, X., Wu, L.,, Zhao, S., Guo, W., Liu, Y., Tang, R., Lian, D., and Chen, E. Apgl4sr: A generic framework with adaptive and personalized global collaborative information in sequential recommendation. In Proceedings of the 32nd ACM international conference on information and knowledge management, pp. 3009- 3019, 2023.
Yang. X., Hu, X., Zhou, S., Liu, X., and Zhu, E. Interpolation-bant contrastive learning for few-label semi-supervised learning. IEEE Transactions on Neu- ral Networks and Learning Systems, pp. 1-12, 2022. doi: 10.1 10.1109/TNNS. 2.22...186222..
Yin, M., Wang, H., Guo, W., Liu, Y., Zhang, S., Zhao, S., Lian, D., and Chen, E. Dataset regeneration for sequen- tial recommendation. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 3954 3954-3965, 2024.
Yang, X., Jin, J., Wang, S., Liang, K., Liu, Y., Wen, Y., Liu, S., Zhou, S., Liu, X., and Zhu, E. Dealmve: Dual contrastive calibration for multi-view clustering. In Pro- ceedings of the 31th ACM International Conference on Multimedia, 2023b.
Yu, H., Liang, K., Hu, D., Tu, W., Ma, C.,, Zhou, S., and Liu, X. Gzoo: Black-bor box node injection attack on graph neural networks via zeroth-order optimization. IEEE Transac- tions on Knowledge and Data Engineering. 2024a.
Yang. X., Liu, Y., Zhou, S., Wang. S., Tu, W., Zheng, Q.. Liu, X., Fang, L., and Zhu, E. Cluster-guided contrastive graph clustering network. In Proceedings of the AAAI con- ference on artificial intelligence, volume 37, pp. 10834- 10842, 2023c.
Yu, H., Ma, C., Wan, X., Wang, J., Xiang, T., Shen, M., and Liu, X. Dshield: Defending against backdoor attacks graph neural networks via discrepancy learning. Net- work and Distributed System Security Symposium, NDSS, 2025.
Yang, X., Tan, C., Liu, Y., Liang, K., Wang, S., Zhou, S., Xia, J., Li, S. Z., Liu, X., and Zhu, E. Convert: Contrastive graph clustering with reliable augmentation. In Proceedings of the 31st ACM International Conference on Multimedia, pp. 007999772222000 2023d.
Yu, S., Liu, S., Wang, S., et al. Sparse low-rank multi-view subspace clustering with consensus anchors and unified bipartite graph. IEEE Transactions on Neural Networks and Learning Systems, 2023a.
Yang. X., Chang, H., Lai, Z., Yang. J., Li, X., Lu, Y., Wang. S., Yin, D., and Min, E. Hyperbolic contrastive learning for cross-domain recommendation. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management, pp. 2920-2929 2929,99992222 2024a.
Yu, S., Wang, S., al. How construct corresponding anchors for incomplete multiview clustering. IEEE Trans- actions on Circuits and Systems for Video Technology, 34 (4):2845-2860, 2023b.
Yu, S., Dong, Z., Wang. S., et al. Towards resource-friendly, extensible and stable incomplete multi-view clustering. In International Conference on Machine Learning, pp. 57415-57440. PMLR, 2024b.
Yang. X., Min, E., Liang, K., Liu, Y., Wang, S., Zhou, S., Wu, H., Liu, X., and Zhu, E. Graphlearner: Graph node clustering with fully learnable augmentation. In Proceedings of the 32nd ACM International Conference on Multimedia, pp. 5517-5526, 2024b.
Zhao, C., Zhao, H., He, M., Zhang, J., and Fan, J. Cross- domain recommendation via user interest alignment. In Proceedings of the ACM Web Conference 2023, pp. 887- 896, 2023a.
Yang, X., Wang, Y., Liu, Y., Wen, Y., Meng, I.., Zhou, S., Liu, X., and Zhu, E. Mixed graph contrastive network for semi-supervised node classification. ACM Transactions on Knowledge Discovery from Data, 2024c.
Zhao, C., Zhao, H., Li, X., He, M., Wang, J., and Fan, J. Cross-domain recommendation via progressive structural alignment. IEEE Transactions on Knowledge and Data Engineering, 2023b.
Yang, X., Jing, H., Zhang, Z., Wang, J., Niu, H., Wang. S., Lu, Y., Wang, J., Yin, D.,. Liu, X., Zhu, E., Lian, D., and Min, E. Darec: A disentangled alignment frame- work for large language model and recommender system. In 2025 IEEF r/rd International Conference on Data Engineering (ICDE). IEEE, 2025a.
Zheng, Q., Yang, X., Wang, S., An, X., and Liu, Q. Asym- metric winged multi-view clustering network for exploring diverse and consistent information. Neural Networks, 179:106563, 2024.
Yang, X., Wang, Y., Chen, J., Fan, W., Zhao, X., Zhu, E.,, Liu, X., and Lian, D. Dual test-time training for out-of- distribution recommender system. JEEE Transactions on Knowledge and Data Engineering, 37(6))3312-3322 2025b. doi: 10. 1291//9KDDD 2.....2222.348161
Zhou, S., Liu, X., Li, M., Zhu, E., Liu, L., Zhang, C., and Yin, J. Multiple kernel clustering with neighbor-kerel subspace segmentation. JEEE transactions on neural networks and learning systems, 31(4):1351-136) 2019.
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Automatically Identify and Rectify; Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
A. Appendix
A.I. Notations & Related Work
A.1.I. NOTATIONS
In this subsection, we provide the notations in Tab. 5.
Table 5. Notation Summary in AIRMVC.
Notations
Meaning
V
The number of view
N
The number of samples in each view
K
The number of class
xx E y
The v-th input data from multi-view
The extracted representations The soft prediction of class probability
y'
The noisy soft prediction of class probability
F
The encoder network
g
The decoder network
The parameters encoder network
The parameters decoder network
m
The mixed soft prediction of class probability
h(-)
The classifier head
The clean probability
s())
Similarity function
a 3
The trade-off hyper-parameters
Crs
The rectification loss
Lcon
The contrastive loss
Lree
The reconstruction loss
A.1.2. RELATED WORK
Contrastive Learning: Contrastive learning (Yang et al., 2022), recognized for its ability to extract robust intrinsic supervisory signals, has attracted considerable attention in various fields, e.g., recommender system (Yang et al., 2025a;b; Zhao et al., 2023a;b; Dang et al., 2025b;a; Yin et al., 2023; 2024; Yang al., 2024a), graph learning (Liu al., 2022b; 2023; Yang et al., 2023c; 2024c; 2023d; Yu et al., 2025; 2024a; Mo et al., 2025; 2024; Huang et al., 2024b;a). The core concept of contrastive learning focuses on maximizing the similarity between positive samples while minimizing the similarity between negative samples within the latent space. Noise Contrastive Estimation (NCE) (Hinton, 2002; Hyvärinen & Dayan, 2005) was introduced, followed by InfoNCE (Van den Oord et al., 2018), which aimed at distinguishing different views of sample in the presence of others. Subsequently, methods like MoCo (He et al., 2020) and SimCLR (Chen et al., 2020) have advanced the learning of image-specific features by bringing positive pairs closer and pushing negative pairs further apart. In the realm of multi-view clustering, several contrastive learning approaches have been proposed (Tian et al., 2020; Hassani & Khasahmadi, 2020; Xu et al., 2022b). For instance, CMC (Tian et al., 2020) introduced contrastive multi-view coding framework to extract meaningful semantic information. MVGRL (Hassani & Khasahmadi, 2020) utilized graph diffusion matrix to generate augmented graphs, which were then leveraged to establish a multi-view contrastive mechanism for downstream tasks.
More recently. MFLVC (Xu et al., 2022b) proposed two objectives for multi-view clustering using high-level features and pseudo-labels within contrastive learning framework. DealMVC (Yang et al., 2023b) introduced dual-calibration mechanism specifically designed for deep multi-view clustering, with calibration contrastive loss that effectively differ- entiates similar yet distinct samples across multiple views. To further enhance the quality of contrastive learning sample pairs, DIVIDE (Lu et al., 2024) adopted random walk approach to iteratively identify reliable data pairs, thus improving the stability and robustness of contrastive learning in multi-view clustering. CANDY (Guo et al.) exploits inter-view similarities as contextual cues to uncover false negatives, while also integrating a spectral- denoising module to refine correspondence in multi-vies view settings. Contrastive learning, as a powerful method for improving feature quality, has proven
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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
highly effective in the MVC field. In this work, we propose noise-robust contrastive learning mechanism to enhance the model's performance and robustness in noisy environments.
Multi-view Learning: Recently, Multi-view Clustering (MVC) (Wan et al., 2022; 2024; Dong et al., 2023b;a; Yu et al., 2023a; 2024b; 2023b; Li et al., 2025; 2023; Zheng et al., 2024) has attracted substantial research interest. Existing MVC approaches can generally be divided into two categories based on cross-view correspondence: MVC with fully aligned data and MVC with partially aligned data. Fully aligned data assumes predefined mapping relationships between every pair of cross-view samples. Several methods have been developed under this assumption, which can be broadly grouped into five main categories: (1) Non-negativy matrix factorization based methods (Wen al., 2018), which aim to discover shared latent factor to integrate information from multiple views; (2) Kernel learning- based methods (Liu et al., 2021), where predefined set of base kernels is assigned to each view, and the kernel weights are optimally fused to improve clustering performance; (3) Subspace-basee methods (Liu et al., 2022a), which assume that all views share a common
latent space and derive clustering results by learning this shared representation; (4) Graph-based methods (Li et al., 2021), which construct a unified graph from multi-view data and utilize spectral decomposition to obtain clustering outcomes; and (5) Deep learning-basee based methods (Yang et al., 2023b), which leverage the powerful representation capabilities of deep neural networks to capture more complex and robust features for clustering.
While these methods have shown strong clustering performance, they typically assume that the features of all views noise-free. In real-world scenarios, however, noise is often present and can significantly degrade their effectiveness. To address the challenge of noisy data, MVCAN (Xu et al., 2024) adopts an unshared network structure and introduces a two-level optimization strategy to enhance robustness in noisy settings. Similarly, RMCNC (Sun et al., 2024) incorporates a noise-tolcrant contrastive loss to counteract the effects of noise in multi-view data. Despite these advancements, existing methods still lack dedicated strategies for explicitly detecting and correcting noise.
To bridge this gap, this paper introduces novel multi-view clustering framework designed to automatically identify and rectify noise. This framework aims to enhance clustering performance and robustness in the presence of real-world noisy data.
A.2. Proof of Theorem. 14
In this subsection, provide the detailed proof of Theorem. 14.
Theorem A.1. The representations E" retain clean information and discard noisy information, which can be presented as:
[(x; v) - S 1 (EE 1(; T(E" : :0') S [x; - -
Proof. To proof Theorem. 14, we first present the following definitions. Definition A.2 (Mutual Information). The mutual information for the representations and input data in multi-view scenario could be expressed as:
I(E:2*) / J
(EEatt) P(E)
p(E, p(E, xt logg )log
dx+
dE
(15)
where x is the positive samples for E is the representations extracted by the encoder network in latent space.
Definition A.3 (Relationship for Mutual Information and Representation). The learned representations E by minimizing Eq. (10) maximize the mutual information, i.e., I(E; ".).
In detail, Eq. (10) maximizes the similarity of the positive samples while minimizing the similarity of negative samples. The estimate of E conditioned on + is more accurate since x= is the similar with æ. Therefore, the mutual information log p(F(=*) will increase by minimizing Eq. (10). The similar definition widely adopted in many other fields (Tsai et al., 2020; Hjelm et al., 2018). Based on Definition. A.3, we define E argmax (E; to denote the representations by minimizing the contrastive loss, i..., maximizing the mutual information.
p(E)
Definition A.4 (Mutual Information Constraint). For the input data æ, positive samples xT, the clean prediction y, and noisy prediction y', we define the mutual information constraint if exists [(:; y/ S and [(x; // > n,
14

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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
Specifically, For the fixed and its positive samples s+, the information gain for the class prediction y is limited. & could be interpreted small value of the information gain contributed by positive samples x+_ In contrast, x contributes greater information gain to the noisy prediction y', which we regard as 17.
Based on the above definitions, we present detailed proof. Similar to (Tsai et al., 2020), the first step is to proof the first inequality. With adopting the Data Processing Inequality (Cover, 1999) the Markov chain <> x -> E, for any E we have:
[(x S (E:
(16)
Therefore, we conclude I y) & ;3). Moreover, the learned representations E" maximize xE; and ;(E"; xx+) is
maximized at [(x; x, we could obtain:
((E"xx)) [(x; x a+), I(E"; x = [xx; x (1))
(17)
Thus, for distribution aexx,,,) y), we have
;(E"xx+) - 2( ;o+ll)) (y). By substitution, could obtain:
a(E";ar: ::y xxx;,=)= - [(;;; a (y)
(18)
After that, we have:
:() [x; t IEE: yyxx))
(19)
= -1(x; y) 1 (x; y + (E"))())))
Therefore, we have:
T(E"; :1E";) :) S [(;;)),
(20)
I(E": :y) 2 [(x; v) (xxy)/x)))>>>)))))))))>)))) 2 [x;
For the second inequality, we could obtain the following formula by expanding I(E*,y') 1/):
vE) = [(x;; [x; (x)) + 11'l=t)
(21)
Moreover, with the y Definition. A.4 and the Markov Chain y' y + + E, we have:
(() S 1xx;// - + (E"; (+) (xxE8') 11 (E';ylz*)
(22)
1(x;y)) -7 0
Therefore, we have completed the proof.
A.3. Additional Experimental Results
In this section, due to the limitation of the original paper pages, we conduct additional experiments including comparison experiments, sensitive analysis, and visualization analysis experiments.
A. COMPARISON EXPERIMENTS
We employ experiments with five deep multi-view clustering methods, i.e., SiMVC (Trosten al., 2021), CoMVC (Trosten et al., 2021), MFLVC (Xu et al., 2022b), DealMVC (Yang et al., 2023b), SURE (Yang et al., 2023a). The results are presented in Tab. 6, 8, 9. Especially, Tab. 9 presents the experimental results with 90% noisy ratio. From those experimental results, we could conclude the following observations.
AIRMVC consistently outperforms state-of-the-art baselines across various metrics and datasets. Specifically, on the BBCSport dataset with 10% noise, AIRMVC achieves notable improvements of 2.58%, 9.94%, and 2.56% in ACC, NMI, and PUR, respectively, compared to the best multi-view clustering algorithm. This improvement can be attributed to AIRMVC's ability to automatically identify and rectify noisy data, ensuring more robust learning process.
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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
100
120
80
40
40
20
NMI WebKB
PUR
ACC
NMI UCI-digit
PUR
Figure 8, Ablation studies on UCI-digit and WebKB datasets with 10% noisy ratio.
The presence of noise in multi-view data often destabilizes the performance of deep multi-view clustering models. As the proportion of noise increases, the clustering performance deteriorates. This decline can be explained by the distortion the underlying clustering structures caused by noisy data.
A.3.2, ABLATION STUDY
In this subsection, we conduct experiments to evaluate the effectiveness the components within AIRMVC. Due to space constraints, we present the experimental results under a 30% noise ratio.
We perform ablation studies validate the contributions of the designed components, including the noisy identification and rectification strategy and the noise-robust contrastive mechanism. Specifically, we use the following notations for the ablation models: "(w/o) D&R" refers to removing the noisy identification and rectification strategy. "(w/o) Con" denotes removing the noise-robust contrastive mechanism, and "(w/o) && Con" indicates the removal of both modules. Additionally, in "(w/o) D&R&Con," an autoencoder network utilized as the backbone to extract representations for downstream clustering tasks. We conduct experiments using three metrics across six datasets, with results shown Fig. Based on the results, we draw the following observations:
Removing any component from the proposed model results in noticeable performance degradation, demonstrating that each module contributes to the overall clustering effectiveness.
The removal of the noisy identification and rectification strategy ("(w/o) D&R") causes greater decline performance than removing the noise-robust contrastive mechanism ("(wlo) Con"), underscoring the critical importance of noise identification and rectification for maintaining robust clustering performance.
A.3.3. DETAILED
ANALYSIS
In this subsection, we conduct detailed experiments to analysis the sensitivity of the hyper-parameter and / in this paper. Sensitive analysis trade-off hyper-paramette a and 8:
To further examine the impact of the parameters and 3 on our model, we performed sensitive experiments on six datasets with 10% noise ratio. In particular, we analyze parameter values within the range of (0.01,0.1 1.0, 10). According the results presented in Fig. 10. We could find the following observations.
When a and 3 approach extreme values, e.g., 0.01, the model's clustering performance deteriorates significantly. This decline can be attributed to the disruption of the balance in the loss function. Besides, we could observe that the model achieves optimal clustering performance when the values of and 3 are set to 1.0. Therefore, we set the balance parameters to 1.0 in our experiments.
Compared to changes in 3, variations in a result in more pronounced changes in the model's performance. This indicates that the noisy identification and rectification module contributes more significantly to enhancing the model's performance.
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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
40
30
20
10
20
10
10
ACC
PUR
NMI
(Wi)) DARK
B(wiN) Con
OOrr
[WWe)D& &Con
(iewe)) D&R
(wio) Con
Ourr
#WW.BAAH
S(AA)AR BONNN Dun
BBCSport
STLI0
Reuters
15
30
45
10
15
PUR
ACC
XMI
PUR
(WIO)DA &Conn
El (wri) D&R
((m/l) Con
Ours
#(WKJBAR &Coe
FOK00 D&B
Bijeed Con
Oars
(mit) D&R
((ei)) Con
[(wejD&R &Cen
BOurs
WebKB
Caltech 101
UCI-digit
Figure 9. Ablation studies BBCSport, Caltech101, STL10, UCI-digit, WebKB and Reuters datasets with 30% noisy ratio.
Sensitive analysis threshold T:
We conduct experiments evaluate the influence of the threshold parameter т. We varied the value of within the range of {0.2, 0.4, 0.6, 0.83. The results are demonstrated in Fig. 6. Based the results, have the following observation. As the threshold increases, the clustering performance of the model improves progressively. We attribute this the fact that higher thresholds reduce the number of incorrect contrastive learning sample pairs, thereby enhancing the model's discriminative ability.
A.3.4. VISUALIZATION ANALYSIS
To gain deeper insights into the representations learned by AIRMVC, we leverage t-SNE (Van der Maaten & Hinton, 2008) to visualize the latent feature space. Specifically, we extract representations using the UCI-digit dataset and map them into a lower-dimensional space for visualization. The results, as shown in Fig. 11, reveal the following observations: as training progresses, the clustering struetures in the UCI-digit dataset become progressively epoch, well-separated and identifiable cluster structures are observed. These results highlight the effectiveness of AIRMVC in uncovering the intrinsic cluster structures of the data.
distinct. By the 200th
A.4. Setting Details of AIRMVC
Hyper-parancn Settings in our AIRMVC:
In this subsection, we report the statistics summary and hyyer-paramedte settings of our proposed method in Tab. 7.
Detailed information about the datasets:
The BBCSport dataset includes 544 sports news articles categorized into five classes: athletics, cricket, football, rugby, and tennis. Each document is described from three different views with dimensions of 2582, 2544, and 2465. This dataset is essential for research in multi-view learning, text classification, and natural language processing, offering a robust foundation for developing and evaluating advanced algorithms.
BBCSport':
R: Reuters is collection of documents. It contains 1200 samples, which can be divided into 5 classes. This
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Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
50-
40-
40
20
10
10
12
10
61
19
0.1
BBCSport-ACC
WCCKB-ACC
Reuters-ACC
STLI0-PUR
20
30
10
001
001
0.1
10
10
10
BBCSport-NMI
WebKB-NMI
Reuters-NMI
STLI0-ACC
73
40.
50
20
10
30
031
61
01
011
10
CO1
CDI
BBCSpprt-PUR
WebKB-PUR
Reuters-
STLIO-NMI
30
50
0.11
10
ED1
Caltech10)
Caltech101-PLS
Caltech101-NM
UCI-digit-NMI
Figure Sensitivity Analysis for and with ACC, NMI, and on BBCSport, WebKB, Reuters, Caltech101, UCI-digit, and STL10 datasets with 10% noisy ratio.
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Automatically
Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
20 Epoch
40 Epoch
60 Epoch
80 Epoch
100 Epoch
120 Epoch
140 Epoch
160 Epoch
180 Epoch
200 Epoch
Figure 11. Visualization of the representations during the training process on UCI-digit dataset.
Table Multi-view clustering performance on six benchmark datasets (Part 3/4). The highest performance metrics emphasized in red,
while the runner-up results are marked in blue.
Noisy Rate
10%
30%
50%
70%
Metric
ACC1
NMI
PURT
ACC²
NMI
PUR
ACC²
NMI
PUR
ACC1
NMI
PUR
SIMVC
CVPR 2021
42.83
11.90
46.88
39.52
12.48
41.54
35.29
11.02
40.07
32.35
05.09
36.76
BBCSport
CoMVC
CVPR 2021
39.71
05.38
40.62
37.50
04.03
37.13
35.48
02.13
35.85
32.17
01.62
35.48
MFLVC
CVPR 2022
46.87
18.69
46.87
44.12
15.49
44.12
40.51
14.44
40.51
39.15
12.18
40.43
DealMVC
ACM MM 2023
40.25
07.56
40.44
35.48
06.27
35.48
31.80
03.94
35.47
30.38
02.89
31.78
SURE
TPAMI 2023
35.26
12.80
37.24
32.35
10,27
36.51
31.55
08.23
36.47
29.27
06.84
26.31
AIRMVC
Ours
49.45
28.63
49.44
45.59
20.11
47.24
45.04
23.34
53.13
40.99
16.52
45.59
SIMVC
CVPR 2021
77.26
13.72
69.99 69.82
62.04
10,99
65.19
60.61
08.00
63.71
$5.00
06.80
56.43
WebKB
CoMVC
CVPR 2021
77.74
10.62
69.80
66.89
08.10
64.58
56,23
07.27
58.12
$4.42
05.17
$5.28
MFLVC
CVPR 2022
77.83
19.56
78.12
64.61
09.42
64.53
62.13
07.43
62.13
$8.61
03.07
$8.61
DealMVC
ACM MM 2023
66.03
15.02
65.27
60.32
04.85
60.32
$9.66
04.63
$8.47
$5.57
$5.57
SURE
TPAMI 2023
67.27
11,10
67.11
62.55
$8.92
$3,91
$7.71
AIRMVC
83,73
27.15
83.73
77.93
08.42
62.89
06.69
62.32
SiMVC
CVPR 2021
25.83
07.80
26.67
22.50
04.69
22.67
19.17
04.12
19.17
17.75
01.83
17.92
CoMVC
CVPR
25.92
06.35
24.50
22.67
05.47
22.67
19.75
02.92
19.75
18.25
01.93
18.25
Reuters
CVPR
34.92
21.24
36.00
31.08
17.94
29.50
29.91
15.77
30.33
27.42
12.07
27.42
DealMVC
ACM MM 2023
30.92
14.14
30.92
28.50
10.53
28.50
27.92
06.16
27.92
26.58
05.74
26.58
SURE
TPAMI 2023
28.35
07.13
28.90
25.58
06.14
26.18
24.57
04.63
25.23
23.07
03.43
23.27
AIRMVC
Ours
48.25
26.34
48.25
46.67
23.54
46.67
44.83
21.72
45.58
41.75
20.91
42.33
dataset is widely used for text classification, information retrieval, and topic modeling, serving as a benchmark for machine learning. also aids educational purposes by providing real-world example for hands-on practice in data analysis and model development, significantly advancing the understanding and solutions for text classification challenges.
UCI-digit": The UCI-digit Dataset, also known as the Optical Recognition of Handwritten Digits, contains handwritten digit images (0-9) represented as 8x8 grayscale matrices, resulting 64 features per image. Each image is labeled with the corresponding digit. This dataset is widely used in academic research for evaluating machine learning models in image recognition and classification, making it an invaluable resource for advancing pattern recognition and computer vision methodologies.
W The WebKB dataset features web pages from four Wisconsin universities, focusing both the content and the links between them. This dual-aspect dataset is ideal for research in web mining, hyperlink analysis, and multi-view learning, providing a comprehensive resource for developing and evaluating algorithms that explore relationships and content dynamics in academic web environments.
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Automatically Identify and Rectify; Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
Table 7. Haper--arameters Statistics in AIRMVC.
BBCSport
WebKB
Reuters
UCI-digit
Caltech101
STL10
Views
2
5
3
5
4
Samples
544
1051
1200
2000
9144
13000
Clusters
5
6
10
102
10
Learning Rate
le-4
le-4
le-5
le-4
le-4
le-4
T
0.8
0.8
0.8
0.8
0.8
0.8
1.0
1.0
1.0
1.0
1.0
1.0
3
1.0
1.0
1.0
1.0
1.0
1.0
Table Multi-view clustering performance on six benchmark datasets (Part 4/4). The highest performance metrics are emphasized in red, while the runner-up results are marked in blue.
Noisy Rate
30%
70%
ACC1
NMI
PUR
ACC1
NMI
PURT
ACC1
NMI
PURT
ACC1
NMI
PURT
SIMVC
CVPR 2021
30.50
30.14
31.10
26.50
19.00
26.50
23.45
18.01
23.70
19.95
11.80
20.00
UCI-digit
CoMVC
CVPR 2021
44.80
42.42
45.10
34.60
33.58
34.85
32.20
31.31
32.55
28.45
27.00
29.45
MFLVC
CVPR 2022
89.80
82.37
89.80
60.50
63.35
60.50
47.05
48.91
47.05
31.90
28.14
31.90
DealMVC
ACM MM 2023
84.85
80.98
84.85
70.80
67.38
70.80
65.55
62.12
65.55
48.90
49.82
48.90
SURE
TPAMI 2023
34,96
14.82
34.96
31.73
13.49
29
28.29
11.96
29.35
26.14
10.08
27.05
AIRMVC
Ours
93.95
89.08
93.95
77.60
76.65
80.75
76.05
68.17
76.05
69.20
60.38
69.20
SIMVC
CVPR 2021
14.88
10.98
16.28
11.72
6.55
12.98
10.79
5.57
11.94
9.63
5.05
10.97
Caltech101
CoMVC
CVPR 2021
15.00
12.92
15.80
14.34
12.26
15.49
10.04
11.66
10.42
9.58
6.53
9.95
MFLVC
CVPR 2022
19.63
20.27
21.78
14.87
16.52
14.33
10.59
13.76
10.79
9.60
6,80
9.63
De
ACM MM 2023
19.90
20.73
22.07
13.09
11.96
17.80
10.14
5.55
10.14
10.05
5.03
10.08
SURE
TPAMI 2023
7.44
17.91
16.29
7.09
15.85
16.03
6.84
14.57
15.01
6.33
12.58
10.62
AIRMVC
Ours
21.45
37.16
34.69
15.89
29.39
27.60
11.80
23.66
23.33
11.89
21.14
20.14
SIMVC
CVPR 2021
19.51
11.33
19.52
17.52
6.83
18.06
15.91
5.45
16.04
13.44
3.62
14.00
CoMVC
CVPR 2021
27.07
21.49
27.36
20.78
15.57
20.70
17.68
16.15
17.75
15.37
13.92
15.56
STLIO
MFLVC
CVPR 2022
24.39
23.34
24.39
21.14
20.19
21.47
20.58
21.92
20.14
19.08
18.24
19.08
DealMVC
ACM MM 2023
24.59
23.51
24.59
21.23
22.83
21.33
20.56
21.78
20.56
19.12
18.27
19.12
SURE
TPAMI 2023
21.14
6.72
21.66
19.36
5.87
20.76
18.34
5.64
19.11
17.33
5.45
18.15
AIRMVC
Ours
28.81
25.04
29.01
22.46
23.64
22.46
21.95
23.09
22.02
20.14
22.66
20.14
The SUNRGBD dataset, essential for indoor scene understanding, contains 10,335 samples across 45 categories, including RGB images, depth images, and 3D point cloud data. Each sample has detailed semantic annotations, covering object categories and spatial locations. This multi-modal dataset supports tasks like scene understanding, object detection, semantic segmentation, and 3D reconstruction. Researchers use SUNRGBD to develop and evaluate algorithms that integrate multi-modal information, advancing indoor scene analysis and computer vision research.
SUNRGBD':
STL10%: The STL10 dataset is key benchmark for unsupervised feature learning, deep learning, and self-taught learning. It contains 13,000 labeled images across 10 classes and 100,000 unlabeled images, each at 96x96 pixels with four views per image. This dataset enables model pre-training on unlabeled data, simulating real-world scenarios, and is crucial for evaluating feature learning and generalization capabilities, advancing representation learning and machine learning research.
Caltech1011 1017: The Caltech101 dataset is a widely used benchmark in machine learning and computer vision, consisting of 9, 144 samples categorized into 102 distinet clusters. It characterized by diversity and complexity, featuring five distinct views that provide complementary information for each sample. These views typically include different feature types representations, making it suitable dataset for evaluating multi-vies clustering and representation learning methods. Due to its rich and heterogeneous structure, Caltech 101 has become standard testbed for assessing the performance of clustering algorithms in handling multi-view and high-dimensional data.
Algorithm: Due to the limited space of the original paper, present the algorithm in this part. The detailed training
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20

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Automatically Identify and Rectify; Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
Algorithm Training Algorithm of our designed AIRMVC
Input: The multi-view dataset (= )== the epochs e; batch size B
Output: The clustering result R.
I: for to
2: E-Step: update the parameters {(uu, ow) in AIRMVC and the hm
3: M-Step:
4: repeat
Obtain representations by encoder network.
6:
Identify the noisy data with Eq. (6).
7:
Rectify the noisy data with Eq. (7).
8:
Calculate the rectification loss, contrastive loss, reconstruction loss with Eq. (8), (11), (12).
Calculate the total loss by Eq3(13).
10: Update model by minimizing with Adam optimizer.
11: until the epoch finishes
12:
end for
13: Output The clustering results R.
Table Multi-view clustering performance on benchmark datasets noise ratio. emphasized in red, while the runner-up results are marked in blue.
highest performance metrics are
Dataset
BBCSport
WebKB
Reuters
Metries
ACC1
NMI
PUR
ACC1
NMI
PURT
ACC1
NMI
PURT
SIMVC
CVPR 2021
29.78
04.15
35.85
52.43
04.60
56.47
16.92
01.08
17.00
CoMVC
CVPR 2021
30.33
01.59
32.75
51.67
03.85
50.15
16.67
01.41
16.67
MFLVC
CVPR 2022
37.13
07.14
32.52
56.14
01.68
56.14
21.33
04.35
21.33
DealMVC
ACM MM 2023
29.78
02.76
30.47
50.77
01.28
50.77
20.87
03.58
20.87
SURE
TPAMI 2023
28.20
03.13
24.26
52.98
04.20
56.61
21.18
02.82
21.75
CANDY
NeurIPS 2024
15.26
01.42
33.48
14.27
02.39
14.27
17.84
04.70
26.50
RMCNC
TKDE 2024
23,90
03.78
23.87
51.87
03.47
50.48
20.17
05.23
20.25
TGM-MVC
ACM MM 2024
17.38
03.57
17.38
50.24
05.21
50.24
20.58
03.87
20.58
SCE-MVC
NeurIPS 2024
37.62
08.47
37.28
51.67
01.20
51.67
16.67
04.76
16.67
MVCAN
CVPR 2024
23.34
01.79
24.68
57.71
03.05
57.15
19.41
04.97
19.83
DIVIDE
AAAI 2024
26.29
02.04
37.32
50.05
03.70
54.34
24.08
06.25
26.42
AIRMVC
Ours
39.52
09.33
40.26
59.18
05.36
60.08
33.50
20.60
35.35
Dataset
UCI-digit
Caltech101
STL10
Metrics
ACCt
NMI
PUR
ACC1
NMI
PUR
ACC1
NMI
PURT
SIMVC
CVPR 2021
15.55
08.64
16.00
07.78
03.16
09.61
11.72
01.71
12.66
CoMVC
CVPR 2021
24.15
26.41
26.95
08.61
05.55
10.56
12.63
08.21
12.75
MFLVC
CVPR 2022
29.25
29.18
29.25
08.43
05.29
08.98
18.04
13.93
18.04
DealMVC
ACM MM 2023
37.40
39.04
37.45
09.96
04.00
09.38
18.45
17.32
18.45
SURE
TPAMI 2023
23.92
08.83
25.13
06.21
10.41
06.85
16.93
04.97
17.59
CANDY
NeurIPS 2024
51.05
42.16
53.70
10.00
10.60
16.56
16.32
15.44
16.72
RMCNC
TKDE 2024
19.15
08.81
21.15
06.56
10.89
06.
13.35
01.26
13.57
TGM-MVC
ACM MM 2024
49.83
63.42
55.59
05.45
17.53
16.21
17.74
15.66
17.24
SCE-MVC
NeurIPS 2024
57.70
49,43
57.15
10.08
18.16
18.41
13.85
10.93
13.59
MVCAN
CVPR 2024
57.25
50.87
57.48
9.07
13.49
3.77
16.15
15.35
16.33
DIVIDE
AAAI 2024
57.05
50.09
57.75
9.02
15.85
13.28
18.09
12.00
18.63
AIRMVC
Ours
58.20
51.94
58.20
10.85
19.01
18.96
19.90
19.92
19.90
21

---

Automatically Identify and Rectify; Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios
process is presented in Algorithm.
A.5. Comparative Algorithms
In this paper, we compare our AIRMVC with baselines, including CoMVC (Trosten et al., 2021), SiMVC (Trosten al., 2021), MFLVC (Xu et al., 2022b), DealMVC (Yang et al., 2023b), SURE (Yang et al., 2023a), CANDY (Guo et al.), TGM-MVC (Wang et al., 2024a), SCE-MVC (Wang et al., 2024b) RMCNC (Sun et al., 2024), and MVCAN (Xu et al., 2024). We list the specific information of those methods as follows:
CoMVC & SiMVC (Trosten et al., 2021): CoMVC and SiMVC are deep multi-view clustering methods that avoid aligning all representations simultaneously. These methods incorporate a contrastive learning strategy to enhance clustering performance.
MFLVC (Xu et al., 2022b); MFLVC introduces two consistency objectives for deep multi-view clustering by employing contrastive learning strategies at both the high-level feature space and the semantic label space.
DeaIMVC (Yang et al., 2023b): DealMVC proposes dual-calibration mechanism tailored for deep multi-view clustering. Its calibration contrastive loss effectively distinguishes between similar yet distinct samples across multiple views.
SURE (Yang et al., 2023a): SURE addresses challenges related incomplete multi-view data by developing noise-robust contrastive loss. This approach is theoretically analyzed handle partially unaligned views and missing samples.
CANDY (Guo al.): CANDY leverages inter-view similarities as context uncover false negatives and integrates spectral-based module for denoising correspondence in multi-view scenarios.
TGM-MVC (Wang et al., 2024a): TGM-MVC employs tree-based framework to effectively capture the heterogencity between different views, offering a unique perspective on multi-view clustering.
SCE-MVC (Wang et al., 2024b): SCE-MVC adopts game-theoretic principles and Shapley values to address multi-view clustering challenges, providing innovative solution to enhance clustering robustness.
RMCNC (Sun al., 2024): RMCNC introduces noise-tolerant contrastive loss, designed to mitigate the impact of misaligned pairs in multi-view clustering tasks.
MVCAN (Xu et al., 2024); MVCAN employs an unshared network structure and implements a two-level optimization strategy, cnabling improved clustering performance in multi-view scenarios.
DIVIDE (Lu et al., 2024): DIVIDE utilizes random walk approach to progressively identify reliable data pairs, enhancing the stability and robustness of contrastive learning in multi-view clustering.
22


Reviews:
[{"review_id": "J9YNqriyPk", "reviewer": "Reviewer_qT2Q", "summary": "To mitigate the impact of noisy data on multi-view clustering models, this paper proposes a method capable of automatically identifying and correcting noise. Specifically, the authors reformulate noise identification as an anomaly detection problem. Then, they design a hybrid correction strategy to enhance model robustness. Extensive experimental results demonstrate the effectiveness of the proposed approach.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Experiments of time and space cost:** Thanks. Following your suggestion, we conducted time and space complexity experiments on the six used datasets with 10% noisy ratio. Specifically, we measure the training time per epoch for all baselines using seconds as the evaluation metric. The space cost experiments are conducted on an NVIDIA A6000 GPU, measured in gigabytes (GB). The results are presented in Tab.1 and Tab.2. From these results, we observe that the time and space costs of AIRMVC remain within an acceptable range. In summary, AIRMVC demonstrates promising clustering performance while maintaining a reasonable computational cost.\n\nTab.1 Time cost for AIRMVC.\n\n| Methods |              | BBCSports |  WebKB  | Reuters | UCI-dight | Caltech101 |  STL10  |  Avg.  |\n|:------------:|:------------:|:---------:|:-------:|:-------:|:---------:|:----------:|:-------:|:------:|\n|     CANDY    | NeurIPS 2024 |  0.0657   | 0.1206  | 0.2861  |  0.3325   |   3.2500   | 3.6200  | 1.2792 |\n|     RMCNC    |   TKDE 2024  |  0.1536   | 0.5148  | 0.4785  |  0.8962   |   3.9800   | 5.6800  | 1.9505 |\n|    TGM-MVC   |  ACM MM 2024 |  0.1206   | 0.2546  | 0.5931  |  0.6752   |   4.4200   | 6.2805  | 2.0573 |\n|    SCE-MVC   | NeurIPS 2024 |  0.1521   | 0.2675  | 0.6428  |  0.6028   |   4.0255   | 6.0865  | 1.9629 |\n|     MVCAN    |   CVPR 2024  |  0.1525   | 0.2756  | 0.4429  |  0.7636   |   4.3580   | 6.6210  | 2.1023 |\n|    DIVIDE    |   AAAI 2024  |  0.0795   | 0.1568  | 0.3524  |  0.3326   |   3.1350   | 3.6248  | 1.2802 |\n|    AIRMVC    |     Ours     |  0.0825   | 0.1486  | 0.3058  |  0.3390   |   3.0800   | 3.5200  | 1.2460 |\n\nTab.2 Space cost for AIRMVC.\n\n| Methods |              | BBCSports | WebKB | Reuters | UCI-dight | Caltech101 | STL10 | Avg. |\n|:------------:|:------------:|:---------:|:-----:|:-------:|:---------:|:----------:|:-----:|:----:|\n|     CANDY    | NeurIPS 2024 |    1.91   |  1.79 |   2.11  |    2.21   |    2.36    |  3.03 | 2.24 |\n|     RMCNC    |   TKDE 2024  |    1.88   |  2.55 |   1.96  |    2.16   |    2.46    |  2.99 | 2.33 |\n|    TGM-MVC   |  ACM MM 2024 |    1.47   |  1.64 |   2.06  |    2.20   |    2.54    |  2.35 | 2.04 |\n|    SCE-MVC   | NeurIPS 2024 |    1.57   |  1.72 |   2.30  |    2.26   |    2.70    |  2.45 | 2.17 |\n|     MVCAN    |   CVPR 2024  |    1.56   |  1.57 |   1.66  |    1.28   |    1.44    |  1.47 | 1.50 |\n|    DIVIDE    |   AAAI 2024  |    2.02   |  1.78 |   2.05  |    2.19   |    2.36    |  2.97 | 2.23 |\n|    AIRMVC    |     Ours     |    1.60   |  1.63 |   1.71  |    1.34   |    1.55    |  1.48 | 1.55 |\n\n**Explanation for symbol in Fig.2:** Thanks. In Fig. 2(a), (b), and (c), the dark blue color represents noisy data. Following your suggestion, we will provide a more detailed explanation in the final version.\n\n**Typos & Format:** Thanks. Following your suggestion, we will revise RQ3 and Eq.8 in the final version and review similar issues to enhance the overall presentation.\n\n**Details for visualization experiments:** Thanks. We visualized the latent space features extracted by the encoder from the UCI-Digit dataset using the t-SNE algorithm. The visualization was performed every 20 epochs for the first 200 epochs. The experiments were conducted on an NVIDIA A6000 platform. We will provide additional descriptions in the future.", "claims_and_evidence": "In the submitted version of the paper, the motivation for handling noise is clearly defined and illustrated in Figure 1. Additionally, the authors conduct experiments to verify that the presence of noise adversely affects multi-view clustering performance. The submitted version effectively clarifies the research problem.", "methods_and_evaluation_criteria": "In this paper, the authors conduct comprehensive experiments on six widely used benchmark datasets. The experimental results demonstrate that the proposed method effectively mitigates the impact of noise on clustering performance.", "theoretical_claims": "In Appendix A.2, the authors provide a mathematical proof, which theoretically supports the proposed method and enhances the credibility of the study.", "experimental_designs_or_analyses": "In this paper, the authors conducted extensive experiments, including comparative analyses under different noise ratios, comprehensive ablation studies, and sensitivity analysis experiments. Additionally, the methods compared in Tables 1 and 2 are all from 2024, ensuring a fair and up-to-date evaluation.", "relation_to_broader_scientific_literature": "Compared to previous studies, this paper proposes a more effective approach to handling noisy data. The experimental results further validate this conclusion.", "essential_references_not_discussed": "The comparison algorithms in the paper are primarily from 2024, incorporating the latest research methods.", "other_strengths_and_weaknesses": "S:\nI. The paper investigates novel methods to mitigate the impact of noise on models, which is a practical area of research.\nII. From the submitted version, it is evident that the authors provide theoretical analysis and conduct extensive experiments.\nIII. The proposed method is clearly described, making it easy to follow.\n\nW:\nI. The authors have conducted detailed experimental validation; however, there is a lack of validation regarding the time and space consumption of the proposed method. I recommend that the authors add experiments to address.\nII. Figure 2 presents the overall framework of the paper. In the upper part of view2, does the dark blue color represent noise? I suggest adding definitions and descriptions of the different colored data in the legend.\nIII. The authors divided the experimental section into four parts, with the fourth part being the sensitivity analysis of the parameters. This part is placed in Appendix A.3.3, but the appendix is labeled as RQ3 instead of RQ4, which needs to be corrected.", "other_comments_or_suggestions": "I. The paper contains a large number of formulas, and the vast majority of definitions and explanations are in accordance with the standards. However, in Equation 8 on page 4, the formula is too large and extends beyond the page. It needs to be adjusted.\nII. It is recommended to add more experimental details for the visualization experiments in Section 5.4.", "questions_for_authors": "See above.", "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": "KcnBtWKN5q", "reviewer": "Reviewer_6d3k", "summary": "The paper considers the problem of multi-view clustering in the presence of noise. In particular, a new approach is proposed that aims to detect noisy samples, characterized as outliers, and to rectify them based on the assumption that the first view is noise-free. In addition, the construction of the pairs in the contrastive loss is improved by taking into consideration the soft clustering labels.\n\n## Update after rebuttal\nAfter the additional clarifications provided by the authors, I have decided to increase my rating. While it still is based on relatively strong assumptions, which should be thoroughly discussed in a limitation section if the paper would be accepted, it could serve as an initial exploration of this setting.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Explanation for adding noise:** Thanks. Different with the noisy alignment, we simulate noisy scenarios by injecting standard Gaussian noise to the original views, excluding the first view. Specifically, we generate random Gaussian noise with the same shape as the view and inject it into the original views at a ratio of x%. The parameter x% scales the generated Gaussian noise, thereby simulating different levels of noise contamination. \n\n**Experiments on clean data:** Thanks. Following your suggestion, we conduct experiments on clean data with six datasets. The results are shown in Tab.1. Due to character limitations, more results can be found in Tab.1 at https://anonymous.4open.science/r/Res-11B2. From the results, we find that AIRMVC achieves promising performance in both clean and noisy scenarios.\n\nTab.1 Clean data performance\n|Datasets|UCI-digit|-|-|WebKB|-|-|STL10|-|-|\n|-|-|-|-|-|-|-|-|-|-|\n|Metric|ACC|NMI|PUR|ACC|NMI|PUR|ACC|NMI|PUR|\n|CANDY|85.45|77.99|85.45|35.15|10.55|34.74|28.15|22.68|28.15|\n|RMCNC|40.51|23.16|35.68|79.05|21.84|79.99|23.05|15.28|24.64|\n|TGM-MVC|64.35|65.76|69.40|79.64|16.61|79.64|28.18|20.86|28.51|\n|SCE-MVC|84.55|76.48|86.15|78.65|19.04|77.54|28.64|24.59|29.05|\n|DIVIDE|89.25|81.52|89.45|69.61|20.20|78.12|29.68|23.63|28.95|\n|Ours|94.55|90.10|94.55|80.65|21.54|80.65|30.26|24.88|30.95|\n\n**Explanation for assumption:** Thanks. We provide explanation from three perspectives.\n\n 1) Different with noisy data align, AIRMVC extends the definition of noisy by considering the presence of noise within views. Since we propose a method for detecting and correcting noise, an \"ideal\" view is required as a reference standard. In the unsupervised multi-view clustering scenario, there is no available label information. Therefore, we assume that the first view serves as an ideal view, acting as pseudo-supervision to correct noise in the other views. \n\n2) We show this assumption with a real-world multi-view scenario, i.e., the ideal view supplements and corrects the other views. For example, consider a case where the first view consists of high-resolution images, while the second view consists of low-resolution images. In the field of super resolution field, it is common to use high-resolution images (ideal view) to supplement information and guide the learning of low-resolution images (other view), e.g., 2019-ICCV-Guided Super-Resolution as Pixel-to-Pixel Transformation and 2021-CVPR-Robust Reference-based Super-Resolution via C2-Matching. Similarly, we select one view as the reference (\"ideal\") view to supplement and correct the other views. \n\n3) Previous works have regarded data partially align as noisy. During the model's testing phase, they use an alignment strategy to align the $v-1$ views to the first view, thereby fusing multi-view feature for clustering, e.g., CANDY (line 53 of https://github.com/XLearning-SCU/2024-NeurIPS-CANDY/blob/main/model.py) and RMCNC (line 236 of https://github.com/sunyuan-cs/2024-TKDE-RMCNC/blob/main/RMCNC_main/sure_inference.py). This alignment operation implies that these papers consider the first view as an ideal view. Therefore, although the scenario settings may differ, to maintain generality, we also treat the first view as an ideal view.\n\n**Explanation for baselines:** Thanks. Previous studies consider data partially align as noisy. In our work, we extend the definition of noise and explore a more common noisy scenario, where noise exists within individual views. Recently, MVCAN is the only work that explores the issue of noisy views, leaving no other methods available for direct comparison. MVCAN incorporated comparisons with numerous contrastive learning-based methods. Following this setup of MVCAN, we evaluated the performance of various algorithms under our proposed noisy setting. To further validate the effectiveness of our approach, we included the latest multi-view clustering methods from 2024 in Tables 1 and 2 of our submitted version. Moreover, our selection of a substantial number of contrastive learning-based methods is that contrastive learning could enhance both the model's robustness and discriminative capability. Therefore, in the absence of directly comparable methods, we select contrastive learning-based methods to demonstrate the effectiveness of our method. \n\n**Explanation for balanced clusters:** Thanks. Cluster balance is a widely adopted default assumption in clustering problems, and we follow this common assumption as well. Additionally, to further verify the cluster balance of samples, we conduct statistical analyses on the datasets used in AIRMVC. The results indicate that the sample classes in the utilized datasets are nearly balanced. Due to space limitations, detailed results can be found in Tab.2 in https://anonymous.4open.science/r/Res-11B2.\n\n**Typos & Presentation:** Thanks. Following your suggestion, we will correct the typos and further improve the presentation.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "While the setup is mostly reasonable, the type of noise added to the samples is not described. Based on the introduction and problem definition, the noise considered in this work is due to the image being corrupted, while previous referenced work mostly considers noise in the sense of alignment (are the two views representing the same object). However, how this noise has been added and how the X% of data in the experiments has been corrupted is unclear.\n\nRelated to this point, the proposed approach builds on the strong assumption of having one clean view for the rectification step. While the authors state that this is done following previous work with references provided, these prior works, to the reviewers knowledge make a different assumption where some data is known to be aligned and some misaligned and do not assume that there is one completely uncorrupted view. What is the effect if this assumption is not valid?\n\nIn summary, additional clarifications on this setup are needed to ensure that the evaluation is fair.", "theoretical_claims": "The paper includes a theoretical interpretation of the noise-robust loss in Theorem 4.1, which appears to be correct.", "experimental_designs_or_analyses": "As mentioned above, the experimental design is somewhat unclear when it comes to the addition of noise and clarifications are required. Beyond this, the experimental design appears sound. However, it would be beneficial to also report the clean performance for reference, despite the focus being mostly on the noisy setting.", "relation_to_broader_scientific_literature": "Within the extended multi-view clustering literature, there has been some work on designing more robust approaches. However, these have mostly been focusing on the design of approaches that are able to handle partial view alignment or incomplete views. While there are certain approaches that aim to address robustness to noise (such as Xu et al, CVPR 2024), it is a less explored domain and the paper contributes a new approach toward it.", "essential_references_not_discussed": "Overall, the reviewer believes that prior work is cited adequately, but believes that the paper would benefit from a clearer discussion of what noise problems the different baselines address, as the baselines are designed for different types of noise.", "other_strengths_and_weaknesses": "Overall, the paper addresses the interesting problem of corrupted views in deep multi-view clustering and the paper is mostly well-written and presents a set of relevant ablation studies to highlight the necessity of the different components. However, the presentation of the problem as well as how this relates to previous works on robustness in the multi-view space, which generally focus on another type of noise, should be improved. In addition it is based on a key assumption (first view is noise-free) and the effect of this assumption should be discussed, as it appears to differ from the assumptions in prior works and thus benefits the proposed approach.", "other_comments_or_suggestions": "The presentation of the problem formulation seems to have been moved out of Sec. 3, while it still is mentioned in Line 139 (can be removed).\nIn line 304, \"sub-optimal\" should maybe be \"runner-up\" or \"second best\".\nFor Table 4, state explicitly that this is the 10% noise scenario.", "questions_for_authors": "Please elaborate the experimental setup and comment on the effect of the assumption on the first view.\nThe work further leverages another assumption, which is the presence of balanced clusters in 3.1. Does this overly bias the model to clustering settings where there are balanced classes?", "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": "zFyTPb0GEz", "reviewer": "Reviewer_jA5D", "summary": "This paper addresses the challenge of noisy data in multi-view clustering by proposing a method called AIRMVC. Specifically, AIRMVC first formulates noise identification and employs a Gaussian Mixture Model (GMM) to achieve this. It then introduces a hybrid rectification strategy with an interpolation mechanism to mitigate the adverse effects of noisy data. The paper validates the effectiveness of AIRMVC on six multi-view clustering datasets.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Additional experiments:** Thanks. Following your suggestions, with NVIDIA A6000 GPU we conduct experiments on CIFAR10 dataset, which contains 60,000 samples, 4 views and 10 classes. Besides, YouTube is a comprehensive video platform. We extract facial images from videos as a real-world data source. These multi-view facial images may include low-quality samples, which are treated as noise in our analysis. The Youtube dataset comprises 38,654 samples, 4 views and 10 classes. Detailed statistic information of the datasets is demonstrated in Tab.1. From the results shown in Tab.2 and Tab.3, we conclude that AIRMVC could achieve reliable performance on both large-scale dataset and real-world dataset, demonstrating its generalization capability.\n\nTab.1 Statistic information of the datasets.\n| Datasets | Class | Sample | View |\n|:--------:|:-----:|:------:|:----:|\n|  Youtube |   10  | 38,654 |   4  |\n|  CIFAR10 |   10  | 60,000 |   4  |\n\nTab.2 Experiment on YouTube dataset. OOM  denotes out-of-memory during training process.\n| Metric |  CANDY |  RMCNC | TGM-MVC | SCE-MVC | MVCAN | DIVIDE |  Ours  |\n|:------:|:------:|:------:|:-------:|:-------:|:-----:|:------:|:------:|\n|   ACC  | 62.86  | 53.05  |  58.26  |  60.54  |  OOM  | 60.16  | 66.23  |\n|   NMI  | 70.06  | 65.27  |  55.91  |  64.22  |  OOM  | 65.38  | 70.94  |\n|   PUR  | 70.20  | 63.81  |  60.12  |  65.54  |  OOM  | 63.01  | 75.10  |\n\nTab.3 Experiment on CIFAR dataset.\n| Noisy   Rate |   0.1  |   0.1  |   0.1  |   0.3  |   0.3  |   0.3  |   0.5  |   0.5  |   0.5  |   0.7  |   0.7  |   0.7  |\n|:------------:|:------:|:------:|:------:|:------:|:------:|:------:|:------:|:------:|:------:|:------:|:------:|:------:|\n|    Metric    |   ACC  |   NMI  |   PUR  |   ACC  |   NMI  |   PUR  |   ACC  |   NMI  |   PUR  |   ACC  |   NMI  |   PUR  |\n|     CANDY    | 20.16  | 12.35  | 21.21  | 18.25  | 11.82  | 18.01  | 16.04  |  9.54  | 16.05  | 14.17  |  9.06  | 14.64  |\n|     RMCNC    | 19.25  | 11.52  | 20.58  | 18.26  | 10.64  | 19.25  | 16.45  |  8.68  | 16.25  | 15.05  |  8.14  | 14.99  |\n|    TGM-MVC   | 17.82  | 10.02  | 18.99  | 15.29  |  7.91  | 14.25  | 13.42  |  6.04  | 13.57  | 11.05  |  5.71  | 12.52  |\n|    SCE-MVC   | 18.25  | 10.55  | 19.54  | 18.02  | 10.00  | 18.57  | 15.15  |  8.02  | 16.05  | 14.23  |  7.64  | 13.16  |\n|     MVCAN    |   OOM  |   OOM  |   OOM  |   OOM  |   OOM  |   OOM  |   OOM  |   OOM  |   OOM  |   OOM  |   OOM  |   OOM  |\n|    DIVIDE    | 20.57  | 11.26  | 21.27  | 18.69  | 10.06  | 19.95  | 16.84  |  8.32  | 17.62  | 14.05  |  6.05  | 14.85  |\n|     Ours     | 22.62  | 13.71  | 23.34  | 21.67  | 13.24  | 22.52  | 20.08  | 12.49  | 20.83  | 17.68  | 10.25  | 18.26  |\n\n**Discussion with MVCAN:** Thanks. We discuss AIRMVC with MVCAN from three key perspectives: \n\n1) Optimization Strategy: MVCAN adopts a two-level iterative optimization framework, consisting of T-level and R-level optimization to refine the network. In contrast, In contrast, AIRMVC focuses on noise detection and correction using a Gaussian Mixture Model (GMM) and directly optimizes the network. \n\n2) Soft Label Acquisition: MVCAN employs a parameter-decoupled model to obtain view-specific representations and soft labels, mitigating the influence of noisy views. AIRMVC leverages a GMM trained with a shared projector and classifier to generate soft labels. \n\n3) Module Design: MVCAN incorporates unshared parameters, distinct clustering optimization functions, and a two-level iterative optimization approach. In comparison, AIRMVC introduces a dedicated noise detection and correction mechanism, along with a noise-robust contrastive learning framework to enhance model robustness.\n\n**Novelty of AIRMVC:** Thanks. The novelty of AIRMVC mainly contains the following perspectives. \n\n1) Leveraging GMM, we reformulate the noise identification as an anomaly identification problem and propose a hybrid rectification strategy to automatically correct the noisy data. \n\n2) We design a noise-robust contrastive mechanism to generate more reliable representations. Theoretically, we have demonstrated that the features generated by this mechanism are more beneficial for downstream tasks. \n\n3) Extensive experiments on different benchmark datasets to verify the effectiveness and robustness of AIRMVC.", "claims_and_evidence": "Not all claims are fully supported. For instance, the paper asserts that no prior work has developed dedicated frameworks for identifying and rectifying noisy data. However, MVCAN (Xu et al., 2024) appears to be an earlier attempt at addressing this issue but is not appropriately acknowledged.", "methods_and_evaluation_criteria": "While the method is designed to address the noisy view problem, the chosen datasets and experimental settings are not sufficiently justified.", "theoretical_claims": "No", "experimental_designs_or_analyses": "Not all experiments are well-designed. Firstly, the datasets used are relatively small (fewer than 13,000 samples), which limits the evaluation of the method’s scalability and generalizability. Secondly, the evaluations are conducted with hand-crafted noise rather than real-world noise, potentially affecting the practical applicability of the method.", "relation_to_broader_scientific_literature": "The paper designs a method for handling the noisy view issue in the multi-view clustering task.", "essential_references_not_discussed": "Although related works are cited, the paper lacks a sufficient discussion on MVCAN (Xu et al., 2024), which may lead to an overstatement of its contributions.", "other_strengths_and_weaknesses": "Strengths:\n\nThe proposed method achieves state-of-the-art performance on the six selected datasets.\n\nWeaknesses:\n\nThe novelty of the paper is questionable, as it overclaims its contribution to handling noisy views. MVCAN (Xu et al., 2024) may already have laid the groundwork for this problem.\n\nThe experimental evaluation is insufficient, relying on small-scale datasets and artificially introduced noise instead of real-world noisy data.\n\nI would consider improving my rating if the authors could give more clarifications or experiment results to address my concerns.", "other_comments_or_suggestions": "I look forward to seeing the method evaluated on large-scale datasets with real-world noise for a more comprehensive assessment of its effectiveness.", "questions_for_authors": "Please see the weaknesses", "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": "LWegRPCzKZ", "reviewer": "Reviewer_yWYk", "summary": "In this paper, the authors propose a novel multi-view clustering method AIRMVC for noisy scenarios. They formulate the noisy identification as the anomaly problem. Besides, a noise-robust contrastive loss is designed to enhance the model performance. Experiments on six datasets show the effectiveness of the proposed method.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Explanation for projector and classifier:** Thanks. We perform feature mapping and transformation in the latent space using a projector, and the sample predictions are obtained through a classifier. The projector and classifier are shared across different views. We will include the corresponding description in the final version.\n\n**Limitations & Future directions of AIRMVC:** Thanks. In AIRMVC, we made an initial attempt to identify and rectify noise in an unsupervised setting and designed a robust contrastive learning method to further enhance the robustness of the model. However, the correction process relies heavily on the accuracy of the predicted distribution, which is the primary limitation of AIRMVC. In the future, improving the accuracy of the predicted distribution and exploring other reliable supervisory signals will be promising research directions.\n\n**Large-scale motivation experiments:** Thanks. Following your suggestions, we conducted experiments on the Caltech101 and STL10 datasets with a 10% noise ratio. The experimental results are presented in Tab.1 and Tab.2. From these results, we observe the same conclusions as those described in the submitted version, presented as follows:\n\n1) Simply merging noisy multi-view data results in the most degraded clustering performance. This is primarily due to the absence of a noise rectification mechanism, which causes the negative effects of noisy views to compound each other. Moreover, the fusion process intensifies the influence of noise, leading to a scenario where multi-view clustering performs even worse than using a single view alone.  \n\n2) In comparison to directly correcting noise based on the first view, our proposed AIRMVC demonstrates superior performance. This advantage arises because direct correction from a single view tends to enforce uniformity across views, potentially suppressing essential complementary information. In contrast, our noise detection and rectification strategy effectively removes noisy samples from each view while preserving beneficial cross-view diversity, thereby enhancing the overall clustering performance.\n\nTab.1 Motivation experiments on STL10 dataset.\n\n| Metric |  Ours  | Directly Rectify | Single View | Noisy data |\n|:------:|:------:|:----------------:|:-----------:|:----------:|\n|   ACC  | 28.81  |      26.41       |    22.22    |   15.05    |\n|   NMI  | 25.04  |      24.25       |    19.04    |   10.78    |\n|   PUR  | 29.01  |      26.80       |    23.18    |   13.78    |\n\nTab.2 Motivation experiments on Caltech101 dataset.\n\n| Metric |  Ours  | Directly Rectify | Single View | Noisy data |\n|:------:|:------:|:----------------:|:-----------:|:----------:|\n|   ACC  | 21.45  |      18.62       |    15.26    |   11.25    |\n|   NMI  | 37.16  |      30.82       |    22.29    |   18.61    |\n|   PUR  | 34.69  |      29.52       |    20.18    |   16.28    |\n\n**Code:** Thanks. Following your suggestion, we will release the code in the final version.\n\n**Notation & Typos:** Thanks. We will add the notations of Eq.10 and correct the typos in page 7. Furthermore, we will review the entire paper to enhance the overall presentation.", "claims_and_evidence": "The motivation of AIRMVC is clearly articulated and supported by experimental validation. Additionally, extensive supplementary experiments are provided in the appendix to further reinforce the findings.", "methods_and_evaluation_criteria": "The authors investigate the problem of multi-view clustering in noisy scenarios, a challenge widely encountered in real-world applications. The proposed method is well-aligned with the stated motivation and is designed to enhance model robustness under noisy conditions, offering practical insights for real-world implementations.", "theoretical_claims": "The authors provide a theoretical proof for noise-robust contrastive learning for supporting the rationale behind this approach.", "experimental_designs_or_analyses": "The authors conducted extensive experiments, with most baseline methods being from 2024, effectively demonstrating the efficacy of the proposed approach.", "relation_to_broader_scientific_literature": "The paper presents a comprehensive and well-rounded literature review.", "essential_references_not_discussed": "The related work is well-presented and the literature review is thorough.", "other_strengths_and_weaknesses": "Strengths:\n\n1.The transformation of noise identification into an anomaly detection problem is an intriguing approach.\n\n2.This paper conducts extensive experiments comparing the proposed method with 2024 state-of-the-art approaches, and the comprehensive experimental results validate its effectiveness.\n\n3.Theoretical analysis demonstrates the robustness of the proposed contrastive learning mechanism in noisy environments.\n\nWeaknesses:\n\n1.In the noise identification module, both the projector and classifier are designed. Are these components shared across multi-views, or do they operate independently? The authors should provide a clear explanation regarding this aspect.\n\n2.The authors have not discussed the limitations of AIRMVC or outlined potential directions for future research.\n\n3.Although the authors conducted explanatory experiments in Figure 3 to support their motivation, they only utilized the relatively small-scale BBCSport dataset. It is recommended to perform experiments on larger datasets to further validate the motivation’s effectiveness.\n\n4.The authors should release the source code to enhance the reproducibility of the study.", "other_comments_or_suggestions": "1.The notation II in Equation (10) should be explicitly defined for clarity.\n\n2.On page 7, line 364, there is a typographical error in the quotation marks for \"w/o D&R&Con.\"", "questions_for_authors": "Please see Weaknesses and suggestions.", "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:

Meta-review: This paper investigates robust multi-view clustering in noisy scenarios. The reviewers acknowledge some strengths:

1）The research addresses an important problem in the field. 
2）A novel robust deep contrastive method for noisy multi-view clustering is proposed.
3）The paper provides comprehensive theoretical analysis and sufficient experimental validation.

Following rebuttal and discussion, all reviewers unanimously recommend acceptance.
Decision: Accept (spotlight poster)