PROTOCOL: Partial Optimal Transport-enhanced Contrastive Learning for Imbalanced Multi-view Clustering
Authors: Xuqian Xue
Yiming Lei
Qi Cai
Hongming Shan
Junping Zhang
Venue: ICML 2025 poster (2025)
Keywords: multi-view clustering
class-imbalanced learning
unbalanced optimal transport
partial optimal transport
Primary area: general_machine_learning->clustering
TL;DR: This paper addresses the critical challenge of class imbalance in multi-view clustering by formulating a partial optimal transport problem and class-rebalanced contrastive learning.

Abstract: While contrastive multi-view clustering has achieved remarkable success, it implicitly assumes balanced class distribution. 
However, real-world multi-view data primarily exhibits class imbalance distribution. Consequently, existing methods suffer performance degradation due to their inability to perceive and model such imbalance. To address this challenge, we present the first systematic study of imbalanced multi-view clustering, focusing on two fundamental problems: *i. perceiving class imbalance distribution*, and *ii. mitigating representation degradation of minority samples*. We propose PROTOCOL, a novel PaRtial Optimal TranspOrt-enhanced COntrastive Learning framework for imbalanced multi-view clustering. First, for class imbalance perception, we map multi-view features into a consensus space and reformulate the imbalanced clustering as a partial optimal transport (POT) problem, augmented with *progressive mass constraints* and *weighted KL divergence* for class distributions. Second, we develop a POT-enhanced class-rebalanced contrastive learning at both feature and class levels, incorporating *logit adjustment* and *class-sensitive learning* to enhance minority sample representations. Extensive experiments demonstrate that PROTOCOL significantly improves clustering performance on imbalanced multi-view data, filling a critical research gap in this field.

PROTOCOL: Partial Optimal Transport-enhanced Contrastive Learning for Imbalanced Multi-view Clustering
Xugian Xue
Yiming Lei? Qi Cai
Hongming Shan'
Junping Zhang'
Abstract
1. Introduction
While contrastive multi-view clustering has achieved remarkable success, it implicitly as- sumes balanced class distribution. However, real- world multi-view data primarily exhibits class im- balance distribution. Consequently, cxisting meth- ods suffer performance degradation due to their in- ability to perceive and model such imbalance. To address this challenge. present the first system- atic study of imbalanced multi-vien clustering, focusing on two fundamental problems: i. perceiv- ing class imbalance distribution, and ii mitigat- ing representation degradation of minority sam- ples. We propose PROTOCOL, a novel PaRtial Optimal TranspOrt-enhanceed COntrastive Learn- ing framework for imbalanced multi-view cluster- ing. First, for class imbalance perception, map multi-view features into consensus space and reformulate the imbalanced clustering as a par- tial optimal transport (POT) problem, augmented with progressive mass constraints and weighted KL divergence for class distributions. Second, we develop a POT-enhanced class-rebalance trastive learning at both feature and class levels, incorporating logit adjustment and plass-sensitive learning to enhance minority sample representa- tions. Extensive experiments demonstrate that PROTOCOL significantly improves clustering per- formance on imbalanced multi-view data, filling critical research gap in this field.
Multi-view clustering (MVC) (Fang et al., 2023; Peng et al., 2019) aims to group samples by integrating complemen- tary information across different views, inspired by hu- mans' ability to perceive their environment through multi- sensory integration (Xu et al., 2013; Chidambaram et al., 2023). With the advancement of deep learning, Deep MVC (DMVC) (Chen al., 2022; Liu et al., 2023) has emerged as the dominant paradigm for its superior performance.
Contrastive multi-view clustering, which combines con- trastive learning with K-means, has become the leading approach in DMVC (Lin et al., 2023b; Li et al., 2022). By treating multi-view features as positive pairs, this ap- proach has achieved significant advances in semantic consis- tency (Xu et al., 2022; Tian et al., 2020; Zhang et al., 2024c), feature discriminability (Lin al., 2023b; Yan et al., 2023; Trosten et al., 2021), and view difference robustness (Xu et al., 2023; Trosten et al., 2023), However, these meth- ods implicitly assume balanced class distribution, which may not hold in real-world multi-view data where class imbalance prevalent. For example, in wildlife monitor- ing systems (Pan et al., 2024), multiple cameras capture rich visual information about animals, yet rare species (e.g., Siberian tigers) are significantly underrepresented compared to common ones (e.g., wild rabbits). Consequently, existing methods suffer significant performance degradation due to their inability to perceive and model such imbalance (Zhang et al., 2023b; Han, 2023).
con-
These observations lead us to think the following question:
'Shanghai Key Laboratory Intelligent Information Process- ing. College of Computer Science and Artificial Intelligence, Fu- dan University, China. *College of Computer Science and Tech- nology, Qingdao University, China. "Shanghai Key Laboratory of Navigation and Location-based Services, School of Electronic Information and Electrical Engincering, Shanghai Jiao Tong Uni- versity, China. "Institute of Science and Technology for Brain- Inspired Intelligence and Key Laboratory of Computational Neuro- science and Brain-Inspired Intelligence, Fudan University. China. Correspondence to: Junping Zhang <jpzhang @ fudan. edu. Yiming Lei <leiyiming @ gdu.edu.cn>.
How to effectively perceive and model class imbalance distribution under unsupervised multi-vier settings?
To tackle this challenge, we decompose it into two funda- mental scientific questions. First, address Q1: how to perceive class imbalance distribution. Our method draws inspiration from two domains: supervised imbalanced clas- sification (Cui et al., 2024; Suh & Seo, 2023; Wang et al., 2023) that leverages ground-truth labels, and self-labeling methods (Asano et al., 2020; Tai et al., 2021; Chapel et al.,
Proceedings of the ndnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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PROTOCOL: Partial Optimal Transport-enhanee Contrastive Learning for Imbalanced Multi-view Clustering
2020) that automatically assign labels during representa- tion learning. This inspires to generate pseudo-labels that align with imbalance class distribution. We propose an imbalance-aware multi-view framework that combines POT with unbalanced optimal transport (UOT) to generate POT labels. This framework en- ables dynamic transportation from sample distribution to the underlying imbalanced class distribution while effectively integrating information across different views.
We propose a POT-enhanced class rebalanced contrastive learning method for imbalanced multi-view clustering, which mitigates representation degradation of minority samples through feature-level logit adjustment and class- level class-sensitive learning.
optimize self-labeling
2. Related Work
2.1. Deep multi-view clustering
Building upon our solution to Q1, we address a second critical challenge Q2: how to mitigate representation degra- dation of minority samples. When using imbalanced POT labels, contrastive learning tends to bias towards dominant classes, leading to degraded representations of minority samples (Suh & Seo, 2023). While supervised methods like resampling (Gao et al., 2023), class-sensitive learning (Han, 2023), and logit adjustment (Cui et al., 2021) can address this issue using ground-truth labels, our unsupervised setting requires a different approach. To this end, we leverage POT labels as weak supervision signals and develop a two-level rebalancing strategy: logit adjustment at the feature level and class-sensitive learning at the class level, effectively enhancing the representations of minority samples.
Deep multi-view clustering primarily encompasses two di- rections based on data completeness: Deep complete Multi- View Clustering (DMVC) and Deep Incomplete Multi-View Clustering (DIMVC).
DMVC focuses on effectively utilizing consistency and complementary information in multi-view data. Recent stud- ies have advanced along three key aspects. 1) View Repre- sentation Enhancement. CoMVC (Trosten et al., 2021) pro- poses simple method to avoid cluster inseparability caused by complete alignment; MFLVC (Xu et al., 2022) introduces a multi-level feature learning framework to resolve conflicts in multi-objective optimization; GCFAggMVC (Yan et al., 2023) strengthens sample structural relationships through global and cross-view feature aggregation. 2) Semantic Consistency Improvement. SEM (Xu et al., 2023) develops self welfh-eigtting method to mitigate representation degra- dation caused by semantic inconsistency; CSOT (Zhang et al., 2024c) enhances multi-view semantic patterns through global semantic alignment; AECoDDC (Trosten et al., 2023) designs an end-to-end contrastive method incorporating DDC unsupervised loss (Trosten et al., 2021). 3) Robustness Enhancement. AR-DMVC and AR-DMVC-AM (Huang et al., 2024) addresses the vulnerability of DMVC models to adversarial attacks without explicitly defined attack targets.
While extensive research explored DMVC, the challenge of class imbalance has been overlooked, limiting its practical applications. To bridge this gap, we propose an imbalanced contrastive MVC method with three key stages. First, we learn view-specific representations through reconstruction loss. Second, we achieve semantic consistency through multi-view contrastive learning. Finally, we address class imbalance through two complementary components: imbal- ance perception and imbalance modeling. For imbalance perception, we reformulate the clustering problem by com- bining unbalanced OT with partial transport constraints, gen- erating POT labels through progressive assignment based on transport costs and dynamic mass adjustment. For im- balance modeling, we leverage these POT labels to adjust the model's s output distribution, effectively mitigating the representation degradation of minority samples.
DIMVC focus on scenarios with missing views (Fang et al., 2022). DSIMVC (Tang & Liu, 2022) proposes a dual-layer optimization framework that employs dynamic view com- pletion and sample selection to mitigate performance degra- dation caused by semantically inconsistent view completion.
These methods demonstrate competitive performance on balanced multi-view data. However, in Section 5, we show that class imbalance significantly impacts both complete and incomplete multi-view clustering, substantially degrading clustering performance and model robustness.
Our main contributions are summarized as follows:
We propose PROTOCOL, a novel imbalanced contrastive multi-view clustering method with three-stage collabora- tive optimization: view-specific feature learning, consen- sus representation learning, and imbalanced distribution modeling. Extensive experiments demonstrate its superior performance over existing methods.
2.2. Optimal transport and clustering
Optimal transport (OT) (Villani, 2009) has emerged as a powerful tool for distribution alignment in machine learn- ing. While traditional OT faced computational challenges, the introduction of entropy-regularized OT (Cuturi, 2013) with the Sinkhorn algorithm enabled its practical applica- tions. To address real-world scenarios with unequal mass
We propose a novel multi-view POT label assignment method that integrates partial optimal transport with un- balanced optimal transport to effectively perceive under- lying class imbalance distributions under unsupervised multi-view setting.
2

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PROTOCOL:
Partial Optimal Transport-ehhaneed Contrastive Learning for Imbalanced Multi-view Clustering
distributions, variants such as partial OT (Caffarelli & Me- Cann, 2010) and unbalanced OT (Chizat et al., 2016) were developed.
where 7/ and 72 control the degree of marginal constraint relaxation. Furthermore, partial OT (POT) introduces total mass constraint À to achieve the transport of partial samples:
The integration of OT in clustering has evolved from early Wasserstein K-means (Cuturi & Doucet, 2014) to deep learn- ing methods (Luo et al., 2023; Lin et al., 2023a; Zhang et al., 2024b; Ben- nen-Bouazza et al., 2022). SeLa (Asano et al., 2020) reformulates pseudo-label assignment as an OT problem. Recent methods addressing class imbalance have made significant progress. SLA (Tai et al., 2021) proposes class-propottional label assignment. DB-OT (Shi et al., 2024) develops dual-boundary constraints. P2OT (Zhang et al., 2024a) introduces progressive partial transport. These developments in OT, particularly its success in handling imbalanced data distributions, motivate our application of OT principles to imbalanced multi-view clustering.
(Q.C), min (EITa(rre)
(6)
where II c) = ={Q E Rexm Qlm S r, Q c, 7 Qlm -}
1Q1, 1n S
We integrate UOT with POT to perceive the underlying class imbalance distribution in multi-view data.
4. Methodology
This section first elaborates on the importance of imbalanced multi-view clustering research and its specific problem set- ting. To address this problem, we propose PROTOCOL, a novel PaRtial Optimal TranspOrt-enhanced COntrastive Learning method, which consists of two key modules: multi- view POT label assignment (Section 4.2) and multi-view class-rebalanced contrastive learning (Section 4.3). Finally, we present comprehensive overview of PROTOCOL and its training procedure in Section 4.4.
3. Preliminary
In this section, we review the development of OT and lay the foundation for our subsequent imbalanced multi-viww method. Given source distribution r and target distribution e, their empirical distributions can be represented as:
4.1. Motivation and Problem Setting
T: c= -, CjOy,'
where 6z, denotes the Dirac function, H; E X and y E Y are samples from the source and target domains respectively. r
Despite significant progress in recent years, most existing DMVC methods still focus on potentially uniformly dis- tributed datasets, which limits their practical applicability. In many real-world applications, datasets often exhibit im- balanced distributions, where the majority of data belongs to a few major classes while the rest is scattered across nu- merous minor classes. Thus, this paper investigates more practical problem setting: imbalanced multi- view cluster- ing, which faces two major challenges: (i) how to perceive class imbalance distribution in an unsupervised scenario; (ii) how to mitigate representation degradation of minority samples. These two challenges are tightly coupled: when the model perceives the class imbalance distribution of the data, it inevitably biases towards majority class samples, thereby leading to representation degradation of minority samples. The solutions to these two challenges are presented in Section 4.2 and Section 4.3, respectively.
Optimal transport theory aims to find an optimal transport plan Q x that minimizes the transportation cost:
min (Q,C), Qell(r.e)
(2)
where C' is the cost matrix, and the transport constraint set defined as:
II(r, c) = 1Q Ruxm QQ1 = c),
(3)
where 1m E Rmx1, 1n E Rax1 are all ones vector: To improve computational efficiency, Cuturi (Cuturi, 2013)
introduced an entropic regularization term H (Q), resulting in the regularized OT problem:
Problem Setting. Given a multi-view dataset {æ" E with imbalance ratio R, which contains N samples across V views, where x! IR denotes the D.- dimensional feature vector of the i-th sample from the e-th view. The imbalance ratio R is defined as the ratio between the number of samples in the smallest and largest clusters, i.e.,
min (Q.C) cQQ)). Qell(r.ee
(4)
R-xx.31V Jv Jo=1
This problem can be efficiently solved using the Sinkhorn algorithm. However, in practical applications. the masses of source and target distributions are often unequal. To address this, unbalanced OT (UOT) relaxes the marginal constraints through KL divergence:
R = min (ainn(na//max(me) k
(Q.C) + 7 Dxi. (Q1,.l7)) QEII(r.a)
min
where n& denotes the number of samples in the k-th cluster. The dataset contains K imbalance clusters to be discovered.
+ DKI (Q 1,l[c),
3

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PROTOCOL: Partial Optimal Transport-enhaneed Contrastive Learning for Imbalanced Multi-view Clustering
4.2. Multi-view POT Label Allocation
or E [0, 1] balances the importance between consensus and view-specific predictions.
We propose multi-view POT label allocation method that learns imbalanced class distribution of multi-view data through multi-view representation learning and POT-based self-labeling mechanism.
Imbalanced Multi-view Self-labeling. To learn the imbal- anced class distribution and avoid degenerate solutions, we add constraints that adaptively allocate labels to different clusters. Formally, the objective functioo for imbalanced multi-view self- soffllabelingss is:
4.2.1. MULTI-VIEW REPRESENTATION LEARNING
First, the raw data X" is transformed into latent represen- tations Z So (xx) E RR-xdd through a learnable en- coder network fe.. To better capture the underlying clus- ter patterns, the representations are refined into structure- aware features S" E RRNx by learning sample relation- ships through transformer attention mechanism (Vaswani et al., 2017). Finally, 5" from all views are aggregated to obtain the consensus representation U E R Mxd.
T E [0,1], Di=1 Ti,k 1, Di=1 T S X,
Vi,
min E(P,T) s.t. T.P
Vi
(12)
Vk
where À > is an adaptive parameter that adjusts the al- location for class k to account for imbalanced distribution. The constraints ensure that each data point is assigned to exactly one label, while allowing the N data points to be distributed among the K classes in a way that reflects the class imbalances.
Multi-view Prediction. Given U RNxdd we first map logits through cosine classifier h Rd K The predicted probability matrix P NNK is obtained by:
Optimal Transport Formulation. The above is an instance of combining unbalanced OT and partial OT. Let P N be the joint probability distribution predicted by the model, and T N be the assigned joint probability distribution. Using the concept of regularized OT (Cuturi, 2013), T is relaxed as an element of the transportation polytope:
P = softmax (of)
Similarly, for each view v E (1,..., V), obtain view- specific predictions:
Pr softmax(h(Z"))
(9)
U(r,c) == (T E E NxK Tik = rr T 1n = =c], (13)
4.2.2. SEBE-LABELING MECHANISM WITH POT
where 1k, 1N are all ones vector, so that r and c are the marginal projections of matrix T onto its rows and columns, respectively. In the imbalanced multi-vier scene, we require T be matrix of conditional probability distribution that splits the data adaptively, which is captured by:
Inspired by supervised learning with true labels y; the model would be trained by minimizing the cross-entropy loss:
1 N
EQQ UN)
log Qu..
(10)
A K
r
1N N
c=
1k-
(14)
where Q is the predicted label of the model. Studies have shown that supervised classification models can achieve su- perior performance with sufficient labeled data (Deng et al., 2009), which has led to extensive research on self-labeling methods (Lee et al., 2020; Zhang et al., 2023a; Li et al., 2023). Thus, we propose to incorporate self-labeling into multi-view clustering tasks. To address the requirement of true labels in Eq. (10), introduce posterior probabil- ity distribution (x)) (denoted matrix T E N where T., represents the probability of sample i belong- ing to class k) and propose a multi-view learning based cross-entropy loss:
With this notation, using Eqs. (5) and (6), we can rewrite the objective function in Eq. (12) as:
LPOT=
min -log (T (15) TEU(m.e)
where U- (TETRN Tik S ST,1,TI = A}:
here (-) is Frobenius dot-product, À is converted to the fraction of selected mass and will increase gradually, and is scalar factor. The first term is exactly L, the DKL term constrains cluster sizes, and the equality constraint ensures balanced sample importance.
1
N
K
4.2.3. PROGRESSIVE POT LABEL OPTIMIZATION
E(P,T) = N
Tu log Pi.k.
(11)
Progressive POT Label Assignment. The solution to the optimization problem in Eq. (15) yields the POT label ma- trix T, where each entry T, represents the probability of sample belonging to class k. The transport mass of POT
where aP ΣV=
p in which Pi,s and pd are obtained from Eqs. (8) and (9), respectively. Here
4

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PROTOCOL: Partial Optimal Transport-enhaneed Contrastive Learning for Imbalanced Multi-view Clustering
labels is regulated by A, which progressively grows to en- able the perception of class imbalance in multi-view data. Inspired by curriculum learning, when À is small in the early stages, only high-confidence samples from P are selected, minimizing the learning cost. As À increases, more sam- ples participate in learning until the completion of difficult sample label assignment. This process naturally integrates imbalanced distribution perception through X, eliminating the need for manual confidence thresholds.
concensus pr U2, and Gig represents the structural relationship between samples, with larger values indicating higher probability that samples belong to the same cluster.
In balaacebl scenarios, Eq. (19) effectively learns dis- criminative features as samples have sufficient opportuni- ties to construct stable cross-view positive pairs through D U.).. The structural relationships G.z. learned through the transformer's self-attention mechanism, capture the inherent similarities between samples, enabling effective similarityddisimiarryy mining through (1 - Gity)
Following (Tarvainen & Valpola, 2017; Laine, 2017; Zhang et al., 2024a), we update À by sigmoid ramp-up function:
However, when applied to imbalanced multi-view data, Eq. (19) leads to representation bias through two mech- anisms. First, from the sampling perspective, majority sam- ples dominate the mini-batch construction, resulting in more frequent positive pair formation through D((H,, U.)). while minority samples suffer from insufficient learning opportunities. Second, from the optimization perspective, although GG captures sample similarities through self- attention, the feature space becomes biased towards major- ity patterns due to their numerical advantage in contrastive learning, leading to compact clusters for majority samples but scattered distributions for minority ones.
A = = + (Amax \base) 5(1-))" (16)
where Abase and Amax define the range of transported mass, and T E [0, 1] represents the normalized training progress,
Efficient Scaling Solution. The optimal transport plan, i.c., the POT label matrix T", can be derived through efficient scaling algorithm:
T = diag(a) Mdiagbb).
(17)
where M = exp(- a and b are two scaling coef- ficient vectors that can be obtained through the following recursion formula:
To address the imbalanced multi-view representation learn- ing problem, we propose two-level rebalancing strategy that operates at both feature and class levels:
T Mb
b-
C² M
5
(18)
Feature-level Rebalancing. We introduce a logit-adjusted contrastive learning mechanism guided by POT labels:
where f = 3 converges. This solution elegantly combines the dynamic growth of X with efficient matrix scaling operations, en- abling the model to progressively assign POT labels while considering multi-view consistency. The complete deriva- tion can be found in Appendix A.
S+c' The recursion will continue until b
exp(P((H)) U.}) +n) log DE exp (P( ((HH;
E Cis (10) M Un
(20)
where 7): = llg (TT) is a logit-adjustment term, defined as the negative logarithm of the sample's cluster (pseudo label T7.) frequency. This term small for high-fequuenc classes, causing minimal logit impact, and large for low- frequency classes, significantly adjusting logits to enhance the importance of repres-eeresenned patterns and compen- sate for representation bias.
Through the learning of these components, PROTOCOL can effectively perceive the imbalanced distribution of multi- view data. This leads to the second challenge: how to mitigate representation degradation of minority samples, which will be addressed Section 4.3.
Class-level Rebalancing. We propose a balanced class alignment strategy that introduces consensus prototypes
4.3. Multi-view Class-rebalanced Contrastive Learning
While contrastive learning has become the de facto method in DMVC for learning semantically consistent representa- tions, its performance significantly degrades under class- imbalanced settings. To analyze and address this limitation, we examine GCTAggMVC (Yan et al., 2023), a representa- tive cructtre-guided contrastive loss:
C = {ci, C2 ..., cx) from POT label. The class-level loss is formulated as:
Σ
-w(p+) ) exp(pt - vb(x.)) Ep, exp(1x x/(2)))
(21)
Ree
P4 E.P.P. UP
D(H
fuvve (H..U
R
log
(19)
H.PHH,, U,
where
where D(HH),U,) = exp( F. M|| 7 measures the similarity between the level feature H and the
HU
w(p+)
Was p+ E Pd
(22)
Wt, p+ = T
5

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PROTOCOL: Partial Optimal Transport-enhaneed Contrastive Learning for Imbalanced Multi-view Clustering
Here w(p+) controls the contribution ratio between view- specific class Wa and consensus class Wt- To make good use of contrastive learning and rebalance the same time, we observe that W 0.8 and wi = 0.2 are a reasonable choice. The whole loss becomes closer to supervised cross-entropy.
Algorithm Multi-view Imbalanced Learning Framework
Input: {æ=)e== Je=1+ V, K, maximum iterations Ti, T2, T3
Output: T and consensus representation U
Stage 1: View-specific Representation
for = =1 Ti do
In addition, the transformation function v².) in Eq. (21) applies different strategies view-specific predictions P" and consensus prototypes T":
2" = So, "" = 9o. (Z")
1/
View-specific encoding
11
View-specific decoding
Minimize Lree
-
1==1 |/000
end for
p (.1(x))) p. ((4), PE P" p F(a)), p PET
Stage 2: Multi-view Representation Alignment
(23)
for t Ti to T2 do
S Transformer( (²) // Structure-aware features
where (a;)) is an identity mapping, and F(x;)) computes class-frequency based C address class imbalance:
H MLP(Z")
// High level features
U = Aggregate (15 11)=)) // Consensus features
p = softmax ( 1) // View-specific predictions
The
P = softmax (oftmax(h(U)))
Consensus predictions
F(x,) Iz Wor
We
(24)
Minimize Lalign = Σ (Lina (H"U) U) +
1=1 T&
Ssem (P", P))
Here, Wc normalizes class contributions based on their rela- tive frequencies in the training data, effectively rebalancing the influence of majority and minority classes during class alignment.
end for Stage Imbalanced Learning for T2 to do
Update Abase (Amax \base) e-((1-))
Overall Objective, The overall loss combines:
Compute M = = exx(-PPee)
Obtain POT labels via efficient scaling algorithm:
Cim C + Cre
(25)
Mb. b (MaTa
scm
T = Miag(a))MMaagl//
Through the two-level rebalancing strategy, our method ef- fectively addresses the class imbalance modeling challenge. At the feature level, adjit-adjusted contrastive learning en- hances the model's sensitivity to minority samples. At the class level, class-weighted consensus prototypes maintain global class consistency. This hierarchical design achieves balanced feature learning while preserving both instance discrimination and class structure, leading to robust repre- sentations for imbalanced multi-view data.
Minimize Lim = Lim + Lim // Rebalanced learning
end for
and class levels alignment:
Calign
w. (H (H" + Czem (P", P)), (27)
4.4. Overview and Training Strategy
where wy the adaptive weight for view v. The feature- level alignment loss Liea follows the structure-guided con- trastive loss in Eq. (19). The class-level alignment loss fyem ensures consistency between view-specific semantic pa and the common semantic P through:
PROTOCOL consists resentations:
consists of three stages to learn multi-view rep-
Stage 1: View-specific Representation. We employ a reconstruction-bent based pre-training strategy to learn basic view-specific representation through auto-encoding. The reconstruction loss is formulated as:
D(IP", P,))
Ceem
log K
(28)
(P) PI..,,
D((P., (,))
Lree
|000"
x"
(26)
where ". and 4" denote the input and reconstructed features of view v, respectively.
Stage 3: Imbalanced Learning. The final stage ad-
dresses the imbalanced learning challenge through POT- label-guided contrastive learning (See Sections 4.2 and 4.3).
Stage 2: Multi-view Representation Alignment. After pre-training, we conduct structure-guue guided fine-tuning for cross-view alignment. The loss function combines feature
These strategies enable PROTOCOL to handle imbalanced multi-view data, as summarized in Algorithm
6

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PROTOCOL:
Partial Optimal Transport-enhaneed Contrastive Learning for Imbalanced Multi-view Clustering
Table I. Statistics of the multi-view datasets.
Imbalance Ratio
Dataset
Samples
Classes
Views
View Features
0.1
0.5
/ /1lma
Hdigit (Chen et 2022)
10000
10
784,256
100/1000
500/1000
900/1000
Fashion (Niao et 2017)
10000
784,784,784
100/1000
500/1000
900/1000
NUS. WIDE (Chua al. 2009)
5000
14.225.144.73.122
100/1000
500/1000
900/1000
Caltech (Fei-Fei et al, 2004)
1400
7
5
100,25,.1984,51222
20/200
100/200
180/200
Cifarl0 (Yan ot al., 2023)
50000
10
512,2048,1024
500/5000
2500/5000
4500/5000
Table 2. Performance Comparison with R= 0.1
Hdigit
Fashion
Caltech
NUS-WIDR
Cifarl0
Methods
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
DSIMVC
0.754
0.790
0.902
0.699
0.685
0.755
0.430
0.656
0.132
0.192
0.677
0.768
0.751
0.864
ARDMYC
0.608
0.727
0.808
0.542
0.747
0.797
0.489
0.1.5
0.534
0.650
0.641
0.798
ARDMVCAM
0.629
0.759
0.824
0.538
0.751
0.799
0.569
0.521
0.702
0,336
0,185
0.613
0.564
0.646
0.748
CoMVC
0.708
0.833
0,894
0.535
0.706
0.756
0.618
0.618
0.701
0.423
0.206
0.619
0.590
0,601
0.747
MFINC
0.696
0.682
0.828
0.804
0.865
0.919
0.640
0.596
0.656
0.437
0.309
0.786
0.846
0.905
0.926
GCFAggMVC
0.716
0.843
0.927
0.693
0.810
0,743
0.642
0.743
0.440
0.295
0.801
0.844
0.912
0.959
ABCoDDC
0.598
0.682
0.783
0.788
0.855
0.912
0,370
0.226
0.476
0,395
0.174
0.590
0.722
0.833
0.911
SEM
0.825
0.835
0.947
0.768
0.851
0.915
0.727
0.797
0.851
0.965
CSOT
0.738
0.729
0.872
0.780
0.838
0.911
0,712
0.617
0,712
0.436
0.311
0.794
0.849
0.913
0.878
PROTOCCT
0.892
0,914
0.960
0.846
0,903
0.955
0.791
0.679
0.791
0.470
0.340
0.816
0.861
0.930
0.967
5. Experiment
degradation under imbalanced scenarios. The degradation becomes more pronounced as R decreases from 0.9 to 0.1, indicating that class imbalance poses fundamental chal- lenge to multi-view clustering.
5.1. Experimental Setup
To evaluate PROTOCOL, we establish a comprehensive benchmark on five widely-used multi-view datasets, as shown in Table 1. To simulate real-world imbalanced see- narios, we create imbalanced versions of these datasets with three imbalance ratios R {0.1, 0.5, 0.9). The R are kept consistent across different views. We place imple- mentation details of PROTOCOL in the Appendix B. We compare PROTOCOL with nine sftt-oof-the-an methods, including six DMVC methods (CoMVC (Trosten et al., 2021), MFLVC (Xu et al., 2022), AECoDDC (Trosten et al., 2023), GCFAggMVC (Yan et al., 2023), SEM (Xu et al.. 2023), CSOT (Zhang al., 2024c)), a DIMVC method (DSIMVC (Tang & Liu, 2022)), and two robust adversarial DMVC methods (AR-DMVC and AR-DMVC- AM (Huang et al., 2024)). We adopt three widely used metrics to evaluate clustering performance: Clustering Ac- curacy (ACC), Normalized Mutual Information (NMI), and Purity (PUR). Our code is available at ht tttp:://gtthtt com/ S Stt////aaaettttaaeeeeee PROTOOOO..
Superior Performance on Severe Imbalance. In the most severe imbalance scenario (Rt = 0.1), while baseline meth- ods suffer from substantial degradation, PROTOCOL shows remarkable robustness. It outperforms the second-best method by 6.7% ACC and 7.1% NMI on Hdigit, and by 4.8% ACC and 3.7% NMI on Caltech, validating its effec- tiveness in handling severe imbalance distribution.
Robustness across Imbalance Ratios. As the imbalance ratio increases (R: 0.1 + 0.5 - 0.9), most methods show improved performance. Notably, PROTOCOL maintains its superiority even under more balanced scenarios, achieving 0.987 ACC on Fashion (R 0.5) and 0.993 ACC on Ci- for10 (R 0.9). These results demonstrate PROTOCOL's 's robust performance in handling both severely imbalanced data and varying levels of class imbalance distributions.
Furthermore, we train the models on training sets with three different imbalance ratios R and evaluate their perception of different classes on balanced test sets. The results for Caltech and Hdigit are shown in Fig. 1, while those for Fashion and Cifar10 are provided in Appendix Fig. 5. All methods show improved performance on balanced test sets compared to imbalanced testing scenarios, mainly due to the reduced uncertainty from tail-class samples. Although the training imbalance ratio remains a key factor affecting performance, notably, P PROTOCOL consistently achieves the best results across different R.
5.2. Main Results
To simulate real-world scenarios, we evaluate all meth- ods on imbalanced multi-view data. Experiments are conducted on five datasets under three imbalance ratios R E {0.1, 0.5, 0.9), as shown in Tables 2 to 4. Based on these results, we have the following observations.
Impact of Class Imbalance. The results reveal a consistent pattern: most baseline methods suffer from performance
To further validate PROTOCOL'S 's capability in handling tail-
7

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PROTOCOL: Partial Optimal Transport-enhaneed Contrastive Learning for Imbalanced Multi-view Clustering
Table Performance Comparison with R= 0.5
Hdigit
Fashion
Caltech
NUS WIDE
Cifarl0
Methods
ACC
NM1
PUR
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
DSIMVC
0.955
0.894
0.958
0.727
0.714
0,732
0.529
0.439
0.551
0.149
0.175
0.545
0.905
0.804
0.905
ARDMVC
0.745
0.704
0,779
0.838
0.838
0,851
0.628
0.625
0.675
0.351
0.183
0.567
0.855
0,736
0.855
ARDMYCAM
0.879
0.932
0.928
0.844
0.850
0.639
0.693
0.375
0.208
0.621
0.972
0.951
0.972
COMVC
0.861
0.937
0.925
0.740
0.771
0.786
0.693
0.626
0.712
0.416
0.148
0.416
0.896
0.872
0.896
MFLYC
0.843
0.765
0.845
0.981
0.963
0.981
0.755
0.633
0.755
0.530
0.312
0.615
0.990
0.972
0.990
GCFAggMVC
0.979
0.944
0.979
0.980
0.957
0.980
0.761
0.638
0.760
0.525
0.299
0.619
0.989
0.970
0.989
AECODDC
0.843
0.895
0.910
0.975
0.952
0,975
0.451
0.304
0.495
0.426
0.164
0.458
0.877
0,802
0.877
SEM
0.980
0.945
0.980
0..982
0.961
0,979
0.759
0.611
0.707
0.475
0.261
0.565
0.990
0.971
0.982
CSOT
0.949
0.753
0.545
0.321
0.631
0.989
0.970
0.976
PROTOCOL
0.983
0.952
0.983
0.987
0.969
0.986
0.767
0.662
0.767
0.542
0.319
0.632
0.991
0.976
0.991
Table 4. Performance Comparison with R= 0.9
Hdigit
Fashion
Caltech
NUS-WIDE
Cifar10
Methods
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
ACC
NMI
PUR
DSIMVC
0.963
0.906
0.965
0.753
0.727
0.753
0.670
0.553
0.670
0.151
0.169
0.532
0.883
0.798
0.893
ARDMVC
0.859
0.831
0,859
0.871
0.885
0.880
0.660
0.592
0.677
0.396
0.216
0.598
0.875
0.753
0.875
ARDMVCAM
0.853
0.946
0.899
0.867
0.884
0.873
0.659
0.591
0.666
0.412
0.238
0.519
0.982
0.961
0.982
COMVC
0.906
0,930
0.906
0.808
0.808
0,816
0.640
0.580
0.646
0,383
0.097
0.383
0.963
0.941
0.963
MFLVC
0.913
0.820
0.913
0.989
0.967
0.989
0.802
0.715
0.802
0.614
0.351
0.614
0.991
0,976
0.991
GCFAggMVC
0.981
0,948
0
0.988
0.970
0.988
0.826
0.757
0.826
0,586
0.333
0.586
0.990
0.974
0.990
ABCODDC
0.964
0.948
0.964
0.986
0.968
0,986
0.460
0.355
0.466
0.469
0.201
0.469
0.976
0.949
0.976
0.982
0,954
0,984
0.983
0.972
0.586
0.360
0.586
0.991
0.975
0.984
CSOT
0.952
0.888
0.952
0.982
0.970
0.982
0.815
0.721
0.815
0.556
0.282
0.556
0.990
0.977
0.982
PROTUCOL
0.984
0.956
0.984
0.991
0.976
0.990
0.896
0.830
0.878
0.634
0.367
0.634
0.993
0.981
0.993
Caltech
Hdigit
Caltachh (A-0.1)
NUS-WIDE (R-0.3)
2.4
0.1
0.5
0.9
0.1
0.5
0.9
R
R
MY.VC
RECHEUC
SBM
(S0
PRO: OCOL
Head
Medium
Tail
Head
Medium
MTLVC
GCTAgghivC
STM
CSOT
PROTOCOL
Figure 1. Clustering performance comparison on balanced test sets.
Figure 2. Head, Medium, and Tail comparison on several datasets.
class samples, we evaluate five competitive methods across head, medium, and tail classes on Caltech and NUS-WIDE datasets, with results for R- = 0.1 shown in Fig. 2 (results for R = 0.5 are provided in Appendix Fig. 6). The results demonstrate that PROTOCOL not only maintains compet- itive performance on head classes but also improves the clustering effectiveness of medium and tail classes. This validates that POT label assignment and class-rebalanced contrastive learning effectively enhance the model's ability to learn discriminative features from tail classes, thereby addressing the representation bias caused by data scarcity.
ates more compact and well-separated clusters. As shown in Fig. 3(e), the clusters learned by PROTOCOL exhibit clearer boundaries and more cohesive structures, indicating its su- perior ability under imbalanced scenarios.
5.3. Ablation Study
We conduct ablation studies on three datasets under R {0.1, 0.5) validate the effectiveness of each component in P PROTOCOL. We compare three variants: (1) Base: Only in- cludes reconstruction loss and multi-view consistency learn- ing; (2) w/ POT: Incorporates POT-based label assignment; (3) w/ POT+CLR (denoted as PROTOCOL): Further adds POT-enhanced
To intuitively demonstrate the clustering effectiveness, we visualize the learned representations using t-SNE in Fig. 3. Compared with four baseline methods, PROTOCOL gener-
(CLR) contrastive learn ing. The results in Table show the contribution of each
8

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PROTOCOL: Partial Optimal Transport-enhanced Contrastive Learning for Imbalanced Multi-view Clustering
(8) MPINC
(b) CSOT
(c) GCFAggMVC
(d) SEM
(e) PACTOCCI
Figure 3. The t-SNE visualization on Hdigit dataset.
Table 5. Ablation Study on Different Components
Caltech
Hdigit
Fashion
Variants
R 0.1
R=
0=1.1
0
R 0.1
R = 0.5
ACC
NMI
ACC
NMI
ACC
NMI
ACC
NMI
ACC
NMI
ACC
NMI
Base
0.719
0.640
0.737
0.616
0.722
0.856
0.979
0.947
0.732
0.845
0.981
0.955
w/ POT
0.772
0.651
0.757
0.634
0.876
0.902
0.980
0.949
0.840
0.900
0.984
0.962
w/ POT+CLR
0.791
0.679
0.767
0.662
0.892
0.914
0.983
0.952
0.846
0.903
0.987 0.969
As shown in Fig. 4(b), ACC fluctuates within small range (0.7-0.8) as Ty and 7 vary. indicating the model's stability to temperature parameters. Based on these results, we set Ty 0.5 and 7 1.0. The Appendix Fig. 7 shows similar stability for the semantic consistency parameter and the base learning weight Abases and set 0.5, Abase = 0.1.
ACC
Clustering Pertormaa nnrerrmacc
Value
ACc
Epoch
6. Conclusion
(a) Convergence analysis
(h) Ty and analysis
In this paper, we propose PROTOCOL, a novel imbalanced multi-view clustering framework that effectively addresses the challenges of class imbalance and tail-class represen- tation bias. Specifically, we introduced POT-based label assignment mechanism that effectively perceives and han- dles class imbalance across multi-views, and designed a POT label-enhanced two-level class rebalanced contrastive learning strategy that enhances tail-class representation. Ex- tensive experiments on five benchmark datasets demonstrate that PROTOCOL consistently outperforms existing methods, particularly in severely imbalanced scenarios. Ablation studies further validate the effectiveness of each component, where the POT mechanism provides significant improve- ments handling class imbalance, while raaalaeebe contrastive learning further optimizes tail-class representa- tion. These results indicate that PROTOCOL provides an effective solution for real-workh multi-view clustering tasks where class imbalance is prevalent.
Figure 4. Convergence and parameter sensitivity on Caltech.
component. First, incorporating POT-based label assign- ment (w/ POT) significantly outperforms the base model (e.g., 15.4% ACC improvement on Hdigit when R 0.1), validating the effectiveness of POT label assignment in han- dling class imbalance. Furthermore, adding POT-guided contrastive learning (w/ POT+CLR further enhances the model performance, demonstrating its capability to improve tail-class representation. These results confirm that both components contribute the overall performance: the POT mechanism provides the most significant improvement in handling class imbalance, while the class-rebalanced con- trastive learning further optimizes tail-class representation.
5.4. Convergence and Parameter Sensitivity Analysis
We conduct convergence and parameter sensitivity analysis on the Caltech dataset, shown in Fig. 4. As shown in Fig. 4(a), both ACC and NMI metrics show stable conver- gence trends, with the model achieving convergence after ap- proximately 15 epochs and maintaining steady performance thereafter. addition, we analyze two key hyperparame- ters: the feature and class temperature parameters Ty and
Acknowledgements
This work was supported by National Natural Science Foun- dation of China NNos.62166059 62471 148, and 62306075), China Postdoctoral Science Foundation and Fellowship Pro- gram of CPSF (No.2024278).

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PROTOCOL: Partial Optimal Transport-cnhaneed Contrastive Learning for Imbalanced Multi-view Clustering
Impact Statement
Cuturi, M. Sinkhorn distances:
lightspeed computation of optimal transport. In Proceedings the 27th Advances in Neural Information Processing Systems, pp. 2292-2300, 2013.
Our research on imbalanced multi-view clustering addresses fundamental challenge in real- woaldworld scenarios, where data from multiple sources (e.g., medical imaging modalities, multi-sensor recordings, and social media platforms) often exhibits natural class imbalance.
Cuturi, M. and Doucet, A. Fast computation of wasserstein barycenters. In Proceedings of the 31 International Con- ference on International Conference on Machine Learn- ing Volume 32, 2014.
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PROTOCOL: Partial Optimal Transport-enhaneed Contrastive Learning for Imbalanced Multi-view Clustering
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12

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PROTOCOL: Partial Optimal Transport-ehhanee Contrastive Learning for Imbalanced Multi-view Clustering
A. Solving Process for POT Label
In this section, we detail how to solve the optimal transport by an efficient scaling algorithm. Our goal to combine partial optimal transport problems and unbalanced optimal transport problems to perceive the class imbalance distribution in multi-view data, with the following objective function:
Lrot = min (T, log P)r + DEL ( 1xlle)
(29)
(eU((.e)
s.t. U [ e R Tlk S r, Tr A3,
(30)
where r - NV Iy the sample distribution constraint, c= オ 1x the class distribution constraint, so that r and e are the marginal projections of matrix T onto its rows and columns, respectively. À is the total mass constraint of the transport matrix T. ,3 is scalar factor.
Inspired by PU (Chapel et al., 2020) and PłOT (Zhang et al., 2024a), we extend the original transport plan T by introducing a virtual cluster Ç. Specifically, we denote the assignment of samples on the virtual cluster as &. Then, we extend T to T, which satisfies the following constraints:
T = ER EERNA, TIkH N IN.
(31)
Due to 12 = A, we know that:
1N = A.
(32)
Therefore,
T T IN
T IN 1I
T 1N 1
(33)
We denote C' [ol P, PNN and replace T with T, thus the Eq. (31) can be rewritten follows:
min (T, C)F (T 1x]("";8) TEU
(34)
A 1
U= (=TTER" Nx(++1 TIk+ = N IN}, c¹
3x+1 400.
(35)
Note that we introduce the weighted KL divergence D with 3K+1 + +oo to strictly enforce the virtual cluster constraint. The sample constraint changes from inequality (5) to equality (=) because the virtual cluster & absorbs the remaining mass, ensuring that the total mass of each sample exactly equals .. The weighted KL divergence is defined as:
Σ
W log
(36)
y/1
Following Cuturi (Cuturi, 2013), we introduce an entropy regularization term to solve the optimal transport efficiently. The regularized version becomes:
min mi + (T Ix|le': ;3).
(37)
Teu
Using the properties of entropy regularization:
(T,C)=-el((n) <(f, C/e log F
(38)
T
e (T, log
cxp( cxp(-C/o) )r
(39)
DrL (T exx(eCC/e;:
(40)
13

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PROTOCOL: Partial Optimal Transport-ehhaneed Contrastive Learning for Imbalanced Multi-view Clustering
Algorithm 2 Efficient Scaling Algorithm for POT
Require: Cost matrix P. mass X, regularization e, weights B
C log P.Ox]
2: M exp(-C//e
3: c² I - X]
4: b + 1x+1
5: f B,+c for ,,...,
6: while not converge do
11x
7: a MO
8: b b+ (Ma))
9: end while
T" diag a M M diag(b)
11: return First K columns of T T
Let M CC/e), the problem becomes:
min (T + (T 1n|cc';
(41)
TEU
Taking the derivative with respect to Ti and setting it to zero:
0
DxL (T) M) M) + DKL 1x]c
(42)
or.
T
= c(log Ti - log Mij + 1) + By log
(43)
cj
This leads to:
B
[
1nl
Tú = Mij exp(
log
(44)
cj
expexp((-
(45)
T INls
Bg Let f, Bete. then 81 fr_ After absorbing constants into the scaling factors:
T, Miby.
(46)
This leads the efficient scaling algorithm iterative updates:
N 1N
a Mb
(47)
c*
- V.
(48)
M
The final transport plan can be recovered as:
T - diag(a) M
(49)
Based on the above derivation, we summarize our solution in Algorithm 2.
14

---

PROTOCOL: Partial Optimal Transport-enhaneed Contrastive Learning for Imbalanced Multi-view Clustering
Fashion
Cifar10
5.6
5.8
6.5
0.5
0.1
0.5
0.9
0.1
0.5
0.9
R
CoMVC
NFLVC
AECOBOC
GCFAgg MVC
SEM
CSOT
PROTOCOL
Figure 5. Clustering performance comparison on balanced test sets.
Caltech (R=0.5)
NUS-WIDE (R=0.5)
0.9
5.0
Head
Medium
Tail
Head
Medium
Tail
MFLVC
GCFAggMVC
SEM
CSOT
PROTOCOL
Figure 6. Head, Medium, and Tail comparison on several datasets.
B. Experimental Supplements
Implementation Details For network architecture, we employ four-layer MLPs for both encoder and decoder. Specifically, the encoder architecture consists of layers with dimensions (input_dim, 500, 500, 2000, 512), while the decoder follows symmetric structure with dimensions (512, 2000, 500, 500, input-dim) dim). Each layer is followed by ReLU activation except for the output layer. The high-level features are obtained by projecting the 512-dimensional features 128 dimensions through an additional MLP. The optimization is performed using Adam optimizer with learning rate 1c-3. The training process consists of three stages: view-specific feature learning with 200 epochs for reconstruction loss, consensus learning with 50-100 epochs for multi-view consistency, and class-rebalanced enhancement with 50-100 epochs for imbalance learning. We set the batch size to 256. We report the average results over three runs with different random seeds.
Figure 7. Parameter sensitivity analysis on Caltech dataset.
15


Reviews:
[{"review_id": "Al5SF6HkAa", "reviewer": "Reviewer_LTVa", "summary": "This paper proposes the first systematic study on the common class imbalance problem in multi-view clustering and develops a new framework called PROTOCOL. This method reformulates the imbalanced clustering problem as a partial optimal transfer problem by mapping multi-view features to a consensus space, and introduces step-by-step quality constraints and weighted KL divergence to perceive class imbalance. At the same time, class rebalanced contrastive learning enhanced by partial optimal transfer is used at the feature and category levels, combined with logit adjustment and category-sensitive learning, to alleviate the representation degradation problem of minority samples.", "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": "We sincerely appreciate your recognition of our work's novelty as the first to identify and systematically study the class imbalance problem in multi-view clustering, as well as your positive feedback on our method's effectiveness and robustness. Furthermore, we are deeply grateful for your thorough review and constructive suggestions on our manuscript.\n\n**Q1:** The inherent challenges of imbalanced clustering.\n\n**A1:** Thank you for your constructive suggestion.  We will further clarify the two main challenges of imbalanced multi-view clustering (see lines 43 and 61) in the **Motivation** subsection of the revised version.\n\nWe will add a **Motivation** subsection in the **Methodology** section to clarify the two key challenges and explicitly indicate how each module of our method addresses these challenges:\n\n**(1) How to perceive class imbalance distribution.** The challenge lies in detecting imbalanced distributions without labeled data in unsupervised settings. Existing methods, assuming uniform class distributions, often fail to handle imbalanced data effectively. This challenge will be addressed in **Multi-view POT Label Allocation** subsection.\n\n**(2) How to mitigate representation degradation of minority samples.** Minority samples, due to their scarcity, often receive insufficient attention during learning, resulting in poor feature representations that inadequately characterize their classes. This challenge will be addressed in **Multi-view Class-rebalanced Contrastive Learning**  subsection.\n\nThis creates a more coherent flow from challenges to solutions, helping readers better understand both our motivation and technical approach.\n\n**Q2:** Validate our method on larger-scale datasets. \n\n**A2:** Thank you for your insightful suggestion. Per your suggestion, we validated our method on larger-scale dataset (CIFAR100 with 60,000 samples). As shown in **Figure A1** of the PDF file provided in the anonymous link  (https://zenodo.org/records/15119555), PROTOCOL achieves the best performance compared to other methods, demonstrating its effectiveness in handling class imbalance ($R$=0.1) on large-scale datasets. \n\nCIFAR100 is considered a large-scale dataset among those commonly used in multi-view clustering [1-4]. In future work, we will continue to explore PROTOCOL's potential on even larger-scale datasets.\n\n[1] A Comprehensive Survey on Multi-View Clustering (TKDE 2023)\n\n[2] Representation Learning in Multi‑view Clustering: A Literature Review (Data Sci. Eng 2022)\n\n[3] Differentiable Hierarchical Optimal Transport for Robust Multi-View Learning (TPAMI 2023)\n\n[4] Adversarially Robust Deep Multi-View Clustering: ANovel Attack and Defense Framework (ICML 2024)\n\n\n\n**Q3:** The advantages of Eq. (28) in imbalanced multi-view clustering scenarios.\n\n**A3:** Good suggestion! Eq. (28) employs contrastive learning to maintain semantic consistency across views for the same class. The denominator term $\\sum_{j=1,j\\neq i}^{K} \\mathcal{D}(\\{P_i^v, P_j^v\\})$ measures negative pair similarities, ensuring comprehensive discrimination between classes. This design helps distinguish minority from majority classes while preserving cross-view semantic consistency, thereby enhancing representation learning for minority classes.\n\nIn imbalanced multi-view clustering, cross-view semantic alignment is crucial due to minority classes' lower error tolerance. Unlike balanced scenarios where abundant samples can help correct semantic bias, minority classes have limited samples to rely on. Cross-view semantic alignment enables different views to complement each other, effectively reducing representation bias for minority classes.\n\nWe will add a clear explanation of Eq. (28) in the revised version to highlight its advantages in imbalanced multi-view clustering scenarios.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "Yes. The methodology of the paper has been reviewed.", "experimental_designs_or_analyses": "Yes. The experimental setting and results have been reviewed.", "relation_to_broader_scientific_literature": "The key contributions of the paper are related to the broader scientific literature on Multi-View Clustering.", "essential_references_not_discussed": "The paper comprehensively reviews the most relevant literature in the fields of Multi-View Clustering.", "other_strengths_and_weaknesses": "Strengths:\n1. The paper innovatively integrates partial optimal transport with contrastive learning, utilizing progressive quality constraints and a weighted KL divergence to effectively perceive and model imbalanced distributions, while simultaneously enhancing the representation of minority samples at multiple levels.\n2. Extensive experiments conducted on five datasets convincingly demonstrate the method’s superior performance in handling imbalanced multi-view data, providing robust empirical support for the proposed approach.\n\nWeaknesses:\n1. Although the paper targets imbalanced clustering, it does not clearly describe the specific operations involved nor adequately articulate the inherent challenges of imbalanced clustering in the motivation section.\n2. The experiments are limited to datasets with a maximum scale of only 50,000 samples; the authors should consider validating their approach on larger-scale datasets.\n3. In regard to Equation 28, which introduces the common semantic loss, the paper should provide a clearer explanation of its advantages and its specific impact on imbalanced clustering scenarios.", "other_comments_or_suggestions": "NA", "questions_for_authors": "NA", "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": "9qndERGIoK", "reviewer": "Reviewer_sJkj", "summary": "The paper introduces PROTOCOL, a new method for imbalanced multi-view clustering. It combines partial optimal transport (POT) with contrastive learning. The approach solves two main problems: perceiving class imbalance distributions through POT-based label assignment and reducing the representation degradation of minority samples using rebalancing strategies at the feature and class levels. Tests on multiple datasets show that PROTOCOL performs better, especially when data is highly imbalanced.", "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": "We sincerely appreciate your recognition of our work's novelty and its potential impact in enhancing multi-view clustering for real-world imbalanced scenarios, as well as your positive feedback on our experimental results. We are also deeply grateful for your thorough review and helpful suggestions.\n\n**Q1:** The computational cost of POT for large-scale applications could be a direction for future optimization.\n\n**A1:** Thank you for your insightful suggestion. In Q4, we have validated PROTOCOL's computational cost on varying data scales (from 5K to 40K data points). The results demonstrate **near-linear growth**, showing PROTOCOL's potential for large-scale applications. In future work, we will continue to investigate and analyze POT's computational efficiency on datasets of even larger scale.\n\n**Q2:** Strengthen the logical connections between components.\n\n**A2:** Good suggestion!  We will enhance the logical structure of **Section 4 (Methodology)** as follows:\n\n**4.1 Motivation**. First, we will clearly articulate the two major challenges in imbalanced multi-view clustering, helping readers better understand the correspondence between challenges and their respective solutions.\n\n**4.2 Multi-view POT Label Allocation** (originally 4.1).  We will explicitly state at the beginning: \"We propose a multi-view POT label allocation method that learns imbalanced class distribution of multi-view data through multi-view representation learning and a POT-based self-labeling mechanism.\"  Additional logical connections will be added between subsubsections to strengthen coherence. At the end, we will add a transition paragraph: \"Through the learning of these components, PROTOCOL can effectively perceive the imbalanced distribution of multi-view data. This leads to the next challenge: how to mitigate representation degradation of minority samples, which we will address in next subsection.\" \n\n**4.3 Multi-view Class-rebalanced Contrastive Learning** (originally 4.2). We will first analyze the fundamental causes of representation degradation in minority samples, then introduce our solution.\n\nAt the end of  **Methodology**, we will summarize how PROTOCOL systematically addresses the two challenges. Specifically, we will add the following description:\"Imbalanced multi-view data is a more realistic application setting. PROTOCOL addresses the two key challenges of imbalanced multi-view data through POT self-label allocation and class-rebalanced contrastive learning.\" \n\nThese modifications will make the logical connections between components more prominent.\n\n**Q3:** Convergence theory analysis.\n\n**A3:** Thank you for your constructive suggestion. Due to space limitations, we provide a brief theoretical analysis of convergence here. In the revised version, we will provide theoretical foundations for the convergence analysis. \n\nOur POT scaling algorithm extends the Sinkhorn-Knopp iteration by incorporating partial optimal transport with weighted KL divergence constraints. The algorithm achieves optimal label assignment through an efficient dual-form scaling iteration process. Based on [1], we prove that when $\\epsilon, \\beta > 0$, the algorithm guarantees linear convergence to a unique solution. The convergence rate depends on the entropic regularization parameter, weighted KL divergence weight, and cost matrix condition number. Our method introduces a dynamic mass parameter $\\lambda$ for smooth transition from high-confidence samples to global optimal solutions. Moreover, experimental results validate both the efficiency and effectiveness of PROTOCOL, demonstrating its stability in handling imbalanced multi-view clustering. \n\n[1] Scaling Algorithms for Unbalanced Optimal Transport Problems (Mathematics of Computation 2018)\n\n**Q4:**  About PROTOCOL's computational cost scaling with dataset size.\n\n**A4:** Thank you for your valuable suggestion. Per your suggestion, we evaluated PROTOCOL's computational cost across four different data scales (5K to 40K samples) on the CIFAR10 dataset. As shown in **Figure A2** of the PDF file provided in the anonymous link (https://zenodo.org/records/15119555), the results demonstrate that PROTOCOL's computational cost scales **nearly linearly** with the number of samples. All experiments were conducted on an NVIDIA GeForce RTX 3090 GPU.\n\n**Q5:** About recent works on imbalanced multi-view clustering and suggested Ref [1].\n\n**A5:** Thank you for your suggestion. To the best of our knowledge, we are the first to systematically study the imbalanced multi-view clustering problem. While [1] is a single-view method for class imbalance problems, different from our multi-view approach, we will discuss it in our revised version.\n\n[1] Adaptive K-means clustering based under-sampling methods to solve the class imbalance problem (Data and Information Management 2024)", "claims_and_evidence": "The claims presented in the paper are robustly bolstered by the experimental evidence. \n1.The claims about POT’s effectiveness for imbalanced MVC are supported by ablation studies and t-SNE visualizations, showing clearer cluster boundaries for imbalanced multi-view clustering.\n2.The superiority over baselines is validated across all datasets and metrics.", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "Yes. The paper is based on theoretical concepts of OT and contrastive learning.", "experimental_designs_or_analyses": "The work performs several experiments on 5 datasets with three different imblance ratios", "relation_to_broader_scientific_literature": "The paper introduces a new method for imbalanced multi-view clustering by combining partial optimal transport (POT) with contrastive learning.", "essential_references_not_discussed": "The literature research section of the paper is quite substantial, but there are still some related papers that have not been mentioned.\nIncluding recent single-view and multi-view class imbalance approaches (e.g., [1]) would enhance the paper's comprehensiveness and contextualize its contributions more effectively.\n[1] Zhou Q, Sun B. Adaptive K-means clustering based under-sampling methods to solve the class imbalance problem[J]. Data and Information Management, 2024, 8(3): 100064.", "other_strengths_and_weaknesses": "Strengths:\n1. Originality: The novel integration of POT and contrastive learning offers a fresh approach to imbalanced multi-view clustering.\n2. Practical Value: Addressing real-world imbalanced data challenges highlights the paper’s potential impact in applications like ecological monitoring.\n3. Thorough Evaluation: Rigorous experiments across datasets and imbalance scenarios demonstrate the framework’s performance.\nWeaknesses:\n1. The computational cost of POT might pose challenges for large-scale applications, which could be a direction for future optimization.\n2. The paper's structure could be clarified to better highlight the logical connections between components. A more explicit explanation of how each module addresses specific challenges would help readers appreciate the framework's coherence.", "other_comments_or_suggestions": "Refer to the weakness", "questions_for_authors": "1. Theoretical Justification: Could the authors elaborate on the theoretical foundation of the POT scaling algorithm, such as its convergence properties? This would significantly enhance the paper's theoretical contributions.\n2. Runtime Analysis: How does the computational cost of PROTOCOL scale with dataset size?", "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": "ImVyVHnVyU", "reviewer": "Reviewer_jNCt", "summary": "In this paper, a novel Partial Optimal Transmission (POT) enhanced contrast learning framework, PROTOCOL, is proposed to address the class imbalance challenge in multi-view clustering. A two-level rebalancing strategy achieves balanced feature learning as well as consistency in view-specific and view-sharing allocation.", "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": "We sincerely appreciate your recognition of both the novelty of our method and the practical value of our motivation, as well as your positive feedback on our paper's representation and experiments. We are also deeply grateful for your thorough review and valuable suggestions.\n\n**Q1:** The empirical setting of w(p+) and the possibility of adaptive learning by the model.\n\n**A1:** Thank you for your helpful suggestion.\n\nYes, we empirically set $w(p_+)$ to 0.8 and 0.2 for the two settings based on experimental validation.\n\nFollowing your suggestion, we implemented adaptive learning for $w(p_+)$ and validated it on three datasets with $R$=0.1. The results show performance improvements of 0.3%\\~0.5% compared to fixed parameters. Notably, the learned parameters (ranging from 0.664\\~0.805 and 0.195\\~0.336) align well with our empirical values (0.8/0.2), validating our empirical setting. We implemented this by randomly initializing the two settings in [0,1], with their sum constrained to 1.\n\n|         | ACC (Fixed: 0.8/0.2) |   ACC (Adaptive)    | $w(p_+)$ (Learned) |\n| :-----: | :----------------------: | :---------------------: | :---------------------: |\n| Caltech |          0.791           | 0.796 ($\\uparrow$ 0.05) |       0.805/0.195       |\n| Hdigit  |          0.892           | 0.895 ($\\uparrow$ 0.03) |       0.664/0.336       |\n| CIFAR10 |          0.861           | 0.864 ($\\uparrow$ 0.03) |       0.782/0.218       |\n\nGiven the improved performance and greater flexibility of adaptive learning, we will adopt this improvement in the revised version. We again thank you for the constructive suggestion.\n\n**Q2:**  Aggregation of view-specific representations into consensus representation.\n\n**A2:**  Thank you for your comment. The consensus representation  $\\mathbf{U}$ is obtained through the following steps:\n\nstep1: View-specific representations $\\mathbf{Z}^v$ are learned through autoencoders from original data.\n\nstep2: Inter-sample structural relationships are captured in relationship matrix $\\mathbf{G}$ through a Transformer-based self-attention mechanism.\n\nstep3: Structure-aware representations are computed as $\\mathbf{S}^v=\\mathbf{Z}^v\\mathbf{G}$ for each view.\n\nstep4: View weights $\\mathbf{w}^v$ are learned through a view weight learning module.\n\nstep5: Final consensus representation is obtained by weighted fusion: $\\mathbf{U}= \\sum_{v=1}^{V}\\mathbf{w}^v\\mathbf{S}^v$.\n\n\n**Q3:** Regarding the imbalanced ratio $R$ in Figure 1.\n\n**A3:** Thank you for your comment. The imbalance ratio $R$ only applies to the training set, while the test set remains balanced. PROTOCOL maintains superior performance across different train imbalance ratios, demonstrating its effectiveness and robustness in handling class-imbalanced multi-view data.\n\n**Q4:** Adding visualization results for more extreme imbalance data.\n\n**A4:** Thank you for your insightful suggestion. Following your recommendation,  we conducted tests on the Hdigit dataset with an even more extreme imbalance ratio of $R$=0.05, with visualization results shown in **Figure A3** of the PDF file provided in the anonymous link (https://zenodo.org/records/15117646). The results demonstrate that, compared to baseline methods, PROTOCOL can effectively identify smaller clusters and clearly distinguish cluster structures of varying scales, validating our method's effectiveness and robustness under extreme imbalance ratios.\n\nTo more intuitively demonstrate PROTOCOL's ability to perceive imbalanced data distributions, we conducted a quantitative analysis of the clustering results from Figure 3 in the original paper and **Figure A3**, where we calculated the number of samples in each class from the test results and computed the actual imbalance ratios.\n\nAs shown in the table below, when the imbalance ratio $R$=0.1, other methods produced actual imbalance ratios between **0.26~0.38**, while PROTOCOL achieved an actual imbalance ratio of only **0.14**. Similarity, when the imbalance ratio $R$=0.05, other methods produced actual imbalance ratios between **0.23~0.37**, while PROTOCOL achieved an actual imbalance ratio of only **0.12**. This indicates that our method can more accurately perceive and maintain the class distribution characteristics of the original data.\n\n| Actual_$R$ | MFLVC | CSOT | GCFAggMVC | SEM  | PROTOCOL |\n| :----: | :---: | :--: | :-------: | :--: | :------: |\n| $R$=0.1  | 0.26  | 0.28 |   0.39    | 0.38 | **0.14** |\n| $R$=0.05 | 0.28  | 0.25 |   0.23    | 0.37 | **0.12** |", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "Yes", "experimental_designs_or_analyses": "Yes", "relation_to_broader_scientific_literature": "Unbalanced multi-view data is very common in real-world scenarios, but has not been explored much. This paper achieves balanced learning by modifying the paradigm of contrastive learning to make the model more sensitive to minority samples.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "Strengths:\n- Good representation.\n- Comprehensive experiments: The superiority and robustness of the method are verified on multiple datasets, covering different imbalance ratios, and ablation studies and visualization analysis are performed.\n\nWeaknesses:\n- Is w(p+) set empirically? Why manually specify such a ratio between view-specific and consensus class alignment? Why not let the model learn adaptively.", "other_comments_or_suggestions": "no", "questions_for_authors": "- How to aggregate view-specific representations into consensus representation U?\n- In Figure 1, why is there still an imbalanced ratio on the balanced test set?\n- It may be clearer for the authors to show a comparison of the effects of different methods' visualizations on synthetic extreme imbalance dataset. Since the visualization results from Fig. 3 show that most of the methods can identify those small clusters, such a demonstration may not achieve the authors' original intention.", "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": "KJlMqSUmsM", "reviewer": "Reviewer_mKm8", "summary": "The paper addresses the class imbalance issue in multi-view clustering by combining UOT and POT to perceive class imbalance, and uses POT-enhanced class rebalance to mitigate the representation degradation of minority samples in contrastive learning. Through comparisons across multiple datasets and multi-view clustering algorithms, the paper demonstrates the superiority of the proposed method under different imbalance ratios.", "questions": "", "limitations": "", "rating": 2, "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": "We sincerely appreciate your recognition of our work's motivation and method.We are also deeply grateful for your thorough review and valuable suggestions.\n\n**Q1:** A intuitive explanation of how Optimal Transport addresses class imbalance.\n\n**A1:** Thanks for your suggestion. We would like to draw your attention to **Subsection 4.1.3**. Specifically, our method perceives class imbalance distributions through the following process:\n\nGiven the model's label predictions $\\hat{\\mathbf{P}}$ and prior distribution constraints $U$, PROTOCOL dynamically adjusts the transport mass (via $\\lambda$) to gradually assign samples to imbalanced clusters (POT label matrix $\\mathbf{T}$):\n\n(1) First assigns high-confidence samples (low transport costs);\n\n(2) Gradually incorporates lower-confidence samples as transport mass increases;\n\n(3) Naturally forms labels reflecting true class distribution.\n\nCombines **imbalanced labels** with **class-rebalanced learning (Section 4.2)** to address minority class representation.\n\nWe will enhance the logical connections between modules in the **Methodology** section of our revised version. \n\n**Q2:** Specific preprocessing.\n\n**A2:**  Thank you for your helpful suggestion. The data preprocessing steps are as follows:\n\nstep1: We start with the class-balanced datasets.\n\nstep2: Based on the imbalance ratio $R$ as defined in Eq. (7), we calculate the sample size for each class in descending order. For instance, with Hdigit dataset at $R$=0.1, class 1 retains all 1000 samples while class 10 keeps 100 samples. The intermediate classes' sample sizes grow linearly. Samples: {1000, 774, 599, 464, 359, 278, 215, 167, 129, 100}.\n\nstep3: For each class, we ensure that the same sample indices are maintained across all views.\n\nstep4: To ensure stability, we employ fixed random seeds during sample selection.\n\nThis preprocessing transforms the dataset into an imbalanced class distribution. The code will be made publicly available upon acceptance.\n\n**Q3:** The experimental procedures for Tables 1 and 2.\n\n**A3:** Thank you for your suggestion. Since you also mentioned Figure 1 and 2, we explain them together.\n* Tables 1 and 2: PROTOCOL's implementation is given in Appendix B. Dataset and preprocessing are provided in Table 4 and A2, respectively. \n* Figures 1 and 2:\n    * Figure 1: The model is trained on imbalanced training sets and evaluated on balanced test sets to assess its perception of different classes. The results demonstrate PROTOCOL's robustness.\n    * Figure 2: We categorize all classes into three groups: Head, Medium, and Tail. The distribution varies by class size:\n        * For 10-class: Head (first 3 classes), Medium (middle 4 classes), Tail (last 3 classes). \n        * For 7-class: Head (2), Medium (3), Tail (2). \n        * For 5-class: Head (1), Medium (3), Tail (1).\nThis categorization aligns with the Head-Medium-Tail definition, as majority samples fall into head classes while minority samples belong to tail classes. The results demonstrate our method's superiority, validating its effectiveness in perceiving actual class distributions.\n\n**Q4:** An easy explanation of the proposed method, data preprocessing, and the anonymous code for validation.\n\n**A4:** Thank you for your suggestion.\n\n* **About an easily explanation of PROTOCOL:** See A1.\n\n* **Data preprocessing:** See A2.\n\n* **Anonymous code:** We have provided our code through anonymous link (https://zenodo.org/records/15119555).\n\n  * **For Testing:** We provide a pre-trained model on the Hdigit dataset with $R$=0.1 to help verify our method's effectiveness.\n\n  * **For Training:** We have released network.py and train.py, which demonstrate the training pipeline to facilitate understanding of our framework.\n\n  * **Environment Setup:** Please create a virtual environment following our instructions for smooth execution of our code.\n\nThe complete source code will be made publicly available upon paper acceptance.\n\n**Q5:** Analysis that Eq. (12)'s constraints reflect class imbalance distribution.\n\n**A5:** Thank you for your suggestion. Eq. (12) captures the class imbalance distribution pattern through two key mechanisms:\n\n(1) The constraints  $\\sum_{k=1}^K \\mathbf{T}_{i,k} \\leq 1$ implement a soft label assignment mechanism, enabling flexible sample-to-class assignments. This allows samples to have varying degrees of association with different classes.\n\n(2) The constraint $\\sum_{i=1}^N \\mathbf{T}_{i,k} \\leq \\lambda$ introduces an adaptive parameter $\\lambda$ to regulate the maximum mass for each class. During the dynamic adjustment of  $\\lambda$, higher confidence samples (majority classes) receive larger mass assignments, while lower confidence samples (minority classes) receive smaller mass assignments.\n\nThen, we transform Eq. (12) into Eq. (15), enabling the model to adaptively capture the inherent patterns of imbalanced class distributions.", "claims_and_evidence": "No. The paper proposes achieving adaptive perception of class imbalance through the adjustment of lambda. However, the explanation does not provide readers with a clear understanding of the adaptive adjustment process of lambda.", "methods_and_evaluation_criteria": "The comparative experimental results and related analysis demonstrate the superiority of the proposed method in addressing the class imbalance problem. However, the explanation of the proposed method is difficult to understand.", "theoretical_claims": "The main text does not include proofs for the theoretical claims.", "experimental_designs_or_analyses": "The study conducts experimental comparisons based on five commonly used multi-view datasets. However, the experimental setup does not clearly explain how the class-imbalanced datasets were constructed from these five datasets for the comparative experiments in Table 2. Additionally, the experimental procedures for Figures 1 and 2 are not clearly described.", "relation_to_broader_scientific_literature": "The primary contribution of this study lies in addressing the class imbalance problem in multi-view clustering by optimizing it with partial optimal transport. Optimal transport has demonstrated strong capability in handling class imbalance problems in previous studies. Based on this, the authors introduce it into multi-view clustering, aiming to mitigate class imbalance within this context.", "essential_references_not_discussed": "The core of the paper lies in introducing Optimal Transport into multi-view clustering. Although the paper provides some transitions and background, the process is not clearly articulated, making it difficult to understand.", "other_strengths_and_weaknesses": "Strength:\nThe authors keenly identified the class imbalance problem in multi-view clustering and addressed it by introducing Optimal Transport, tackling the issue from two perspectives: perceiving class imbalance and mitigating representation degradation of minority samples. \nWeakness:\n1) he paper does not provide a clear and intuitive explanation of how Optimal Transport addresses class imbalance, making it difficult for readers to comprehend the construction of the proposed method. \n2) The authors conducted experiments with different imbalance ratios on common multi-view datasets, but the specific preprocessing steps were not detailed. \n3) Furthermore, the experimental procedures for Tables 1 and 2 were not provided.", "other_comments_or_suggestions": "[1]Given that the paper does not provide an easily understandable explanation of the proposed method and that data preprocessing is required to evaluate its clustering performance on class-imbalanced multi-view data, this process should be explicitly presented. Therefore, anonymized open-source code should be considered to facilitate a comprehensive understanding and verification of the proposed method’s effectiveness.", "questions_for_authors": "[1]Why do the constraint conditions in Equation (12) reflect the distribution pattern of class imbalance?", "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: The paper proposes PROTOCOL, a new framework for imbalanced multi-view clustering. All reviewers acknowledge the novelty of this work and the thoroughness of its experimental analysis, unanimously recommending a Weak Accept (WA) rating. Based on this consensus, I recommend accepting the paper.
Decision: Accept (poster)