Hypergraph-Enhanced Contrastive Learning for Multi-View Clustering with Hyper-Laplacian Regularization
Authors: Zhibin Gu
Weili Wang
Venue: NeurIPS 2025 poster ()
Keywords: Multi-view Clustering
Primary area: general_machine_learning

Abstract: Deep multi-view clustering (DMVC) has emerged as a promising paradigm for integrating information from multiple views by leveraging the representation power of deep neural networks. However, most existing DMVC methods primarily focus on modeling pairwise relationships between samples, while neglecting higher-order structural dependencies among multiple samples, which may hinder further improvements in clustering performance. To address this limitation, we propose a hypergraph neural network (HGNN)-driven multi-view clustering framework, termed Hypergraph-enhanced cOntrastive learning with hyPEr-Laplacian regulaRization (HOPER), a novel model that jointly captures high-order correlations and preserves local manifold structures across views. Specifically, we first construct view-specific hypergraph structures and employ the HGNN to learn node representations, thereby capturing high-order relationships among samples. Furthermore, we design a hypergraph-driven dual contrastive learning mechanism that integrates inter-view contrastive learning with intra-hyperedge contrastive learning, promoting cross-view consistency while maintaining discriminability within hyperedges. Finally, a hyper-Laplacian manifold regularization is introduced to preserve the local geometric structure within each view, thereby enhancing the structural fidelity and discriminative power of the learned representations. Extensive experiments on diverse datasets demonstrate the effectiveness of our approach.

Hypergraph-Enhanced Contrastive Learning for Multi-View Clustering with Hyper-Laplacian Regularization
Zhibin Gu Weili Wang**
Colleeee of Computer and Cyber Security, Hebei Normal University, China
Hebbi Provincial Key Laboratory of Network & Information Security, Hebei Normal University, China Heebei Provincial Engineering Research Center for Supply Chain Big Data Analytics Data Security, Hebei Normal University, China 'Independent Researcher, China guzhibin @ wwwhhhhu..uu.....m weiliw295 gmail.com
Abstract
Deep multi-view clustering (DMVC) has emerged as a promising paradigm for integrating information from multiple views by leveraging the representation power of deep neural networks. However, most existing DMVC methods primarily focus on modeling pairwise relationships between samples, while neglecting higher- order structural dependencies among multiple samples, which may hinder further improvements in clustering performance. To address this limitation, we propose hypergraph neural network (HGNN)
multi-view -iew clustering framework, termed Hypergraph-ennancee cOntrastive learning with hyPEr-Laplaccan reg- ulaRization (HOPER), novel model that jointly captures high-order correlations and preserves local manifold structures across views. Specifically, we first construct view-specific hypergraph structures and employ the HGNN to learn node represen- tations, thereby capturing high-order relationships among samples. Furthermore, design hypergraph-driven dual contrastive learning mechanism that integrates inter- view contrastive learning with intra-hyperedge contrastive learning, promot- ing cross-view consistency while maintaining discriminability within hyperedges. Finally, hyper-Laplacias manifold regularization introduced to preserve the local geometric structure within each view, thereby enhancing the structural fidelity and discriminative power of the learned representations. Extensive experiments on diverse datasets demonstrate the effectiveness of approach.
Introduction
Multi-view data, collected from diverse sources or extracted via multiple feature extractors, contain both consensus and complementary information. As such data become increasingly prevalent in real-world applications, multi-view learning has emerged as fundamental paradigm in machine learning for enhancing downstream performance by leveraging cross-view correlations [1]6). Among its various tasks, multi-view clustering (MVC) plays a pivotal role unsupervised learning by partitioning samples into meaningful groups without label supervision, thereby facilitating effective data analysis and organization 10
With the advance of deep representation learning, variety of deep multi-view clustering (DMVC) methods have emerged, which can be broadly categorized into two main paradigms: representation
"Corresponding author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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bearning-based and graph learning- based approaches [ The former typically leverages self- supervised learning frameworks extract informative and discriminative latent representations directly from raw input features [12 For instance, Wu et al. [1] employed view-specific deep autoencoders to extract embedded features and applied self-weighted contrastive fusion to learn robust global features. Cui et al. [16] enhanced information consistency across views and reduced redundancy by maximizing the lower bound of sufficient representation. Although deep representation learning methods have achieved significant success, they often struggle to explicitly model the complex relationships between samples, particularly those arising from intricate data structures. To address this limitation, deep graph learning methods have gained attention by using a shared graph neural network (GNN) encoder and projection head to represent each view as a graph, enabling unified cross- view representation learning in common latent space [17 For example, Xia et al. (20) employed graph convolutional networks (GCNs) to learn modality-specific representations, and introduced contrastive losses to encourage discriminative and flustering-friendly alignment across modalities. Similarly, Du et al. [21] utilized multiple GCNs with shared weights to extract view-specific representations, and incorporated clustering embedding layer to jointly optimize representation learning and clustering performance. In addition, Dong et al. [22] performed contrastive learning the graph structure level under the guidance of consensus graph, thereby capturing the underlying structural information of the data.
Despite the performance improvements achieved by deep multi-vien clustering (DMVC) methods through modeling pairwise relationships among samples, several critical limitations remain to be addressed. First, most existing DMVC methods primarily focus modeling pairwise correlations between samples, while overlooking high-order and complex interactions among data points. This simplification significantly limits their ability to capture rich structural priors that critical for effective clustering. Second, many contrastive learning- false negative problem, where semantically similar samples from different views are incorrectly treated as negatives. This misidentification undermines the discriminative power of the learned representations. Third, these methods often lack explicit constraints to preserve high-order local geometric structures in the latent space, which are essential for maintaining topological consistency and enhancing the robustness of clustering.
DMVC approaches suffer from the
To address the limitations of existing deep multi- clustering methods, we propose a hypergraph- enhanced contrastive learning approach with hyper-Laplacian regularization. Specifically, for each view, we construct hypergraph based on the sample features. This hypergraph structure, along with the corresponding features, is then input into hypergraph neural network with shared weights to learn view-specific node representations, capturing high-order correlations among the data. Subse- quently, hypergraph-inducee dual contrastive learning mechanism is employed regularize the node representations: the inter-view contrastive loss regularization enhances consistency across views, while the intra-view contrastive loss regularization helps mitigate the false negative issue, promoting more discriminative representation learning. Finally, we introduce a hyper-Laplacian manifold regu- larization term to preserve the view-specific high-order local geometric structure. further enhancing the discriminative power of the node representations. In summary, the contributions of the proposed framework are as follows:
We introduce a hypergraph neural network (HGNN)-based representation learning frame- work for multi-view clustering, which captures high-order data correlations by leveraging a hypergraph structure and shared-weight HGNN,
We propose a ppergraph-enhancee dual contrastive learning mechanism, which consists of an inter-view contrastive loss to reinforce consistency across different views and a intra- hyperedge contrastive loss enhance the discriminability of individual samples within each hyperedge.
We incorporate hyper-Laplacian manifold regularization to preserve view-specific higher- order local geometric structures, thereby further enhancing the robustness and effectiveness of representation learning.
Experimental results demonstrate the superiority of our approach, highlighting its effective- ness in capturing high-order correlations and improving clustering performance compared to existing methods.

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2 Related work
2.1 Hypergraph neural network
hypergraph 9 = (V,E) is a generalized graph structure capable of modeling high-order relation- ships, where denotes the set of vertices and & denotes the set of hyperedges. The hyperedges can be represented using an incidence matrix H E {0, 1| where each entry h(u, e) equals if vertex v belongs to hyperedge e, and 0 otherwise. Each hyperedge is associated with a non-negative weight, which can be encoded in diagonal matrix W E IR E|x(ē] with diagonal elements w(e). The degree of a vertex and hyperedge are defined as:
d(v) Σ w(e)h(u,e) d(e) = Eh(u,e), CEE
(1)
VEV
which can be organized into diagonal matrices D, and De, respectively.
Based on these definitions, the normalized hypergraph Laplacian matrix is formulated as:
LH D. HWD H
(2)
Owing to the expressive power of hypergraph structures in modeling high-order relationships, hy- pergraph neural networks (HGNNs) have attracted increasing attention in recent years. The general HGNN framework typically consists of two key components: hypergraph construction and hypergraph convolution [23] According to whether hyperedge construction is performed explicitly implic- itly, hypergraph construction methods can be broadly categorized into four types: distance-based, representation-bute based, attribute-based, and network-based approaches [24]. Hypergraph convolutions can be further classified into spatial and spectral methods, depending on how the convolutional opera- tors are defined [25]. Recently, hypergraph- based models have demonstrated impressive performance in clustering tasks. For instance, [26] and (27 leverage hypergraphs to effectively capture attribute information and high-order structural dependencies, achieving strong results in single-vier niew node classification and clustering. However, most existing approaches are tailored to single-view settings, and relatively limited attention has been paid to exploring hypergraph learning in the context of multi-view clustering.
2.2 Multi-view contrastive clustering
In the domain of multi-view clustering, contrastive learning demonstrated strong potential in promot- ing cross-view alignment (2)33) For instance, Trosten et al. (34) enhanced multi-view clustering by aligning representations the instance level. Similarly, Xu et al. (35) introduced contrastive learning at multiple feature levels, including high-level semantic consistency and cluster-level con- sistency across views. Their approach effectively mitigated the negative impact of view-specific inconsistencies in low-level features, resulting in more stable representation alignment. Pan and Kang (36] proposed method that first obtains smooth node representation through graph filtering and then learns robust consensus graph guided by graph contrastive loss for clustering. Xu et al. (37 introduced self-supervised framework that utilizes global pseudo-labels help different views collaboratively learn discriminative features, improving both the consistency and robustness of multi-view clustering. addition, Zhang et al. [38 leveraged contrastive learning to align generated and real views by applying diffusion and reverse denoising processes to intra-view data, enabling the model capture distributional consistency and improve clustering performance.
3 Method
In this section, we introduce the proposed HOPER model. We first provide an overview of the HOPER framework, then describe the latent representation learning based on hypergraph neural net- works, the hypergraph-enhaneed dual contrastive learning mechanism, and the hypergraph Laplacian regularization. Lastly, present the unified loss function that integrates all these components.
3.1 Framework outline
Given a multi-view dataset (X" E NR.... M with N samples and M views, where X denotes the raw input of the v-th view, the goal of multi-vien clustering is to partition the data into K clusters.

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X
E1
gz H
z
HGNN
p1
MLP
p
Head
X
D1
Linter (P', pi)
Shared Weights
Shared Weights
Ged (ZM H
XM
EM
ZM
HGNN
PM
MLP
MM
Head
M
DM
Lintra (P', pt)
Pretrain
>,T X
80112
R
v=1
P
Finetune
Lreg (Pt, Lnp))
L Linter + d + 22 freg
Unified Rep.
Result
J Figure I: Illustration of the HOPER model. Given a multi-view dataset {X" Je=1- we first learn latent representations and build view-specific hypergraphs. These are fed into shared HGNN generate embeddings. Then, dual contrastive learning mechanism enhances consistency and discrimination. Finally, hyper-Laplacian regularization preserves the local geometric structure.
The overall framework of the proposed HOPER model is illustrated in Figure I Specifically, for each view, first employ autoencoder to project the raw features into latent space and then construct a corresponding hypergraph structure based on the latent representations. The sample features and the corresponding hypergraph structure are then fed into hypergraph neural network (HGNN) dual
with shared parameters to learn node representations. Subsequently, a hypergraph-enharr contrastive learning strategy is applied to the embeddings improve both cross-view consistency and sample-level discriminability. Finally, a hyper-Laplacins regularization term is introduced to automatically preserve the local high-order geometric structure of each view in the embedding space.
3.2 Hypergraph construction and HGNN-based representation learning
To effectively model high-order correlations among data instances, we first construct view-specific hypergraph structures. Considering that raw multi-view data may contain noise and redundant information, directly constructing hyperedges based on the original features can degrade the quality of the hypergraphs. To address this issue, instead of relying
raw input features, we adopt an autoencoder to project the original data X into compact latent space. Specifically, the autoencoder comprises an encoder Z [X";; 0*) and decoder X x = g(Z"; d²), where 0 and Φ are trainable parameters. The model is trained to minimize the reconstruction loss, as defined in Eq. (3).
M X
LR
X
After training, compact latent embeddings Z" are obtained from the encoder module. Subsequently. multi-view hypergraph structures constructed by applying k-nearest neighbors strategy these latent embeddings, where k is predefined parameter specifying the number of neighbors to select. Specifically, for each view, we compute the pairwise Euclidean distances between all samples to capture local geometric relationships. For each sample, we identify its top-k nearest neighbors and construct hyperedge connecting the sample with its neighbors. This process generates collection of hyperedges that encode high-order relationships beyond simple pairwise connections, represented by the incidence matrix H Finally, the hypergraph for the w-th view obtained, denoted as g" (V",E"), with feature matrix Z and incidence matrix H

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To further enhance the discriminative capability of latent representations by leveraging high-order relationships among samples, we incorporate a hypergraph neural network (HGNN) into our frame- work to learn more expressive node embeddings. Specifically, we adopt a two-layer HGNN module composed of stacked hypergraph convolution layers for node representation learning. Following 23 hyperedge convolutional layer is formulated as:
P = o "DW'D " O))
where a denotes the nonlinear activation function, O2 denotes the learnable parameter, Pf is the node representation I layer. P Z". Notably, the HGNN network of different views share parameters in order to better align the learned representations across views.
3.3 Hypergraph-enhancee dual contrastive learning
Multi-view data provide complementary perspectives of the same underlying object, and typically exhibit semantic consistency across views. This cross-view consistency can be effectively exploited through contrastive learning. However, existing multi-view contrastive learning methods focus on aligning paired samples across views, treating them as positives while largely ignoring intra-view structural characteristics. Specifically, in each view, samples connected by the same hyperedge in the underlying hypergraph often interact through a message passing scheme, which can induce an over- smoothing effect making originally distinguishable samples overly similar in representation space. While such samples may share local semantic information, they should still remain discriminative to preserve meaningful structural distinctions. The failure to account for this nuance limits the expressiveness of the learned representations, ultimately hindering clustering performance.
To address this limitation, propose hypergraph-enhaar nism, which jointly performs inter-view and intra-view contrastive learning. Specifically, inter-view contrastive learning aligns representations across views by encouraging cross-view consistency, while the intra-view contrastive learning leverages hyperedge structural information to enhance the discriminabiliiyy among samples within each view.
dual contrastive learning mecha-
Inter-view contrastive loss: This loss function is typically designed to compare node representations learned from different views, aiming to maintain consistency across views. Let pa denote the node features, i.e., the output of the projection head for node representations. Specifically, representations of the same instance across different views are treated as positive pairs, while all other instances are regarded as negative pairs. The inter-view contrastive loss Linter is defined as:
exp (s( P )/T)
Cinter (p.) log
(5)
ビ== Em exp
where denotes the temperature parameter, s-) denotes the similarity function which is implemented as cosine similarity.
Intra-view contrastive loss: Due to the strong connectivity introduced by hyperedges, the message passing mechanism in HGNN may lead an over-smoothing issue, where node representations tend to become Indisinguushabll-essseee
for nodes connected by the same hyperedge-thur undermining their discriminative power [39]. To mitigate this, we introduce an intra-view contrastive learning strategy that enhances the distinctiveness of individual samples. Specifically, each node is treated positive pair with itself, while other nodes within the same hyperedge are considered negative samples. The intra-view contrastive loss Lintra is formulated as
exp (s(P) D/)/T)
Linua (p.) log Σj ΣJENY exp (s(p), DT)/T)'
(6)
where N denotes the set of neighbors which are in the same hyperedges as node i in v-th view. In experiments, the temperature parameters in Equation (5) and Equation (6) are shared optimized.
By integrating the aforementioned dual contrastive learning strategy, the model not only enforces global alignment across views but also enhances local discriminability within each view, thereby yielding more robust and semantically meaningful representations.
3.4 Hyper-Laplacian regularization
To better preserve the intrinsic local structure of the data, we incorporate a hypergraph Laplacian regularization term into model. By leveraging the hypergraph Laplacian, this regularizer embeds
5

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Algorithm Hypergraph-enhanced Multi-view Representation Learning
Input:
Multi-view raw features /=*1 number of clusters K
Output: Cluster assignments via k-means unified representations Pretraining:
2: for each view e = 1 to M do
3: Pretrain the view-specific autoencoder by optimizing Eq.(3)
4: end for
5: Feature Encoding:
6: Obtain node features {Z") ===1 from encoder networks
M.M
7: Hypergraph Construction:
8: Construct view-specific hypergraphs via k-NN strategy on Z
9: Joint Optimization:
10: for = 1 to Timax do
11: Update the shared hypergraph encoder and projection head by optimizing Eq.
12: end for
13: Fusion:
14: Compute unified representations using Eq.
15: Clustering:
16: Apply k-means to obtain final clustering results
the manifold assumption into the learning process that is, if multiple data points are close in the intrinsic geometry of the data space, their representations in the latent space should also be similar. This mechanism promotes smoothness of the learned representations over the hypergraph, thereby enhancing the model's ability to capture higher-order structural information and improving its generalization performance on downstream tasks. The mathematical expression is as follows:
M Lreg Σ (r((PL;((P)))
where LE is hyper-graph Laplacian matrix of the w-th view. By introducing this hyper-Laplacian regularization, model gains the ability exploit richer structural information beyond simple pairwise constraints, leading to improved representation quality and better generalization performance across downstream tasks.
3.5
The overall loss function
By integrating the intravviw and inter- view contrastive loss, and the hypergraph Laplacian regular- ization, the overall loss function of the proposed HOPER model is formulated as follows:
C = Linter + X Cintra + XzCreg
(8)
Overall, the optimization our method consists of two stages: initialization and fine-tuning. During the initialization stage, we first pretrain view-specific autoencoder for each view by minimizing the reconstruction loss, as defined Eq. Once pretraining is completed, we construct a hypergraph structure for each view based the learned latent representations. In the fine-tuning stage, the entire network trained by optimizing the objective function given in Eq. (8) After optimization, the learned node embeddings from all views concatenated to form the unitied representation P:
Nx Σ
P P= [P_ P=P- P2
p=.
PMP
E
where d, denotes the dimension of P Finally, the unified representation P is used input to the k-means algorithm to produce the clustering results. The whole learning process is summarized in Algorithm
3.6 Comparison with Previous Studies
Although recent studies have explored Hypergraph Contrastive Learning (HCL) 40.44 and Hyper- Laplacian Regularization [5451), approach differs fundamentally from these existing methods.

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generally treat multi-view data as augmented variants of a single view, whereas our framework defines multi-view data heteroge- neous feature sets extracted from the same instance, capturing genuinely distinct and complementary perspectives. Second, the learning objectives differ significantly: [2 primarily target node classification, while 4 focuses on recommendation tasks. In contrast, our model ís specifically designed for unsupervised multi-view clustering, aiming to discover shared semantics and cross-view consistency without label supervision. Although [44] incorporates HCL into multi-view clustering, the two methods diverge fundamentally in terms of model design motivation, the perspective for exploiting multi-view data, and the contrastive learning mechanism. Furthermore, while some studies have incorporated shallow learning paradigms based matrix/tensor factorization graph refersepreentttinn, lacking the representational capacity of deep neural models. In contrast, our approach leverages deep learning framework that integrates Hyper-Laplache Regularization with hypergraph neural networks, enabling richer feature representations and improved clustering quality.
First, regarding application scenarios, existing HCL methods A0 42
Regularization into multi-view clustering [45] most adopt
4 Experiments
This section presents a comprehensive empirical evaluation of the proposed HOPER model, en- compassing experimental settings, performance comparisons, parameter sensitivity analysis, feature visualizations, and ablation studies.
4.1 Experimental settings
Datasets: To comprehensively evaluate the ef- fectiveness of the proposed HOPER framework, we conduct experiments on six publicly avail- able multi-view datasets. Their statistical details are shown in Table [ BBCsport contains 544 samples with 2 views, corresponding five cat- egories. Synthetic3d a 3-D dataset containing 600 samples with 3 views. WebKB contains 203 web pages of 4 categories. Each web page is described from 3 views. COIL-20 consists of 1440 samples with views which belongs to 20 categories. Handwritten contains 2000 samples of handwritten digits from 0-9, where each sam- ple is described from views. Hdigit digit dataset from MNIST Handwritten Digits and USPS
Table 1: Statistics of six benchmark datasets.
Dataset
#Samples
#Views
#Clusters
BBCSport
544
2
5
Synthetic3d
600
3
WebKB
1051
2
2
COIL-20
1440
3
20
Handwritten
2000
6
10
Hdigit
10000
2
10
Handwritten Digits which consists of 10000 samples described by 2 views.
Evaluation metrics: For evaluation, three widely-used metrics, including the clustering Accu- racy (ACC), Normalized Mutual Information (NMI), Adjusted Rand Index (ARI) are calculated to comprehensively compare the performance of various methods.
Comparison methods: We compare our framework with the following otate-of-the-art DMVC algorithms to investigate the effectiveness of our framework, i.e., MFLVC (2022) (35], CVCL (2023) 53 De (2023) (54), SEM (2023) (55), DIVIDE (2024) (56), MAGA (2024) 33
The proposed framework consists of two main modules: initialization and fine-tuning. In the initialization module, we utilize a four-layer autoencoder obtain the latent embeddings. The number of nearest neighbors of hyperedge construction is tuned over (5, 10, 15, 20, 25, 30) on different datasets. In the fine-tuning module, we optimize the hyperpa- rameters A1 and Az. Based on empirical observations, we perform a grid search over the values (0.0001, 0.001, 0.01, 0.1, 1, 10) to select the optimal values for both hyperparameters on multiple datasets. The best performance is obtained under the combination of X = 5 and X = 0.0001. These specific values were then used for all experiments reported in this paper. The training process consists of 2000 epochs for the autoencoder initialization phase and 200 epochs for the fine-tuning phase. We employ cosine learning rate decay to adjust the learning rate dynamically. All experiments are conducted using the Torch framework on an NVIDIA GeForce RTX 3090 GPU.
Implementation details:
7

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Table 2: Clustering performance across benchmark datasets.
Dataset
Metric
MFLVC
CVCL
DealMVC
SEM
DIVIDE
MAGA
HOPER
ACC
0.7224
0.6211
0.8070
0.6085
0.4467
0.5533
0.9504
BBCSport
NMI
0,5344
0.3645
0,6559
0.3666
0.1507
0.2808
0.8509
ART
0.5874
0.3137
0.6005
0.2918
0.1091
0.2286
0.8677
ACC
0,9500
0,9546
0,8033
0.9467
0.9497
0.9600
0.9717
Synthetic3d
NMI
0.8218
0.8158
0.5797
0.8095
0.8083
0.8388
0.8775
ARI
0.8582
0.8689
0,5667
0.8494
0.8553
0.8846
0.9165
ACC
0.7174
0.7181
0.6974
0.9486
0.8325
0.90T0
0,9829
WebKB
NMI
0.2986
0.2832
0,2474
0.6809
0.1791
0.4201
0.8416
ARI
0.1885
0,7810
0.1552
0.7897
0.2985
0,5986
0.9249
ACC
0.3875
0.6882
0,2299
0.7403
0.6486
0.4569
0.8285
COIL-20
NMI
0.5450
0.7851
0,4783
0.8296
0.7608
0,6317
0.8880
ARI
0.3093
0.7007
0.1735
0.6588
0.5466
0.4151
0.7869
ACC
0.8990
0.9194
0.8220
0.7645
0.8708
0.9415
0.9685
Handwritten
NMI
0.8259
0.8878
0.8163
0.7285
0.8277
0.9083
0.9317
ARI
0.7939
0.8473
0.7367
0.6317
0.8086
0.8854
0.9308
ACC
0.9882
0,9505
0.9980
0.9864
0.9646
0.9954
0.9961
Hdigit
NMI
0.9841
0.8900
0.9934
0.9606
0.9103
0.9856
0.9876
ARI
0,9882
0.8930
0.9980
0.9701
0.9229
0.9898
0.9961
4.2 Performance comparison
Table summarizes the performance of all methods, with the best and second-best results highlighted in bold and underlined, respectively. The experimental comparison demonstrates that the HOPER model achieves highly competitive clustering performance compared to existing baseline methods across all evaluation metrics. For instance, the COIL-20 dataset, HOPER improves upon the second-best SEM model by approximately 8.8%, 5.4%, and 12.8% in terms of ACC, NMI, and ARI, respectively. These results validate that approach, leveraging hypergraph-enhanced contrastive learning and hypergraph Laplacian manifold regularization, enhances the discriminability of latent representations, thereby improving clustering performance. Moreover, although the HOPER model does not achieve the best result on the Hdigit dataset, its accuracy is nearly 100% and only 0.19 lower than that of DealMVC, further validating the effectiveness of our approach.
4.3 Parameter sensitivity analysis
In the HOPER model, two hyperparameters, A and X2 are introduced to balance the contrastive learning objective and the hyper-Laplacian regularizationn term. To evaluate the model's sensitivity, we conduct grid search over The clustering results (ACC) on various datasets are reported in Figure 2 On Synthetic3D, WebKB, and COIL-20 datasets, HOPER demonstrates consistent and stable clustering performance across the range of parameter values. Some fluctuations are observed on BBCSport, Handwritten, and Hdigit datasets, which may be attributed to the trade-off between the regularization terms affecting the discriminative quality of the learned representations. Overall, despite minor variations, HOPER maintains robust and competitive clustering results within the evaluated hyperparameter ranges.
21, 3, 4, 5) and A2 {0.0001, 0.0002, 0.0003, 0.0004, 0.0005).
4.4 Visualization of representation evolution
In this section, we present qualitative analysis of the proposed HOPER model on the BBCSport dataset by visualizing the learned representations at different stages of the framework. As shown in Figure 3 subfigures (a) and (b) illustrate the raw data from two views, X and X while (c) and (d) show the corresponding latent embeddings Z and Z obtained via the autoencoder module. Compared with the raw inputs, the latent embeddings reveal a clearer clustering structure, suggesting that the autoencoder effectively denoises the data and captures more compact representations. Subfig- ures (e) and (f) visualize the node representations p1 and p2 refined by the hypergraph contrastive learning module and the hypergraph Laplacian regularization. These representations exhibit more dis- criminative and well-separated clusters than their latent counterparts, highlighting the effectiveness of the proposed hypergraph-baat based enhancements in capturing high-order and local relational structures

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10
1.
088
Eos
go.
Eos
0.4
0.2
0.0
12(-101)
12(110-)
12
3
BBCSport
(b) Synthetic3d
(c) WebKB
0.8
80.6
Eas
30.6
2
2
12(-197)
12
12
(d) COIL-20
(e) Handwritten
(f) Hdigit
Figure 2: Hyperparameter sensitivity analysis of the HOPER model on multiple datasets.
within each view. Finally, subfigure (g) depicts the unified representation aggregated from multiple views. exhibits the most compact and separable cluster structures among all stages, demonstrating the ability of HOPER to effectively exploit cross- view complementary information and enhance the overall representation quality, thereby leading to improved clustering performance.
(a) View X!
(b) View 2: x
(c) View 1:
(d) View z
(e) View I: P
(f) View 2: p2
Unified P.
Figure 3: Visualization of the learned representations at different stages of the HOPER.
4.5 Convergence analysis
In this subsection, we demonstrate the convergence HOPER across six datasets by reporting the loss values. As shown in Figure the horizontal axis represents the training epochs and the vertical axis denotes the loss value. It can observed that the loss drops rapidly during the first 100 epochs and then gradually decreases until convergence.

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4.6 Ablation studies
As defined in Eq. 8, the overall loss function of HOPER consists of three components. To investigate the individual contribution of each term, we conduct ablation studies by systematically removing each component and retraining the model under the same experimental set- tings. Table the clustering performance on multiple datasets under different loss configurations, where checkmark indicates that the corresponding loss term is included. The experimental results demonstrate that removing any single component from the com- plete HOPER model consistently leads to performance degradation across all datasets, with some cases exhibiting significant drops. This highlights that HOPER effectively integrates vnter-view contrastive learning, intra-view view contrastive learning, and hypergraph Laplacian manifold regularization, which together promote cross-view consistency in sample representations while preserving inter-sample discriminability, ultimately enhancing clustering performance.
00-
sucoport
Wetks
CoI-22
60
Handomiten
Hage
30
20
Epochs
Figure 4: Convergence analy- sis of the HOPER model on multiple datasets.
Table 3: Ablation study on the effects of individual loss components in HOPER.
Components
BBCSport
Synthetic3d
WebKB
Lintra
Linter
Lreg
ACC
NMI
ARI
ACC
NMI
ARI
ACC
NMI
ARI
0,8897
0.7785
0.8076
0.9650
0.8624
0.8990
0.9686
0.7520
0.8659
0.9449
0.8371
0.8529
0.9500
0.8117
0.9504
0.9724
0.7744
0.8815
0.5147
0.4724
0.2553
0.9667
0.8607
0.9027
0.9629
0.7151
0.8387
0.9504
0.8509
0.8677
0.9717
0.8775
0.9165
0.9829
0.8416
0.9249
Components
COIL-20
Handwritten
Hdigit
Lintra
Linter
Lreg
ACC
NMI
ARI
ACC
NMI
ARI
ACC
NMI
ARI
0,7910
0.8740
0.7597
0.8285
0.8573
0.7857
0.7022
0.8661
0.7173
0.7549
0.8781
0.7358
0.8695
0.8529
0.7915
0.8471
0.9117
0,8406
0.7847
0.8687
0.7496
0.8240
0.8814
0.8410
0.9268
0.8439
0.6537
0.8285
0.8880
0.7869
0.9685
0.9317
0.9308
0.9961
0.9876
0.9961
Conclusion
This paper proposes a novel multi-view clustering framework, HOPER, which integrates hypergraph- enhanced contrastive learning with hypergraph Laplacian regularization learn discriminative feature representations. Specifically, HOPER captures high-order relationships among samples through hypergraph construction and hypergraph neural networks. To further improve representation quality, a hypergraph-driverr dual contrastive learning mechanism is introduced, comprising inter-view contrastive learning and hera-hy contrastive learning, which promotes cross-viee view consistency while preserving discriminability within hyperedge. In addition, hypergraph Laplacian regularization employed to preserve high-order local structural information. Extensive experiments on benchmark datasets demonstrate that HOPER achieves highly competitive performance, validating its effectiveness for discriminative representation learning.
Limitations
potential limitation of our method its relatively higher computational complexity compared to traditional graph-based approaches. This is because hypergraphs introduce hyperedges that connect multiple nodes to capture high-order relationships, leading to more complex operations involving the incidence and Laplacian matrices than in conventional graphs where edges link only two nodes.
Acknowledgements
This work was supported by the Natural Science Foundation of Hebei Province (No. F2025205006), the Science Foundation of Hebei Normal University (No. 1.2025338) and the Backbone Talent Program (Program for Returned Overseas Scholars) (No. A2025016).
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Reviews:
[{"review_id": "yVC8aHOodK", "reviewer": "Reviewer_Htnz", "summary": "This paper proposes HOPER, a novel multi-view clustering framework that integrates hypergraph-enhanced contrastive learning with hypergraph Laplacian regularization to learn discriminative feature representations.", "questions": "1, Hypergraph Contrastive Learning has been proposed in: \"Multi-view Mixed Attention for Contrastive Learning on Hypergraphs. In Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval\", \"Multi-view Hypergraph Adaptive Contrastive Learning. In Pacific-Asia Conference on Knowledge Discovery and Data Mining\", \"Multi-view hypergraph contrastive policy learning for conversational recommendation. In Proceedings of the 46th international ACM SIGIR conference on research and development in information retrieval\", \"Cross-view graph contrastive learning with hypergraph. Information Fusion, 99, 101867.\"\nThe authors should clarify the differences between their method and other methods.\n2. Hyper-Laplacian Regularization has also been proposed in: \"Hyper-Laplacian regularized multi-view clustering with exclusive L21 regularization and tensor log-determinant minimization approach. ACM Transactions on Intelligent Systems and Technology, 14(3), 1-29\", \"Hyper-Laplacian Regularized Concept Factorization in Low-Rank Tensor Space for Multi-View Clustering. IEEE Transactions on Emerging Topics in Computational Intelligence\", \"Hyper-Laplacian regularized multi-view subspace clustering with low-rank tensor constraint. Neural Networks, 125, 214-223\", \"Hyper-Laplacian regularized nonconvex low-rank representation for multi-view subspace clustering. IEEE Transactions on Signal and Information Processing over Networks, 8, 376-388.\"\n The authors should also clarify the differences between their method and other methods.\n3. In summary, the two main contributions have been proposed in previous methods. The authors should clarify that their method is not a simple combination of existing methods. Moreover, these methods should also be compared in experiments.", "limitations": "1. The novelty is limited: Hypergraph Contrastive Learning and Hyper-Laplacian Regularization have all been proposed in previous studies.\n2. The comparisons have not included previous methods using Hypergraph Contrastive Learning and Hyper-Laplacian Regularization.", "rating": 2, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 1, "strengths_and_weaknesses": "Strengths：\n1. The structure of this paper is great.\n2. The experiments are comprehensive.\n3. The motivation is clear.\n\nWeaknesses:\n1. The novelty is limited: Hypergraph Contrastive Learning and Hyper-Laplacian Regularization have all been proposed in previous studies.\n2. Figure 2 is less informative.", "was_revised": false, "final_justification": "", "rebuttal": "**Weakness 1: The novelty is limited: Hypergraph Contrastive Learning and Hyper-Laplacian Regularization have all been proposed in previous studies.**\n\n**A1:** Thank you for your valuable comment. While it is true that hypergraph contrastive learning and hyper-Laplacian regularization have been previously studied, we respectfully emphasize that our method is substantially different in both application scope and technical integration, and is not a straightforward combination of existing techniques.\n\n**First**, the application domains are different. Existing Hypergraph Contrastive Learning methods have predominantly focused on single-view node classification tasks. In contrast, our method is designed for multi-view unsupervised clustering, which poses distinct challenges and requires different methodological considerations.\n\n**Second**, although some prior works have incorporated Hyper-Laplacian Regularization into multi-view clustering, these are mostly shallow models that apply Laplacian constraints on subspace representations to preserve local structures. In contrast, our work is, to the best of our knowledge, the first to introduce Hyper-Laplacian Regularization into a deep learning-based multi-view clustering framework. Rather than regularizing subspace representations, we apply the regularization directly on the learned feature embeddings to enhance their discriminability, which in turn improves clustering performance.\n\n**In summary**, although related concepts have been explored previously, our method is novel in both its application domain and technical design. Specifically, we are, to the best of our knowledge, the first to integrate hypergraph neural networks into the multi-view clustering setting, which represents a meaningful advancement in this area.\n\n**Weakness 2: Figure 2 is less informative.**\n\n**A2:** Thank you for your comment. In the revised manuscript, we will improve Figure 2 by adding clearer annotations and visual enhancements to better convey the model architecture and overall workflow.\n\n**Question 1: Hypergraph Contrastive Learning has been proposed in [1][2][3][4], The authors should clarify the differences between their method and other methods.**\n\n**A3:** Thank you for your insightful question. While References [1]–[4] have indeed applied Hypergraph Contrastive Learning, our method differs from them in several fundamental aspects.\n\n**First**, the **application scenarios** are different. Although some of these works (e.g., [1], [2], [4]) mention “multi-view” in their titles, they actually operate on single-view data. Specifically, their so-called \"multi-view\" refers to augmented versions of the same view, whereas in our work, \"multi-view\" denotes heterogeneous features extracted from the same instance, representing truly distinct views. To further explain this difference from information theory, the multi-view data $\\mathbf{X}^1$ and $\\mathbf{X}^2$ in our work are extracted from $p(x_1,y)$ and $p(x_2,y)$. The multi-view data in references [1],[2],[4] are genereated from $p(x,y)$ by adding additional information randomly or user-defined data pattern.\n\n**Second**, the tasks being addressed are not the same. References [1], [2], and [4] focus on node classification tasks, while [3] deals with recommendation. In contrast, our method is designed for unsupervised multi-view clustering, which poses different challenges and objectives.\n\n**Third**, our contrastive learning mechanism is also different. We propose a novel dual contrastive learning strategy that performs both cross-view and within-view contrast. By integrating this dual mechanism, our model not only enforces global alignment across views but also enhances local discriminability within each view, leading to more robust and semantically meaningful representations.\n\n**In summary, although prior works have explored Hypergraph Contrastive Learning, they differ significantly from ours in terms of the data setting, task, and methodological design.**\n\n**Question 2: Hyper-Laplacian Regularization has also been proposed in [5][6][7][8]. The authors should also clarify the differences between their method and other methods**\n\nThank you for your insightful comment. While it is true that Hyper-Laplacian Regularization has been utilized in previous works [5–8], our method is substantially different from these approaches in several key aspects:\n\n**Modeling paradigm:** Prior works [5–8] are based on shallow subspace clustering models. They typically use self-representation techniques to construct subspace representations, followed by spectral clustering. In contrast, our method adopts a deep learning-based framework that directly learns discriminative feature embeddings tailored for clustering, offering better scalability and representation power.\n\n**Target of regularization:** In [5–8], Hyper-Laplacian Regularization is applied to the subspace representation matrices to preserve local geometric structures within the learned subspaces. In our approach, the regularization is imposed on the latent feature embeddings generated by the deep network. This allows the model to explicitly encourage local smoothness and structure preservation in the learned feature space, which is more effective for clustering tasks.\n\n**Overall framework:** Our model integrates hypergraph neural networks, a dual hypergraph contrastive learning mechanism, and Hyper-Laplacian Regularization into a unified deep framework. This holistic design enables the model to capture both high-order correlations across views and local geometric consistency within each view, significantly improving clustering performance.\n\n**In summary**, although our work builds upon the idea of Hyper-Laplacian Regularization, we adopt a fundamentally different model structure and apply the regularization in a novel context. To the best of our knowledge, this is the first deep multi-view clustering framework to incorporate Hyper-Laplacian Regularization at the feature level. We will further clarify these differences in the revised manuscript.\n\n**Question 3:  In summary, the two main contributions have been proposed in previous methods. The authors should clarify that their method is not a simple combination of existing methods. Moreover, these methods should also be compared in experiments.**\n\nA5:  As detailed in our responses to **Q1** and **Q2**, although Hypergraph Contrastive Learning [1–4] and Hyper-Laplacian Regularization [5–8] have been studied in previous literature, our method is not a straightforward combination of existing techniques. Instead, it introduces several key innovations that distinguish it fundamentally from prior approaches: \n\n**Distinct application scenario and task:** Prior works mostly focus on single-view data or different tasks such as node classification or dialogue recommendation. In contrast, our method is specifically designed for unsupervised multi-view clustering, where each view represents truly heterogeneous feature sets of the same instance. This task poses unique challenges and requires tailored model designs.\n\n**Novel deep learning framework integration:** Existing Hyper-Laplacian Regularization methods [5–8] are shallow models applied to subspace representations, whereas we integrate hypergraph neural networks, a dual hypergraph contrastive learning mechanism, and Hyper-Laplacian Regularization into a unified deep architecture. This joint design enables learning of discriminative latent feature embeddings with strong local and global structural consistency.\n\n**Innovative contrastive learning strategy:** Our dual contrastive learning approach simultaneously enforces global alignment across views and local discriminability within views, which is not explored in prior works and is crucial for robust multi-view representation learning.\n\n**In summary, our work presents a fundamentally different and novel solution for deep multi-view clustering by innovatively integrating and extending existing techniques within a new application and model paradigm.**\n\nRegarding the suggestion to include experimental comparisons with these prior methods, we fully acknowledge the importance of empirical validation. However, most of the referenced methods address different research problems or adopt substantially different modeling paradigms. For example, [1], [2], and [4] focus on single-view node classification, [3] targets dialogue recommendation, and [5]–[8] are shallow subspace clustering models. As such, direct quantitative comparisons may not be meaningful or fair. Nevertheless, we will further highlight these distinctions in the revised manuscript and include detailed discussions to help clarify the positioning of our work within the broader research landscape.\n\n[1] Multi-view Mixed Attention for Contrastive Learning on Hypergraphs. ACM SIGIR Conference on Research and Development in Information Retrieval.\n\n[2] Multi-view Hypergraph Adaptive Contrastive Learning. PAKDD.\n\n[3] Multi-view hypergraph contrastive policy learning for conversational recommendation. ACM SIGIR conference on research and development in information retrieval.\n\n[4] Cross-view graph contrastive learning with hypergraph. Information Fusion, 99, 101867.\n\n[5] Hyper-Laplacian regularized multi-view clustering with exclusive L21 regularization and tensor log-determinant minimization approach. ACM TIST, 14(3), 1-29.\n\n[6] Hyper-Laplacian Regularized Concept Factorization in Low-Rank Tensor Space for Multi-View Clustering. IEEE Transactions on Emerging Topics in Computational Intelligence. \n\n[7] Hyper-Laplacian regularized multi-view subspace clustering with low-rank tensor constraint. Neural Networks, 125, 214-223\".\n\n[8] Hyper-Laplacian regularized nonconvex low-rank representation for multi-view subspace clustering. IEEE Transactions on Signal and Information Processing over Networks, 8, 376-388."}, {"review_id": "0W7C1ZZ9ZE", "reviewer": "Reviewer_mwWy", "summary": "In this work, the authors propose a hypergraph-enhanced contrastive learning method for multi-view clustering. The method leverages hypergraph structures and a weight-sharing hypergraph neural network to capture high-order data correlations. In addition, it introduces an inter-view sample discriminability enhancement strategy, which effectively alleviates the issue of weak discriminability caused by information propagation in hypergraph neural networks. Extensive experiments validate the feasibility and effectiveness of the proposed model.", "questions": "Please see Weaknesses.", "limitations": "This work is a fundamental study in deep clustering and does not exhibit obvious limitations.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths：\n1. Introducing hypergraph neural networks into multi-view clustering effectively captures high-order data correlations. This idea is highly innovative.\n\n2. The simultaneous use of inter-view and intra-view contrastive losses significantly enhances the discriminability of learned sample representations, which is highly beneficial for clustering tasks.\n\n3.  A series of experiments, including ablation studies, thoroughly validate the superior clustering performance of the proposed model.\n\nWeaknesses：\n\n1. The detailed process of hypergraph construction is missing.\n\n2. In Equation (9), there seems to be a typographical error in the size of the variable P.\n\n3. In Figure 2, the font size of the axis labels and tick marks is too small.\n\n4. The manuscript lacks convergence experiments.\n\n5. Compared with pre-training followed by fine-tuning, how does the clustering performance of the jointly optimized approach compare?", "was_revised": false, "final_justification": "", "rebuttal": "**Weakness 1：The detailed process of hypergraph construction is missing.**\n\n**A1:**  Thank you for your constructive comment. To elaborate, the hypergraph construction in our method is based on a k-nearest neighbors (k-NN) strategy tailored for multi-view data. Specifically, for each view, we compute the pairwise Euclidean distances between all samples to capture local geometric relationships. For each sample, we then identify its top-k nearest neighbors and form a hyperedge that connects this sample with those neighbors. This results in a set of hyperedges that represent high-order relations beyond simple pairwise connections. By leveraging these hyperedges, the hypergraph can effectively encode complex structural and contextual information inherent in each view. This design enables our model to better capture local manifold structures and preserve intrinsic data geometry, which are critical for robust and discriminative representation learning. We will provide a detailed description of this process in the revised manuscript to clarify the construction and its rationale.\n\n**Weakness 2：In Equation (9), there seems to be a typographical error in the size of the variable P.** \n\n**A2:** Thank you for pointing out this issue. We have carefully reviewed Equation (9) and confirmed the typographical error regarding the size of the variable P. The correct dimension should be  ${\\mathbb{R}}^{N \\times \\sum\\limits_{v=1}\\limits^M d_{v}}$, where $d_{v}$ denotes the dimension of $\\mathbf{P}^v$. We will correct this in the revised manuscript to ensure clarity and accuracy.\n\n**Weakness 3: In Figure 2, the font size of the axis labels and tick marks is too small.**\n\n**A4:** Thank you for your detailed comment. We will address this issue in the revised manuscript by enlarging the axis labels and tick marks to improve readability.\n\n**Weakness 4:  The manuscript lacks convergence experiments.**\n\n**A5**  Thank you for pointing this out. To address this concern, we will include convergence experiments in the revised manuscript to illustrate the training stability and efficiency of our proposed method.\n\n**Weakness 5:  Compared with pre-training followed by fine-tuning, how does the clustering performance of the jointly optimized approach compare?**\n\n**A5:** Thank you for this insightful comment. \nOur framework employs a two-stage optimization, pre-training followed by fine-tuning to balance view-specific representation learning and view-consistent information capture. During the pre-training process, view-specific autoencoders are trained to preserve view-specific information and obtain representative view-specific embeddings. The embeddings serve as inputs for hypergraph construction and hypergraph encoder. During the fine-tuning process, we aim to capture the view consistent information from the view-specific embeddings through contrastive learning strategy. To clarify, in this stage, the view-specific autoencoder models are frozen.\n\nCompared with joint optimization, our two-stage approach offers **explicit consistency extraction**. It enables clear separation of view-consistent information through distinct optimization phases. In contrast, jointly optimization would require handling dynamic hypergraph structures, as continuously updated embeddings from the autoencoders would modify hyperedge connectivity during training. We will further elaborate on this point in the revised manuscript."}, {"review_id": "b2LTn7Oi6o", "reviewer": "Reviewer_4ypD", "summary": "The manuscript addresses a key limitation of current deep multi-view clustering methods that overlook higher-order sample interactions by focusing only on pairwise relations. To tackle this, the authors leverage hypergraph neural networks combined with a dual contrastive learning strategy to improve cross-view alignment and intra-hyperedge discrimination. The integration of hyper-Laplacian regularization further preserves local manifold structures. Experimental results on multiple benchmarks validate the method’s superior clustering performance.", "questions": "(1) The definitions and roles of inter-view and intra-view contrastive losses are not clearly articulated. It remains unclear how each specifically contributes to cross-view consistency and within-view discriminability.\n\n(2) Equation (7) lacks a detailed explanation of the construction of the hypergraph Laplacian matrix and the mechanism behind the hyper-Laplacian regularization term.\n\n(3) Figure 2 indicates that the proposed method exhibits stable performance on some datasets but fluctuates significantly on others. The manuscript should discuss potential reasons for this variation in robustness.\n\n(4) While hypergraph construction is intended to capture high-order relations to enhance representation learning, the underlying mechanism is not sufficiently explained and would benefit from a more in-depth discussion.", "limitations": "A potential limitation of hypergraph modeling is the increased computational complexity associated with capturing high-order relationships. This aspect should be explicitly acknowledged and discussed in the manuscript.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths：\n\n(1) The manuscript is well-structured, and the overall logic is rigorous and coherent.\n\n(2) The use of high-order structural priors and contrastive learning to facilitate clustering-friendly representation learning is a novel and interesting idea.\n\n(3) The experimental setup is clearly presented, and the proposed method achieves better performance than recent multi-view clustering approaches.\n\nWeaknesses:\n\n(1) The description of the dual contrastive losses is insufficient and requires further clarification.\n\n(2) The descriptions of some equations are insufficient; specifically, the temperature parameters in Equations (5) and (6) lack clarity regarding whether they are shared or separately optimized. \n\n(3) There are formatting inconsistencies, including mixed italic and upright subscripts in Equations (5) and (6), as well as inconsistent table header styles.", "was_revised": true, "final_justification": "This paper proposed a simple but effective method, and I have no further concerns.", "rebuttal": "**Weakness 1: The description of the dual contrastive losses is insufficient and requires further clarification.**\n\n**A1:**   Thank you for your valuable feedback. We agree that the original explanation of the dual contrastive losses could benefit from further clarification. To clarify, our proposed hypergraph-enhanced dual contrastive learning jointly optimizes two complementary objectives. The inter-view contrastive loss aligns representations of the same instance across different views, enforcing global semantic consistency. Meanwhile, the intra-view contrastive loss addresses the over-smoothing issue caused by message passing within hypergraphs by treating each node as a positive pair with itself and considering other nodes within the same hyperedge as negatives. This promotes local discriminability and preserves meaningful structural differences within each view. By combining these two losses, our model effectively captures both cross-view alignment and fine-grained intra-view distinctions, leading to more robust and semantically rich representations. We will further elaborate on this point in the revised manuscript.\n\n**Weakness 2:  The descriptions of some equations are insufficient; specifically, the temperature parameters in Equations (5) and (6) lack clarity regarding whether they are shared or separately optimized.**\n\n**A2:** Thank you for your comment. The temperature parameters in Equations (5) and (6) are the same and shared for both inter-view and intra-view losses. We wii clarify this in the revised manuscript to avoid confusion.\n\n**Weakness 3:   There are formatting inconsistencies, including mixed italic and upright subscripts in Equations (5) and (6), as well as inconsistent table header styles.**\n\n**A3:** Thank you for pointing this out. We will correct the formatting inconsistencies in Equations (5) and (6) and standardize the table headers in the revised manuscript.\n\n**Question 1:  The definitions and roles of inter-view and intra-view contrastive losses are not clearly articulated. It remains unclear how each specifically contributes to cross-view consistency and within-view discriminability.** \n\n**A4:** Thank you for your valuable comment. We will clarify the definitions and roles of the inter-view and intra-view contrastive losses in the revised manuscript. Specifically, the inter-view loss enforces alignment of the same instance across different views to ensure cross-view consistency, while the intra-view loss enhances discriminability within each view by leveraging hypergraph structure to prevent over-smoothing. This distinction will be clearly articulated to better demonstrate how each loss contributes to the overall representation learning.\n\n**Question 2: Equation (7) lacks a detailed explanation of the construction of the hypergraph Laplacian matrix and the mechanism behind the hyper-Laplacian regularization term.**\n\n**A5:**  Thank you for your valuable comment. A hypergraph $\\mathcal{G} = (\\mathcal{V}, \\mathcal{E})$ is a generalized graph structure modeling high-order relationships, where $\\mathcal{V}$ is the set of vertices and $\\mathcal{E}$ the set of hyperedges. The hyperedges are represented by an incidence matrix $\\mathbf{H} \\in \\\\{0,1\\\\}^{|\\mathcal{V}| \\times |\\mathcal{E}|}$, where $h(v,e)$ if vertex $v$ belongs to hyperedge $e$, and 0 otherwise. Each hyperedge is associated with a non-negative weight encoded in a diagonal matrix  $\\mathbf{W}$. The degrees of vertices and hyperedges are defined as $d(v) = \\sum_{e \\in \\mathcal{E}} w(e) h(v, e)$ and $d(e) = \\sum_{v \\in \\mathcal{V}} h(v, e)$, which correspond to diagonal matrices $\\mathbf{D}_v$ and $\\mathbf{D}_e$, respectively. Based on these definitions, the normalized hypergraph Laplacian matrix is formulated as $\\mathbf{L}_H = \\mathbf{D}_v - \\mathbf{H} \\mathbf{W} \\mathbf{D}_e^{-1} \\mathbf{H}^\\top$, capturing the high-order structure of the data. The hyper-Laplacian regularization term $\\mathrm{tr}(\\widetilde{\\mathbf{P}}^{v} \\mathbf{L}_H^v (\\widetilde{\\mathbf{P}}^v)^{\\top})$ encourages smoothness of the learned representations over the hypergraph, preserving intrinsic local geometry and enhancing the model’s capacity to capture complex structural information. We will further elaborate this construction and its mechanism in the revised manuscript.\n\n**Question 3: Figure 2 indicates that the proposed method exhibits stable performance on some datasets but fluctuates significantly on others. The manuscript should discuss potential reasons for this variation in robustness.**\n\n**A6:**  The observed variation in performance stability across different datasets may be attributed to differences in data characteristics such as sample size, feature heterogeneity, and noise levels. For datasets with more complex structures or higher noise, the model may experience greater fluctuations during training. We will include a detailed discussion of these factors and their impact on robustness in the revised manuscript.\n\n**Question 4: While hypergraph construction is intended to capture high-order relations to enhance representation learning, the underlying mechanism is not sufficiently explained and would benefit from a more in-depth discussion.**\n\n**A7:**  In our method, hypergraphs are used to model high-order relationships by connecting multiple related samples through hyperedges, which allows capturing complex structural information beyond pairwise connections. This facilitates more expressive feature learning by encouraging smoothness and consistency among groups of related nodes, thus enhancing the quality of learned representations. We will expand the discussion of this mechanism in the revised manuscript to clarify its role and benefits in representation learning.\n\n**Limitations: A potential limitation of hypergraph modeling is the increased computational complexity associated with capturing high-order relationships. This aspect should be explicitly acknowledged and discussed in the manuscript.**\n\n**A8:** Thank you for your insightful comment. We acknowledge that hypergraph modeling, while effective at capturing high-order relationships, does introduce increased computational complexity compared to traditional pairwise graph methods. This complexity arises from the construction and processing of hyperedges that connect multiple nodes simultaneously. In the revised manuscript, we will provide a more detailed discussion on this point."}, {"review_id": "aKmSjrvdGy", "reviewer": "Reviewer_S36h", "summary": "This work proposes a hypergraph neural network-based framework for deep multi-view clustering. The method addresses the limitation of existing approaches that focus primarily on pairwise relationships by introducing view-specific hypergraphs to model high-order sample dependencies. It further incorporates a dual contrastive learning strategy to enhance both cross-view consistency and intra-hyperedge discriminability. In addition, a hyper-Laplacian regularization term is employed to preserve local geometric structures within each view. Together, these components contribute to improved clustering performance through more comprehensive structural representation.", "questions": "See Weaknesses.", "limitations": "No discussion of limitations or societal risks is provided. It would be beneficial for the authors to acknowledge any potential drawbacks or broader consequences of the proposed method.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths：\n1. The paper introduces view-specific hypergraphs to capture high-order sample relationships, addressing limitations of pairwise multi-view clustering.\n2. A novel inter-view and intra-hyperedge contrastive learning framework enhances cross-view consistency and within-hyperedge discriminability.\n3. Experiments on multiple benchmarks show superior performance over recent methods, supported by visualizations that aid interpretability.\n\nWeaknesses:\n1. The introduction lacks adequate clarification of some necessary concepts, making certain sections difficult to understand. For instance, when the authors mention using hypergraphs to model high-order correlations, it is unclear whether these high-order correlations refer to inter-view or intra-view relationships.\n2. Section 3.3 lacks a clear explanation of the motivation behind the Hypergraph-enhanced Dual Contrastive Learning. The phrase “treating them as positives” is ambiguous, as it is unclear what “them” specifically refers to. Clarifying this point would help improve understanding.\n3. The single line of ``Input'' in the pseudocode is insufficient, as it omits the hyperparameters \\(\\lambda_1\\) and \\(\\lambda_2\\).\n4. Some experimental settings are unclear. For example, the parameter configurations in Section 4.1 (“Implementation details”) are inconsistent with the hyperparameter values reported in Section 4.3, and no explanation is provided for this discrepancy.", "was_revised": true, "final_justification": "In the rebuttal, the authors' response has addressed my concerns.  I would like to keep my original positive score.", "rebuttal": "** Weakness 1: The introduction lacks adequate clarification of some necessary concepts, making certain sections difficult to understand. For instance, when the authors mention using hypergraphs to model high-order correlations, it is unclear whether these high-order correlations refer to inter-view or intra-view relationships.**\n\n**A1:** Thank you for your constructive comment. In our method, the high-order correlations captured by the hypergraph primarily refer to intra-view structural relationships among samples within the same view. These correlations are modeled by connecting multiple similar samples through shared hyperedges, which reflect complex local structures beyond pairwise interactions. In contrast, inter-view consistency is addressed through our proposed inter-view contrastive learning mechanism. We will clarify this distinction more explicitly in the revised manuscript to improve overall conceptual clarity.\n\n**Weakness 2: Section 3.3 lacks a clear explanation of the motivation behind the Hypergraph-enhanced Dual Contrastive Learning. The phrase “treating them as positives” is ambiguous, as it is unclear what “them” specifically refers to. Clarifying this point would help improve understanding.**\n\n**A2: ** Thank you for your helpful feedback. The phrase “treating them as positives” specifically refers to sample pairs representing the same instance across different views in the inter-view contrastive learning component. These pairs are treated as positive examples, while all other instances are considered negatives. The intra-view contrastive learning component, on the other hand, treats each sample as a positive with itself and treats its neighbors within the same hyperedge as negatives, in order to mitigate the over-smoothing issue caused by message passing in hypergraph neural networks. We will revise this section to clearly distinguish these elements and better explain the underlying motivation in the revised manuscript.\n\n**Weakness 3: The single line of ``Input'' in the pseudocode is insufficient, as it omits the hyperparameters  $\\lambda_1$ and  $\\lambda_2$.**\n\n**A3: **  Thank you for your careful observation. We acknowledge that the current “Input” line in the pseudocode is incomplete and omits important hyperparameters $\\lambda_1$ and $\\lambda_2$. In the revised manuscript, we will update the pseudocode to explicitly include all relevant hyperparameters in the input specification to ensure completeness and clarity.\n\n\n**Weakness 4: Some experimental settings are unclear. For example, the parameter configurations in Section 4.1 (“Implementation details”) are inconsistent with the hyperparameter values reported in Section 4.3, and no explanation is provided for this discrepancy.**\n\n**A4:**  Thank you very much for your valuable comment. The inconsistency between the parameter configurations described in Section 4.1 and the hyperparameter values reported in Section 4.3 was due to a typographical oversight on our part. In fact, the hyperparameters follow the settings described in Section 4.3, where $\\lambda_1$  is chosen from the range \n[1,2,3,4,5] and $\\lambda_2$ from [0.0001,0.0002,0.0003,0.0004,0.0005]. We will clarify this point in the revised manuscript to ensure transparency and consistency throughout the paper.\n\n**Limitations: No discussion of limitations or societal risks is provided. It would be beneficial for the authors to acknowledge any potential drawbacks or broader consequences of the proposed method.**\n\n**A5:**  Thank you for your valuable suggestion. One potential limitation of our method is the increased computational complexity introduced by hypergraph modeling. This is mainly due to the need to capture high-order relationships through hyperedges connecting multiple nodes simultaneously, which results in larger and denser incidence matrices and more complex message-passing operations. In the revised manuscript, we will provide a more detailed discussion of this limitation."}]

Author rebuttal:

Meta-review: This paper presents a new hypergraph-enhanced contrastive learning framework for multi-view clustering, which effectively integrates hypergraph neural networks with dual contrastive learning and hyper-Laplacian regularization to capture high-order sample dependencies. While one reviewer raised concerns about novelty, the other three reviewers recognized its innovation, where the integration of these components into a unified framework, along with inter-view discriminability enhancement, demonstrates practical innovation and empirical effectiveness. Considering the method’s superior performance across multiple benchmarks and its novel use of view-specific hypergraphs address key limitations in existing multi-view clustering approaches, the paper is recommended for acceptance.
Decision: Accept (poster)