Multi-View Graph Clustering via Node-Guided Contrastive Encoding
Authors: Yazhou Ren
Junlong Ke
Zichen Wen
Tianyi Wu
Yang Yang
Xiaorong Pu
Lifang He
Venue: ICML 2025 poster (2025)
Keywords: Multi-view Clustering
Unsupervised Learning
Graph Learning
Primary area: deep_learning->selfsupervised_learning

Abstract: Multi-view clustering has gained significant attention for integrating multi-view information in multimedia applications. With the growing complexity of graph data, multi-view graph clustering (MVGC) has become increasingly important. Existing methods primarily use Graph Neural Networks (GNNs) to encode structural and feature information, but applying GNNs within contrastive learning poses specific challenges, such as integrating graph data with node features and handling both homophilic and heterophilic graphs. To address these challenges, this paper introduces Node-Guided Contrastive Encoding (NGCE), a novel MVGC approach that leverages node features to guide embedding generation. NGCE enhances compatibility with GNN filtering, effectively integrates homophilic and heterophilic information, and strengthens contrastive learning across views. Extensive experiments demonstrate its robust performance on six homophilic and heterophilic multi-view benchmark datasets.

Multi- View Graph Clustering via Node-Guided Contrastive Encoding
Yazhou Ren JunLong Ke
Zichen Wen
Tianyi Wu Yang Yang' Xiaorong Pu" Lifang He
Abstract
distinction between the data associated with the ego node and that of its edges, which delineate relationships with neighboring nodes (Tang et al., 2022; Xiao et al., 2022; Chen et al., 2022). However, some methods overly em- phasize edge and neighborhood data, often neglecting the intrinsic information of the ego node. This imbalance has led to suboptimal performance on certain datasets, some- times even underperforming compared to Multi-Layer Per- ceptrons (MLPs) (Tang et al., 2022; Xiao al., 2022). On the other hand, some approaches rely heavily on the ego node's ' attributes to maintain model performance after multi- ple layers of processing in Graph Neural Networks (GNNs). While this preserves some robustness, it limits the ability to leverage contextual information from neighboring nodes, leading to subpar results on specific datasets (Chen et al., 2022).
Multi-view clustering has gained significant at- tention for integrating multi-view information in multimedia applications. With the growing com- plexity of graph data, multi-view graph clustering (MVGC) has become increasingly important. Ex- isting methods primarily use Graph Neural Net- works (GNNs) encode structural and feature in- formation, but applying GNNs within contrastive learning poses specific challenges, such as inte- grating graph data with node features and han- dling both homophilic and heterophilic graphs. To address these challenges, this paper introduces GoideG Contrastive Encoding (NGCE), a novel MVGC approach that leverages node fea- tures guide embedding generation. NGCE en- hances compatibility with GNN filtering, effec- tively integrates homophilic and heterophilic in- formation, and strengthens contrastive learning across views. Extensive experiments demonstrate its robust performance on six homophilic and het- erophilic multi-view benchmark datasets.
In the realm of graph contrastive learning for mueti-view graph clustering (MVGC), capturing node differences and diversity within graphs plays a crucial role in designing effective contrastive learning methodologies (Hassani & Khasahmadi, 2020). Traditional approaches have largely re- lied on the homophily assumption (McPherson et al., 2001), but more recent studies have begun to explore the effective- ness of these methods in the context of heterophilic graphs. For example, COMPLETER (Contrastive Prediction for In- complete Multi-view Clustering) (Lin et al., 2021) has been introduced for heterophilic graphs. It integrates reconstruc- tion, cross-view, contrastive learning, and cross-view dual prediction to simultaneously achieve data recovery and con- sistency learning for incomplete multi-view data. (Hassani & Khasahmadi, 2020) proposes contrastive multi-view rep- resentation learning on graphs (MVGRL) by performing rep- resentation learning by contrasting two diffusion matrices transformed from the adjacency matrix. HGRL (Chen et al., 2022) leverages the preservation of original node features and the capturing of non-local neighbors enhance node representations heterophilic graphs. GREET (Liu et al., 2023) distinguishes between homophilic and heterophilic edges, employing low-pass and high-pass filters to seize the corresponding information. Building upon generation meth- ods, DSSL (Xiao et al., 2022) decouples diverse patterns in local neighborhood distribution to capture both homophilic and heterophilic information. NWR-GAL (Tang al., 2022) underscores the significance of topological structure
1. Introduction
Multi-view clustering (MVC) is an important unsupervised learning task in the machine learning community (Li al., 2014; Xu al., 2022; Yin al., 2020; Tan al., 2023; Zhang al., 2023; Liu et al., 2020; Chao al., 2024; Guo & Ye, 2019; Zhang et al., 2024; Liu et al., 2019; Wu et al., 2020). It is designed to integrate diverse and complemen- tary information across multiple views for clustering(K? Ke et al., 2024; Huang et al., 2021; Ren et al., 2024a; Wu et al., 2024; Ren et al., 2024b). Recent advances in unsupervised learning for graph data have increasingly emphasized the
"School Computer Science and Engincering, University of Electronic Science and Technology of China 'Shnzhen Insti- tute for Advanced Study, University of Electronic Science and Technology of China 'Department of Computer Science and En- gineering. Lehigh University. Correspondence to: Junlong Ke <junlong ke @ @wulook.ccom>..
Proceedings of the 42nd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

---

Vulti-View Graph Clustering via Node-Guided Contrastive Encoding
within graphs, reconstructing neighborhoods based local structure and features. MUSE (Yuan al., 2023) innovates by creating two subviews the original view, applying information fusion controller for view utilization.
node features, and contrastive fusion mechanism across views. Together, these elements form a compre- hensive process for node-guided multi-view co-coding,
We conduct extensive experiments on six homophilic and heterophilic benchmark datasets to evaluate the performance of NGCE. Our results show that the pro- posed NGCE adeptly accommodates both homophilic and heterophilic datasets within the multi- graph clustering domain, achieving state-of-the-ard perfor- mance metrics.
However, these methodologies either lack efficacy in het- erophilic graphs or underperform in homophilic scenarios. We attribute this limitation to an explicit differentiation between homophilic and heterophilic information through decoupling or view reconstruction, or an overemphasis one aspect over the other. This leads to an inadequate in- teraction between homophilic and heterophilic information during contrastive analysis. A more natural approach would be to integrate both aspects within a unified representation framework, raising the key question: How can we encode both types of information without compromising either?
2. Related Work
2.1. Multi-View Graph Clustering
With the rapid progress of GNNs, there has been growing interest among researchers in leveraging graph structural information for multi-view clustering (MVGC). By combin- ing with graph convolutional encoders, MVGC aims to learn the graph's 's underlying semantic information and divide the nodes into different clusters. In recent years, a plethora of methods addressing MVGC have surfaced. O2MAC (Fan et al., 2020) can be credited pioncer in applying GNNs to MVGC. Their approach involves encoding multi-view graphs into a dinen-iimeniional space using a single-view graph convolutional encoder and a multi-view graph struc- ture decoder. Building on this foundation, (Cheng et al., 2020) introduces novel design of two--wtohht wvo-pathway graph en- coders, facilitating the mapping of graph embedding fea- tures and the acquisition of view-consistent information. Meanwhile, (Hassani & Khasahmadi, 2020) proposes an in- novative GNN-based solution specifically tailored for multi- view self- supervisedd learning, aiming to acquire both node and graph-level representations. In a similar vein, (Pan & Kang, 2021) applies contrastive learning techniques to unearth shared geometric and semantic patterns, enhane- ing the learning of a consensus graph. (Xia et al., 2022b) takes systematic approach, exploring cluster structures through graph convolutional encoder trained to learn the self-expression coefficient matrix. However, a common challenge across these methods lies in their high sensitivity to the homophily of graphs. In other words, when these models are applied to graphs exhibiting strong heterophily, their effectiveness may fall short of expectations.
Our approach involves guiding view feature encoding with node features, followed by adaptive weighting that accounts for graph homophily and joint information aggregation us- ing a similarity matrix derived from refined node embed- dings. Recognizing the strengths of traditional GNNs in graph structure mining, as well as the challenges posed by GNN transformations, we propose encoding the original graph structure with GNNs while integrating node features to adapt representations for traditional GNNs. This ap- proach eliminates the need to explicitly distinguish between homophilic and heterophilic graph components. We begin by constructing a node correlation matrix and employing pseudo- to quantify the homophily of the original adjacency matrix, thereby allocating weights to selectively preserve original structural information. Additionally, we introduce random mask to the original node feature in- formation, generating an additively noisy feature matrix. Subsequently, we leverage GNNs' message passing and neighborhood aggregation mechanisms to recover the noisy features, with a contrastive loss applied between the re- covered and original feature representations. Finally, we utilize inter-view contrastive learning foster complemen- tary learning across views. The main contributions of this paper can be summarized as follows.
We propose NGCE, a novel contrastive learning model for homophilic and heterophilic graphs. To the best of our knowledge, NGCE is the first graph contrastive learning method guided by the principle that ho- mophilic and heterophilic information in graph data should not be isolated, but rather processed within a unified node-guided framework to preserve its interac- tive essence in MVGC.
2.2. Contrastive Learning
Contrastive learning has garnered considerable attention in the realm of unsupervised learning, showcasing remarkable performance across multitude of tasks, particularly on images (Hjelm et al., 2018; Chen et al., 2020b; Grill et al., 2020; Zbontar et al., 2021; Zhong et al., 2021; Yang et al., 2024) and graphs (Velickovic et al., 2019; You et al., 2020;
We develop an effective joint process for MVGC that integrates several key components: an edge and node embedding similarity matrix sensitive to graph ho- mophily, a contrastive coaming-guided graph encoding mechanism driven by the recovery of noise-enhanced
Zhu et al., 2020; Xia et al., 2022a; Bielak et al., 2022; Hu et al., 2021). The underlying principle involves maximizing
2

---

Vulti-View Graph Clustering via Node-Guided Contrastive Encoding
the similarity among positive pairs while minimizing the distance between negative pairs, as outlined by (Hadsell et al., 2006). In general, positive pairs consist of augmented versions of the same instance, while pairs involving differ- ent instances are considered negatives. Various loss func- tions have been introduced for this purpose, including the triplet loss (Chopra et al., 2005), noise contrastive estima- tion (NCE) loss (Gutmann & Hyvärinen, 2010), and normal- ized temperature-scaless cross-entropy loss (NT-Xent) (Chen et al., 2020a). Presently, numerous research endeavors lever- age contrastive learning methods in the realm of clustering tasks, significantly contributing to the progress of clustering and unsupervised representation learning. (Zhong et al., 2020) suggests converting the maximization of mutual in- formation into minimizing contrast loss, resulting in notable enhancements when applying contrast learning to diminish within-class variability. However, it fails to accommodate the prevalent graph data. (Hassani & Khasahmadi, 2020) proposes contrastive multí-view representation learning on graphs (MVGRL) by performing representation learning by contrasting two diffusion matrices transformed from the adjacency matrix. However, it relies heavily on data aug- mentation techniques and primarily utilizes graph structure information, specifically the adjacency matrix. We lever- age node feature information to guide graph-contrastive en- coding, thereby obtaining enhanced graph representations, harmonizing homophilic and heterophilic information in MVGC, and preserving their interactive essence.
3.1. Node-Guided Contrastive Encoding Module
3.1.1. GRAPH JOINT PROCESS
To enhance the proposed framework's 's capability for effec- tive neighborhood integration, it is critical ensure that substantial portion of nodes adjacent to the encoded em- beddings share the same class as the node in focus since the original node features will be unavailable for later pro- cessing. Considering that nodes within the same category have comparable feature vectors due to identical labels, our methodology prioritizes exploiting this feature similarity for joint graph encoding that combines edge and node relation- ships.
Initially, we employ autoencoders to distill and refine the feature vectors of nodes within the graph:
Z" (xx;
(I)
X X = g" (a(""";;
(2)
where, for the n-th view, Z" refers to the node embeddings, 0t and 6 refers to the encoder and decoder's 's learnable parameters that are unshared, respectively, X refers to the original node features, while a--) refers to the activation function.
Subsequently, to uncover node correlations, we evaluate the cosine similarity between node features, leading the formulation of the correlation matrix S for the n-th view:
3. Method
S = Sim (Z", ))",,,
(3)
As shown in Fig. 1, the proposed approach consists of two components: i) Node-Guided Contrastive Encoding Mod- ule: This module introduces an innovative encoding strategy that achieves graph joint encoding across different views, guided by the node's original features. This approach com- prises two key modules: an adaptive weighted sum based on similarity graphs and contrastive learning, implemented after reconstructing node features through GNN under the influence of additive noise. The former is tailored to inte- grate node features into the joint encoding output adaptively, whereas the latter aims to guide the encoding process by enabling the joint encoding to exhibit restorative proper- ties that are based on the augmenad original node features. This process is designed ensure that the in- tegrity of homophilic and heterophilic information exchange within the graph data is preserved, thereby yielding univer- sally applicable output encoding; ii) Cross-View Contrast Module: To enhance the learning of view consistency and complementarity. we adapt the centroids of clusters and the k-nearest neighbor samples as additional positive and negative samples, respectively, significantly improving the efficacy of view integration.
where the function Sim(...) refers to cosine similarity in vector space.
Using S as the basis for encoding the graph does improve its homophily to some extent. However, focusing solely on node features while ignoring the inherent structural aspects of the graph may not optimally serve the encoding goals. Therefore, we argue for a strategic inclusion of the struc- tural nuances of the original graph in our encoding efforts to ensure increased level of homophily. Considering that the higher homophily degree indicates that the similarity information on the graph is dominant, and vice versa for the dissimilarity information, this involves the development of an adaptive graph encoding strategy where we aim to evaluate and weigh the degree of homophily of the original graph. Naturally, we utilize the homophily degree to assign weights A and Shh However, the homophily degree of a given graph is difficult to measure due to the lack of true la- bels in the unsupervised scenario. Thus, we propose to learn the pseudo-label information (Arazo et al., 2020) using the consensus embedding H of Eq. (12) of the last iteration, and use the pseudo-labe -lbel information and adjacency relationship information to approximate the homophily weight w for
3

---

Multi- View Graph Clustering via Node-Guided Contrastive Encoding
X
A
Input
View
Cross- View Contrast Module
Node-Guided Contrastive
A
Encoding Module
f
Node-Guided Contrastive
X Q E
Encoding Module
Coo O x
(Ack Noise By Mask) X
z
Contrastive
L2
H
X
Loss
J oint Process
Node- uided
wided Contrastive
W
A"
w" S
Encoding Module
A
A
View V
Training
GNN
GNN
Contrastive Loss
Y
Clustering
(A O V 1.))
lemeans
H
(A) - 1.)
Output
Original
Node-Guided
Refined
Cross-view F Fusion
Node-G Gided
X
A
Z
h
Node F Features
Graph E Embedding
Node Features
Wight
oint Embedding
Adjacency Matrix
Original
X
Recovered Node
F Features
Y
Pseudo-Labed
Matrix
w
Homophily Wight
H
Consensus Embedding
Figure 1. The illustration of NGCE graph clustering framework. The inputs each view are the node feature matrix X and the adjacency
matrix A of views. The output of the framework is the consensus embedding H. after which used as input for K K-means clustering. Dashed arrows represent the backward propagation.
the n-th view:
3.1.2. NODE-GUIDEE CONTRASTIVE ENCODING
CA Y. 1.) 1
Furthermore, we design the node node-guided optimization pro- cess, aiming harness the true features of nodes to steer the encoding phase within the joint process. Inspired by the Denoising Autoencoder (DAE) (Vincent al., 2008) and GraphMAE (Hou et al., 2022), we replaced the encoder and decoder in DAE with parameter-free GNNs. In this adaptation, node features are treated as denoising coding objects, which facilitates the training of the node-guided graph embedding A. In this process, works analogous the parameters of the encoder and decoder.
S
(4)
En 1,5)
where, w refers to the weight reflective of the homophily degree from the preceding iteration, with @ indicating the Hadamard product. E {0, 1j representing the one- hot encoded pseudo labels from the clustering of the consen- sus embedding H, where refers to the number of nodes and refers to the number of clusters. refers to the identity matrix.
More precisely, we actively encourage the post-encoding aggregation procedure, guided by the encoded graph, to exhibit restorative capabilities towards the original features after noise is masked. This strategy, as substantiated by sub- sequent experimental validations, proves to be compatible with both homophilic and heterophilic graph data. Through such design, not only maintain the interaction between homophilic and heterophilic information within the graph data but also guide an effective excavation of this infor- mation. This methodology underscores the importance of preserving the intrinsic data structure while facilitating a nuanced representation of the graph data, accommodating both similarity and diversity within the graph structure.
Ultimately, this leads to graph joint encoded embeddings that integrate both the homophily assessment and the origi- nal structural framework:
A = ST ="=
(5)
In order guide the autoencoder f"(-), we apply recon- struction loss on Xpred and X as follows:
C 1(g" (X
(Xp Xprea: X)
(6)
= (f
where I(::-) denotes loss function.

---

View Graph Clustering via Node-Guided Contrastive Encoding
We first add random mask as noise the original matrix X of node features. In practice, we randomly drop some node features in the graph with a probability of Pe by adding random mask as noise to the original matrix X. Specifically, xd
we can reformulate the loss function such that:
Cer N
Xzy)²
(10)
we sample a binary masking matrix E E {0, 1) x from
ΣΣ
To -.))~x,,)
the Bernoulli distribution with a probability of (1 Po), i..., eij Bernoulli (1 - Pe), i E element-wise multiplication with the node features matrix:
and perform
where the first term minimizes the change in features when node features are preserved, while the second term forces nodes to conform to their original features when node fea- tures are not preserved, essentially establishing an adaptive mechanism for selecting positive and negative samples. This involves selecting unpreserved features as positive samples and the variation component of preserved features them- selves as negative samples.
X
E.
where @ denotes the Hadamard product, X represents the original node features and X refers to the node features with random mask (noisy features).
Then, we utilize GCN's neighborhood aggregation mecha- nism to recover the feature information following the addi- tion of noise, which can be represented from X X X", where X GCN (Àn, X) refers to the node features recovered by the aggregation mechanism of parameter-free GCN: X GON(A" X), which can be formulated as:
For the n-th view, considering the dimensionality of node- guided graph embedding A is excessively large for cross- view fusion processes, we employ parameter-free GCNs once dimensionality reduction mechanism. This pro- cess results in compressed representations h" that are di- mensionally aligned with node features Z":
H ( X.
h" GCN(A" Zz),
(11)
H(+)) = D : AD H + X,
we obtain node-guided joint embeddings he for the n-th view.
where (()) refers to the output of l-th layer while D refers to the degree matrix of A. Residual connections have been integrated to avoid potential gradient problems. The depth of our GCN is defined in terms of order, which is set as a fixed hyperparameter in our framework. We force the n-th view's recovered node features matrix X be equal to the original node features X as formulated:
3.2. Cross- View Contrast Module
In the context of multi-view tasks, it is acknowledged that distinct views offer varying levels of information, charac- terized by both consistency and complementarity (Jia et al., 2020; Wu et al., 2019). Initially, we obtain pode-guided embeddings h" for n-th view. To optimally leverage this diverse yet complementary information across views, our approach aims to synthesize a consensus embedding rich in information by amalgamating the node-guided joint em- beddings h" from each individual view (Jia et al., 2022). Acknowledging the differential informational value across views necessitates the implementation of a weighting mech- anism, predicated on an assessment of each view's 's infor- mational quality. This approach is designed to ensure that contributions from various views to the overarching con- sensus embedding are proportionate to their evaluated sig- nificance. In essence, view's embedding that exhibits high degree of similarity to the consensus embedding H is deemed to possess significant information, thereby warrant- ing a higher weight allocation, and the inverse applies for lesser similarity. The consensus embedding H is derived as follows:
C
Σ
x)²
1 ΣΣ x.))²
N2
Nº
(x
x (Xi: x2
No
x²
N
+ ΣΣ 19 )),
(9) where, the Ih and TH functions work as indicators, with the former being when E., = 1 and otherwise, and the latter vice versa. Specifically,, in Eq. (9), the first term minimizes the agreement between the reconstructed node features and the features of the masked nodes in the encoder graph, since there is no valid information correlation in these nodes; the second term drives the GCN with graph joint encoding embeddings to retain critical unmasked node information.
V
H =
wh'" ==1
(12)
In other words, given the variation component as X" X.y>
where w represents the weight allocated the node-guided
5

---

Multi-View Graph Clustering via Node-Guided Contrastive Encoding
joint embeddings of the n-th view, determined through:
Datasets
Clusters Nodes Features
Graphs (hr)
eva"
ACM
3
3025
1870
g' g2
w
max (eval, eva", eva V ).
(13)
DBLP
4
4057
334
G (0.80).9*006677 (0.667) (0.32)
IMDB
3
4780
1232
(0.44)).PP0066))
(0.40))
This weight, who is deduced from an evaluation function designed to measure the congruence between the consen- sus embedding and each view's embedding h", i.e. eva" = eval evalinttoo// (h", H). The hyperparameter p fa- cilitates the modulation of view weights, either enhancing or diminishing their impact. To culminate, the consensus embedding H undergoes k-means clustering to ascertain the clustering outcomes.
Texas
5
183
1703
(0 (O.09))
Chameleon
5
2277
2325
(0.23), (0
Wisconsin
5
251
1703
(00.19).
Table I. The statistics information of the six graph datasets. (lrr)
refers to the homophily rate calculated by true labels.
indicates the class assigned to node i. Both Cx and ez derived from the k-means clustering result applied to H from previous iteration.
Inspired by the methodologies outlined in (Yuan et al., 2023; Hassani & Khasahmadi, 2020), we refine the joint node rep- resentation H by integrating a contrastive loss component. This component aims to further enhance the learning of view complementarity reflected in H. We employ a vari- ant of NT-Xent loss (Chen et al., 2020a) our contrastive learning loss function. Crucially, for an embedding h, of node i within the consensus embedding H, we select the embeddings of its Newn nearest neighbor nodes within H as positive samples. For the selection of negative samples, we adopt a method inspired by that described in (Chao al., 2024). Specifically, after a predetermined number of training epochs, once the cluster centers are considered suf- ficiently stable to represent high-confidence and disparate class prototypes, we opt for representations from cluster centers of different classes (C& where k f c:), which are identified from H in the previous iteration and represent high-confidence, disparate class prototypes. This process can be formulated as follows:
3.3. Model Optimization
Learning from previous deep clustering studies (Ren et al., 2025), we design the overall optimization objective for NGCE, which can be formulated as:
Liotal = Lo + LRee
V
(15)
Σ ==1
ce + L82 + ERee
Ltotal can be divided into two main sections: unsupervised node embedding learning and contrastive learning. The unsupervised node embedding learning component LRee drives the optimization of refined node features Z. The contrastive learning component LG includes the loss func- tions Lei and Lc2- In the former, we apply noisy masks as perturbations to node features to drive the optimization of node- graph embedding A, while in the latter, we utilize contrastive learning based on cluster centroids to op- timize cross-view consensus embedding H. For the sake of cross-dataset robustness and simplicity in hyperparameter tuning, omitted the weight of the loss term.
N Keen
Lc2 AL
log
Σ m=1
(hr.Pi,m)
i=1
Nuan
p(mm)
Σ
(14)
where h; refers to the feature of node i within the consensus embedding H. Ps.m refers to the feature representation of the m-th nearest neighbor of node i, drawn from P(h,). which denotes the set of Nenn nearest neighbors of h; in H. Nenn indicates the number of nearest neighbors selected, which is fixed 20 in our implementation. -(--) denotes the cosine similarity function. N refers to the total number of nodes, while represents the total number of clusters. A denotes the loss coefficient, and we have empirically set its value to Níe-Ij based on experimental results. The indica- tor function [4] yields a value of if the condition specified in [] is met, and O otherwise. Herein, denotes the cur- rent training epoch and T, is a predefined byperparameter; this loss component is thereby activated only when t 2 Ti. Ca represents the cluster center for the k-th class, and C;
4. Experiments
4.1. Experimental Setup
4.1.1. DATASETS.
We used six MVG datasets. The homophilous graph datasets include: ACM (Fan et al., 2020), DBLP (Fan et al., 2020) and IMDB (Fan al., 2020). The heterophilous graph datasets include: Texas, Chameleon (Rozemberczki et al., 2021) and Wisconsin (Pei et al., 2020). In the appendix, we provide details and sources of the datasets.
Table summarizes the statistics of these six datasets. The top half of the table shows the statistics information for the homophilous graph datasets and the bottom half shows the
6

---

Multi-Vics View Graph Clustering via Node-Guided Contrastive Encoding
ACM (hr 0.82 0.64)
DBLP (hr 0.80
0.67 & 0.32)
IMDB (hr 0.48 & 0.62 & 0.40)
Methods
NMI%
ARI%
ACC%
F1%
NMI%
ARI%
ACC%
F1%
NMI%
ARI%
ACC%
F1%
VGAE (2016)
49.1
54.4
82.2
82.3
69.3
74.1
88.6
87.4
0.4
0.9
44.2
35.7
DAEGC (2019)
63.8
70.1
89.0
88.9
30.8
33.4
66.5
65.6
0.6
1.0
37.9
35.3
AGE (2020)
73.5
78.9
92.4
45.0
47.6
75.3
4.4
43.2
42.2
O2MAC (2020)
69.2
73.9
90.4
90.5
72.9
77.8
90.7
90.1
0.3
0.2
40.2
35.4
MvAGC (2020)
67.4
72.1
89.8
89.9
77.2
82.8
92.8
92.3
1.3
-1.8
48.5
28.2
AGCN (2021)
68.4
74.2
90.6
90.6
39.7
42.5
73.3
72.8
0.3
1.4
54.5
31.1
MCGC (2021)
71.3
76.3
91.5
91.6
83.0
77.5
93.0
92.5
5.2
10.3
58.3
38.8
DCRN (2022)
71.6
77.6
91.9
91.9
49.0
53.6
79.7
79.3
0.2
0.1
53.4
25.5
DuaLGR (2023)
73.2
79.4
92.7
92.7
75.5
81.7
92.4
91.8
6.2
12.5
52.0
44.7
CMGEC (2023)
69.1
72.3
90.7
72.4
78.6
91.0
90.4
5.1
48.4
51.0
BMGC (2024)
78.4
83.3
94.1
94.2
80.1
85.4
94.0
93.6
5.5
4.9
44.1
40.7
SMVC (2024)
72.4
78.0
92.3
92.0
76.1
81.6
92.4
92.0
8.0
7.2
41.3
37.2
VGMGC (2025)
76.3
81.9
93.6
93.6
78.3
83.7
93.2
92.7
0.8
3.2
52.6
32.8
NGCE (ours)
80.5
85.0
94.7
94.8
79.1
84.0
93.3
92.8
5.6
12.7
54.6
43.4
Table The results of clustering on homophilous graph datasets. We express all evaluative metrics as percentages. The best and runner-up results highlighted with bold and underline. respectively.
Texas (hr 0.09 & 0.09)
Chameleon (hr 0.23 & 0.23)
Wisconsin (hr 0.19 & 0.19)
Methods
NMI%
ARI%
ACC%
F1%
NM1%
ARI%
ACC%
F1 %
NMI%
ARI%
ACC%
VGAE (2016)
12.7
21.7
55.3
29.5
15.1
12.4
35.4
29.6
10.5
13.7
49.3
34.1
DAEGC (2019)
6.4
2.6
31.7
25.0
9.1
5.6
32.2
31.2
10.6
3.4
32.7
28.3
AGE (2020)
7.5
7.3
36.6
36.6
8.6
7.6
32.4
32.4
9.3
1.3
31.1
31.1
O2MAC (2020)
14.6
46.7
29.1
12.3
8.9
33.5
28.6
11.0
40.0
27.9
MvAGC (2020)
5.4
1.1
54.3
19.8
10.8
3.3
29.2
24.3
8.1
4.8
47.7
20.6
AGCN (2021)
15.4
18.1
61.8
43.0
6.7
6.1
32.5
6.4
49.8
24.9
MCGC (2021)
12.7
12.9
51.9
32.5
9.5
5.9
30.0
19.1
12.9
5,9
51.8
30.7
DCRN (2022)
10.7
15.1
55.2
27.6
8.7
5.7
30.9
21.9
10.8
16.0
50.2
34.1
DuaLGR (2023)
32.6
26.0
54.3
46.4
19.5
16.0
41.1
37.7
34.1
28.8
56.4
47.1
BMGC (2024)
29.1
15.8
42.5
38.3
9.4
5.9
30.8
30.7
34.0
24.3
51.5
40.8
VGMGC (2025)
35.4
26.0
46.9
22.4
40.1
39.5
41.6
56.6
49.6
NGCE (ours)
47.8
54.9
77.6
46.2
22.6
19.3
42.2
38.4
46.8
46.4
73.7
47.2
Table 3. The results of clustering on heterophilous graph datascts. results highlighted in bold and underlined, respectively.
We express all evaluative metrics percentages. The best and runner-up
statistics information for the heterophilous graph datasets.
ule, aiming to encode more complementary information from multiple views and depict data more comprehensively BMGC (Shen et al., 2024) addresses view imbalance in multi-relational graphs by proposing unsupervised domi- nant view mining and dual signals guided representation learning. SMVC (Chen et al., 2024) is a structural deep multi-view clustering method that integrates top-level ab- straction with underlying details to jointly optimize cluster assignments and feature embeddings. VGMGC (Chen et al., 2025) introduces variational graph generator to infer reli- able consensus graph from multiple graphs, aiming better utilize both view-specife and view-common information for multiview graph clustering, For all baselines, we use results reported in the original papers conduct experiments with their default parameters setting.
4.1.2. BASELINES.
Several baselines are replicated for comparison with our model. VGAE (Kipf & Welling, 2016) is classical single- view clustering method. O2MAC (Fan al., 2020) is the method that learns from both node features and graphs. MvAGC (Lin & Kang, 2021) and MCGC (Pan & Kang, 2021) are two methods based on graph filters to learn a consensus graph for clustering. DualGR (Ling et al., 2023) leverages soft-label and pseudo-label to guide the graph re- finement and fusion process for clustering. CMGEC (Wang al., 2023) utilizes multi-graph attention fusion encoder with multi-view mutual information maximization mod-

---

Multi- Graph Clustering via Node-Guided Contrastive Encoding
ACM (hr 0.82 & 0.64)
Chameleon (hr 0.23 & 0.23)
Methods
NM1%
ARI%
ACC%
F1%
NM1%
ARI%
ACC%
F1%
NGCE (w/ Re
62.4
65.9
86.8
86.9
15.5
11.6
33.0
27.7
NGCE (w/ Lc)
75.6
81.3
92.1
92.2
20.4
17.5
39.9
35.9
NGCE (w/o Lct)
79.4
83.9
93.7
93.7
20.7
17.5
40.2
36.4
NGCE (w/o Cc2)
77.6
83.1
93.4
93.5
21.4
18.7
11.3
37.2
NGCE (w/o A)
61.6
67.6
80.5
81.3
10.1
6.6
27.1
20.3
NGCE (w/o Z)
68.3
71.4
89.8
90.9
17.1
15.6
35.1
31.3
NGCE
80.5
85.0
94.7
94.8
22.6
19.3
42.2
38.4
Table 4. The ablation study results of NGCE on ACM and Chameleon. The original results are shown in bold. w/o À denotes the replacement of joint process with adjacency matrix A, w/o Z denotes the replacement of refined node features Z with an affinity matrix built directly form original node features.
and Lc dominate the total losses in terms of their impact on model performance. To be more precise, the effects of L01 and Lc2 the performance metrics of the model are remarkably similar. Implementing these components resulted in an increase in ACC of 1.0% and 1.3% on the ACM dataset and 2.0% and 1.0% on the Chameleon dataset. Furthermore, in comparison, LRee has a more significant impact on the performance metrics than Lc. with the ap- plication of these losses leading to an increase in ACC of 7.9% and 2.6% on the ACM dataset, and 9.1% and 2.2% the Chameleon dataset, respectively. Through ablation studies, we have validated the effectiveness of Le1 and Lc² within the contrastive learning loss Lc. This confirms the efficacy of our dual contrastive learning designs: contrast- ing the noised node features processed by GCN with their original node features, and cross-view node-guided joint embeddings comparisons. These results demonstrate the effectiveness of including specific contrasting elements to improve the model's 's ability to generate strong and meaning- ful embeddings, utilizing both intra-view effectiveness and inter-view complementarity.
0.8
ADM Charskee
0.0
0.7
0.6
0.5
0.5
0.3
0.4
ACM
0.9
5
7
13
15
5
9
11
13
15
order
order
(a) ACC
(b) NMI
Figure 2. Parameter sensitivity analysis for order in homophilic graph dataset ACM and heterophilic graph dataset Chameleon.
4.2. Overall Results
Tables 2 and 3 present the results of all compared meth- ods on homophilous and heterophilous graph datasets, from which we have the following observations. The experimen- tal results on the homophilous graph dataset ACM demon- strate that NGCE highly competitive with the state-of-the- art models, with significant improvements in all evaluative metrics. Morcover, NGCE outperforms other baselines on heterophilous graph datasets, i.e., Chameleon and Wis- consin, which are typically challenging for most models. Our model performs better than the baselines in most of the evaluation metrics.
4.3.2. EFFECT OF EACH COMPONENT.
Since our model is based on the notion of node-guided graph encoding and consensus embedding encoding, the fusion of graph in joint process and node representation, along with the refinement of node features, is a critical component of NGCE. We conducted ablation studies to evaluate their im- pact on the performance of NGCE, where we replace graph joint encoded embeddings A with adjacency matrix A, re- fined node features Z with affinity matrix based on original features X, the results are detailed in Table 4. The results highlight that omitting either joint processing node fea- ture refinement significantly degrades model performance. Specifically, compared to the bascline model, the ablation experiments on the ACM dataset resulted in a decrease in ACC of 14.2% and 4.9 4.9%; on the Chameleon dataset, there was decrease in ACC of 15. 1 and 7.1 %. Results high-
4.3. Ablation Studies and Analysis
1. EFFECT OF EACH LOSS.
To understand the importance of the unsupervised node em- beddings learning and contrastive learning, we removed reconstruction loss Lee of the autoencoder and the con- trastive learning loss Le for the proposed NGCE. Further- more, for the contrastive learning loss Lo, ablation study were also separately carried out on its components Lei and Lc2. We removed each loss in homophilic graph dataset ACM and heterophilic graph dataset Chameleon, respec- tively, to observe the changes in performance. The experi- mental results are shown in Table 4. As can be seen, LRee
8

---

View Graph Clustering via Node-Guided Contrastive Encoding
light the importance of refining node features, which leads to meaningful representation in the node-guided process and validates the effectiveness of the strategy involving the weighted sum of the refined representational node similarity matrix with the original adjacency matrix.
Another promising direction is developing and integrating a dedicated encoder that learns node features directly from the graph's 's topology. This would allow the model to function effectively even without pre-defined node attributes, signifi- cantly broadening its applicability. We plan to explore these extensions in future work.
4.3.3. PARAMETER SENSITIVITY ANALYSIS
The sensitivity analysis for order hyperparameter in ho- mophilic graph dataset ACM and heterophilic graph dataset Chameleon is shown in Fig. 2. From the spatial domain point of view, order controls the aggregation order of the graph filter. The higher order enables nodes to aggregate information from more distant ones, while nodes can only access feature information of closer nodes in lower orders. As can be seen from Fig. 2, ACC on the ACM dataset ex- hibits fluctuations around 93% when order less than 11, while on the Chameleon dataset ACC remains relatively sta- ble at around 42% under the same condition. However, for order values greater than 15, there is a sharp deterioration in the performance metrics for both datasets, dropping to around 45.4% for ACM and around 26.1 % for Chameleon.
5. Conclusion
In this paper, we introduce novel graph-based contrastive learning framework for multi-view graph clustering, which effectively handles both homophily and heterophily in graph data. We propose that the homophilic and heterophilic in- formation of graph data should not be separated, but rather processed within unified framework to preserve its interac- tive essence. Consequently, we have developed multi-view graph clustering method called Encoding (NGCE). Specifically, NGCE includes joint pro- cess that integrates a graph and node embedding similarity matrix sensitive to the degree of graph homophily, a con- trastive learning-guus grnidiggguuiedddd graph encoding mechanism driven by the degree of recovery of and a mechanism for contrastive fusion across views. The experimental results show that the proposed NGCE adeptly accommodates both homophilic and heterophilic datasets within the multi-view graph clustering domain, achieving state-of-the-art performance metrics.
Contrastive
node features,
4.3.4. COMPLEXITY ANALYSIS
Let M be the representation of the maximum number of neu- rons embedded within the hidden layers of the autoencoder, Z denotes the maximum dimensionality of the embedding features, T denotes the number of iterations for the outer loop, and K, V. and N stand for the numbers of clusters, views, and examples respectively. The K K-means and tar- get distribution computations are performed once per outer loop iteration. Thus, their contribution to the total com- plexity will be T x O ZK, giving O(TNZK) The autoencoder adheres to complexity of M²)) The operation of GNN can be seen multiplying an N x N ma- trix by an NN x Z matrix, with a time complexity of O(N²Z) Z) in an iteration. So, the total time complexity of our method is (T N N(Z K + V 22 + NZ)). The complexity of NGCE can be further reduced by methods such as anchor graphs, but this is beyond the scope of the proposed method.
A Acknowledgements
This work was supported in part by National Key Research and Development Program of China (Nos. 2024YFC231 10800 and 2024YFC2310800 10801), National Natu- ral Science Foundation of China (No. 62476052), Sichuan Science and Technology Program (No. 2024NSFSC1473), and Central Guidance for Local Science and Technology Development Fund Projects (No. 2024ZYD0268).
Impact Statement
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
4.3.5. LIMITATION OF THE PROPOSED METHOD
Despite its demonstrated capabilities, NGCE depends on the availability of node features. This characteristic inherently limits its direct applicability to datasets where such features are sparse or absent. However, we posit that this limitation is not insurmountable and presents avenues for future investi- gation. To extend our approach such scenarios, one poten- tial strategy involves leveraging random walks to generate node embeddings. This technique, frequently employed in established graph embedding methods like Deep Walk (Per- ozzi et al., 2014), can capture structural information from the graph, thereby creating feature representations for nodes.
References
Arazo, E., Ortego. D., Albert, P., O'Connor, N. E., and McGuinness, K. iseudo-labeling and confirmation bias in deep semi-supervised learning. In IJCNN, pp. 1-8, 2020.
Bielak, P., Kajdanowicz, T., and Chawla, N. V. Graph barlow twins: A seperiupe representation learning

---

Multi-View Graph Clustering via Node-Guided Contrastive Encoding
framework for graphs. KBS, 25:: 109631, 2022.
Hadsell, R., Chopra, S., and LeCun, Y. Dimensionality
reduction by learning invariant mapping. In CVPR, pp. 1735-1742, 2006.
Chao, G., Jiang, Y., and Chu, D. Incomplete contrastive multi-view clustering with high-confidence guiding. In AAAI, pp. 11221-11229, 2024.
Hassani, K. and Khasahmadi, A. H. Contrastive multi view representation learning on graphs, In ICML, pp. 41 4116- 4126. PMLR, 2020.
Chen, B., Xu, S., Xu, H., Bian, X., Guo, N., Xu, X., Hua, X., and Zhou, T. Structural deep multi-view clustering with integrated abstraction and detail. Neural Netw., 175 (C), July 2024. ISSN 0893-6080.
Hjelm, R. D., Fedorov, A., Lavoie-Marchildoos S., Grewal, K., Bachman, P., Trischler, A., and Bengio, Y. Learning deep representations by mutual information estimation and maximization. In ICLR, 2018.
Chen, J., Zhu, G., Qi, Y., Yuan, C., and Huang. Y. Towards self-supervised learning on graphs with heterophily, In CIKM, pp. 201-22222 201-211, 2022.
Hou, Z., Liu, X., Cen, Y., Dong, Y., Yang, H., Wang. C., and Tang, J. Graphmae: Self-supervised masked graph autoencoders. KDD, pp. 594 604, 2022.
Chen, J., Ling, Y., Xu, J., Ren, Y., Huang. S., Pu, X., Hao, Z., Yu, P. S., and He, L. Variational graph generator for multiview graph clustering. TNNLS, pp. 1-14, 2025.
Hu, Y., You, H., Wang, Z., Wang, Z., Zhou, E., and Gao, Y. Graph-mlp: node classification without message passing in graph. arXiv preprint arXiv:2 04051, 2021.
Chen, M., Wei, Z., Huang, Z., Ding, B., and Li, Y. Simple and deep graph convolutional networks. In ICML, pp- 1725-1735. PMLR, 2020a.
Huang, Z., Ren, Y., Pu, X., and He, L. Non-linear fusion for self self-paced multi-view clustering. In ACM MM, pp. 321 1211-3219, 2021.
Chen, T., Kornblith, S., Norouzi, M., and Hinton, G. A simple framework for contrastive learning of visual rep- resentations. In ICML, pp. 1597-1607. PMLR, 2020b.
Jia, X., Jing, X.-Y., Zhu, X., Chen, S., Du, B., Cai, Z.,, He, Z., and Yue, D. Semi-supervised multi-view deep discriminant representation learning. TPAMI, 43(7):2496- 2509, 2020.
Cheng, J., Wang, Q.. Tao, Z., Xie. D., and Gao, Q. Multi- view attribute graph convolution networks for clustering. In IJCAI, pp. 2973-2979, 2020.
Jia, X., Jing, X.-Y., Zhu, X., Cai, Z., and Hu, C.-H. Co- embedding: semi-supervised multi-view representation learning approach. Neural Computing and Applications, pp. 1-21, 2022.
Chopra, S., Hadsell, R., and LeCun, Y. Learning a sim- ilarity metric discriminatively, with application to face verification. CVPR, pp. 539-546, 2005.
Ke, J., Wen, Z., Yang. Y., Cui, C., Ren, Y., Pu, X., and He, L. Integrating vision-language semantic graphs in multi-view clustering. In ISCAI, pp- 4273-4281, 2024.
Cui, G., Zhou, J., Yang, C., and Liu, Z. Adaptive graph encoder for attributed graph embedding. In KDD, pp. 976-985, 2020.
Kipf, T. N. and Welling, Variational graph auto-encoders. arXiv preprint 1rXiv:1611.07308 2016.
Fan, S., Wang, X., Shi, C., Lu, E., Lin, K., and Wang, B. One2multi graph autoencoder for multi-view graph clustering. In WWW, pp. 3070-3076, 2020.
Li, S.-Y., Jiang, Y., and Zhou, Z.-H. Partial multi-view clustering. In AAAI, 2014.
Grill, J.-B., Strub, F., Altché, F., Tallec, C., Richemond, P., Buchatskaya, E., Doersch, C., Avila Pires, B., Guo, Z., Gheshlaghi Azar, M., et al. Bootstrap your own latent-a new approach to supf-vupe learning. NeurIPS, 33: 21271-21284, 2020.
Lin, Y., Gou, Y., Liu, Z., Li, B., Lv, J., and Peng. X. Com- pleter: Incomplete multi-view clustering via contrastive prediction. In CVPR, pp. 11174-11183, 2021.
Lin, Z. and Kang, Z. Graph filter-based multi-view at- tributed graph clustering, In IJCAI, pp. 2723-2729, 2021.
Guo, J. and Ye, J. Anchors bring ease: An embarrassingly simple approach to partial multi-view clustering. In AAAI, pp. 118-125, 2019.
Ling, Y., Chen, J., Ren, Y., Pu, X., Xu, J., Zhu, X., and Hc, Dual label-guides graph refinement for multi-view graph clustering. In AAAI, pp. 8791-8798, 2023.
Gutmann, M. and Hyvärinen, A. Noise-contrastive estima- tion: A new estimation principle for unnormalized statis- tical models. In AISTATS, pp. 297-304. JMLR Workshop and Conference Proceedings, 2010.
Liu, J., Cao, F., Gao, X.ZZ,, Yu, L., and Liang, J. A cluster- weighted kernel k-means method for multi-view cluster- ing. AAAI, pp. 4860 4867, 2020.
10

---

Multi-View Graph Clustering via Node-Guided Contrastive Encoding
Liu, X., Zhu, X., Li, M., Tang, C., Zhu, E., Yin, J., and Gao, W. Efficient and effective incomplete multi-view clustering. In AAAI, pp. 4392-4399, 2019.
Velickovic, P., Fedus, W., Hamilton, W. L., Liò, Bengio, Y., and Hjelm, R. D. Deep graph infomax. ICLR, 2(3):4, 2019.
Liu, Y. Tu, W., Zhou, S., Liu, X., Song, L., Yang, X., and Zhu, E. Deep graph clustering via dual correlation reduction. In AAAI, pp. 7603-7611. 2022.
Vincent, P., Larochelle, H., Bengio, Y., and Manzagol, P.-A. Extracting and composing robust features with denoising autoencoders. In ICML, pp. 1096-1103, 2008.
Liu, Y., Zheng, Y., Zhang, D., Lee, V., and Pan, S. Beyond smoothing: Unsupervised graph representation learning with edge heterophily discriminating. AAAI, pp. 4516- 4524, 2023.
Wang. C.,, Pan, S., Hu, R., Long, G., Jiang, J., and Zhang, C. Attributed graph clustering: A deep attentional embed- ding approach. In IJCAI, pp. 3670-3676, 2019.
Wang, Y., Chang, D., Fu, Z., and Zhao, Y. Consistent mul- tiple graph embedding for multi-view clustering. TMM, 25: 15:1008-1011 2023.
McPherson, M., Smith-Lovin, L., and Cook, M. Birds of feather: Homophily in social networks. Annual review of sociology, 27(1):415-4444 2001.
Wu, F, Jing, X.-Y., Zhou, J., Ji, Y., Lan, C., Huang, Q. and Wang. R. remi-supervised multi-view individual and sharable feature learning for webpage classification. In wWW. pp. 3349-3355, 2019.
Pan, E. and Kang, Z. Multi-view contrastive graph cluster- ing. NeurlPS, 34:2148 2159, 2021.
Pei, H., Wei, B., Chang, K. C. C.. Lei, Y., and Yang, B. Geom-gen: Geometric graph convolutional networks. In ICLR, 2020.
Wu, J., Xie, X., Nie, L., Lin, 7., and Zha, H. Unified graph and low-rank tensor learning for multi-view clustering. In AAAI, pp. 6388-6395, 2020.
Peng. Z., Liu, H., Jia, Y., and Hou, J. Attention-driven graph clustering network. In ACM MM, pp. 335-943,222 2021.
Wu, S., Zheng, Y., Ren, Y., He, J., Pu, X., Huang, S., Hao, Z.., and He, L. Self-weighted contrastive fusion for deep multi- view clustering. TMM, 2024.
Perozzi, B., Al-Rfou, R., and Skiena, Deepwalk: online learning of social representations. In KDD, pp. 701-710, 2014.
Xia, J., Wu, L., Chen, J., Hu, B., and Li, S. Z. Simgrace: A simple framework for graph contrastive learning without data augmentation. In WWW, pp. 1070-1079, 2022a.
Ren, Y., Chen, X., Xu, J. Pu, J., Huang, Y., Pu, X., Zhu, C.. Zhu, X., Hao, Z., and He, L. A novel federated multi- view clustering method for unaligned and incomplete data fusion. Information Fusion, 108: 102357, 2024a.
Xia, W., Wang, S., Yang. M., Gao, Q., Han, J., and Gao, X. Multi-view graph embedding clustering network: Joint self- superviseo and block diagonal representation. Neu- ral Networks, 145:1-9, 2022b.
Ren, Y., Pu, J., Cui, C., Zheng, Y., Chen, X., Pu, X., and He, L. Dynamic weighted graph fusion for deep multi-view clustering. IJCAI, pp. 4842-4850, 2024b.
Xiao, T. Chen, Z., Guo, Z., Zhuang, Z., and Wang. S. Decoupled sulf-super learning for graphs. NeurlPS, 35:620-634, 2022.
Ren, Y., Pu, J., Yang, Z., Xu, J., Li, G., Pu, X., Yu, S., and He, Deep clustering: comprehensive survey. TNNLS, 36(4):5858-5875 2025.
Xu, J., Li, C., Ren, Y., Peng. L., Mo, Y., Shi, X., and Zhu, X. Deep incomplete multi-view clustering via mining cluster complementarity. In AAAI, pp. 8761-8766 2022.
Rozemberezki, B., Allen, C., and Sarkar, R. Multi-scale attributed node embedding. J. Complex Netw, 9(2): cnab014, 2021.
Yang. X., Hu, X., Zhou, S., Liu, X., and Zhu, E. Interpolation-based contrastive learning for few-label semi-supervised learning. TNNLS, 35(2):2054-2055. 2024.
Shen, Z., He, H., and Kang, Z. Balanced multi-relational graph clustering. In ACM MM, pp. 4120 1120-4128,, 2024.
Yin, M., Huang, W., and Gao, J. Shared generative la- tent representation learning for multi-view clustering. In AAAI, pp. 6688-6695, 2020.
Tan, Y., Liu, Y., Wu, H., Lv. J., and Huang, S. Metric multi-view graph clustering. In AAAI, pp. 9962-9970, 2023.
You, Y., Chen, T., Sui, Y., Chen, T., Wang, Z., and Shen, Graph contrastive learning with augmentations. NeurIPS, 33:5812-5825 2020.
Tang, M., Li, P., and Yang, C. Graph auto-encoder via neighborhood wasserstein reconstruction. In ICLR, 2022.

---

Multi-View Graph Clustering via Node-Guided Contrastive Encoding
Yuan, M., Chen, M., and Li, X. Muse: Multi-view trastive learning for heterophilic graphs. In ACM CIKM, pp. 3094-3103, 2023.
Zbontar, J., Jing. L.,, Misra, LeCun, Y., and Deny, S. Barlow twins: Self-supervised learning via redundancy reduction. ICMI,, pp. 12310-12320, 2021.
Zhang, C., Li, H., Lv, W., Huang, Z., Gao, Y., and Chen, C. Enhanncdd tensor low-rank and sparse representation recovery for incomplete multi-view clustering. In AAAI, pp. 11174-11182. 2023.
Zhang, C., Jia, X., Li, Z., Chen, C., and Li, H. Learning cluster-wise anchors for multi-view clustering. AAAI, pp. 16696-16704, 2024.
Zhong, H., Chen, C., Jin, Z., and Hua, X.-S. Deep ro- bust clustering by contrastive learning. arXiv preprint arXiv:2008. 03030, 2020.
Zhong. H., Wu, J., Chen, C., Huang, J., Deng, M., Nie, L.., Lin, Z., and Hua, X.-S. Graph contrastive clustering. In ICCV, pp. 9233-9233, 2021.
Zhu, Y., Xu, Y., Yu, F., Liu, Q., Wu, S., and Wang, L. Deep graph contrastive representation learning, arXiv preprint 1rX1::2006.04131,, 2020.
12

---

View Graph Clustering via Node-Guided Contrastive Encoding
A. Details of Experiments
Algorithm 1 Multi-View Graph Clustering via Node-
Guided Contrastive Encoding (NGCE)
A.1. Metrics
Input:
The adjacency matrices {A") and node feature matrices {X")
Following previous works, four commonly used metrics, i.e., normalized mutual information (NMI), adjusted rand index (ART), accuracy (ACC), and Fl scores (F1), are adopted to evaluate the clustering performance.
Inétialization phase
Apply the k-means algorithm to original node feature matrices {X") I==1 for the pseudo label matrix Y of the
first iteration Train phase
A.2. Visualization of learned consensus embedding
while not reaching the maximum iterations not reach- ing exit condition do for n in 1, 2.... V do Calculate Z" and X pred based on Eq. (3) and (4) Calculate S based on Eq. (5)
To unveil the inherent clustering structure, we have also employed I-SNE algorithm for the visualization of all six datasets to depict the distribution of the learned consensus embedding H. As depicted in Fig. 3, the visual results high- light that NGCE exhibits an enhanced clustering structure.
It the first iteration do
Calculate wn based on Eq. (6) with pseudo label matrix Y from Initialization phase
A.3. Details of Datasets
else do
The experiments were conducted on six MVG datasets: ACM, DBLP, IMDB, Texas, Chameleon, and Wisconsin. Details and sources of the datasets are presented subse- quently.
Calculate w based on Eq. (6) with pseudo label matrix Y from last iteration
Calculate A n and X based on Eq. (7) and (9)
Calculate X by X GCN X) based on
Eq. (10)
Homophilous graph datasets: ACM is a paper net- work from the ACM database and is composed of two graphs: the co-paper network and the co-subject net- work; DBLP is a network sourced from the DBLP database?, consists of three graphs: co-author, co- conference, and co-term; IMDB is a movie network that originates from the IMDB dataser', including graphs of both co-actors and co-directors.
Calculate h and wi based Eq. (13) and (16)
end for
Update H based on Eq. (15)
for e in 1, 2... V do
Update with H base on k-means end for end while Output: Consensus embedding H
Heterophilous graph datasets: Texas is a webpage graph from WebKB Chameleon
subset of the Wikipedia networks; Wisconsin is webpage graph from WebKB Since Texas, Chameleon and Wiscon- sin single-view graph data, we copy the graph the second view.
In the task of multi-view graph clustering, the objective is to group a set of n nodes into k clusters. To achieve this, we utilize G = (V, E) to denote graph. Here, V represents the nodes set, and the set of all nodes belonging class i is represented as V,, with N |V] and & C V x V represents the edge set with selfloops. The feature matrix for the nodes is denoted as X E R-xxd and the symmetric adjacency matrix of the graph G is represented by A E R. RNNN with elements a.j = 1 indicating the presence of an edge between node and node j. and a.j = otherwise. Additionally, we define the degree matrix of A as D; = Σ, aij. enabling the normalization of each view's to À = (D) 10--A.. A. The normalized graph Laplacian matrix is defined as L = I-A A, with I representing the identity matrix.
B. Algorithm
The proposed NGCE model is summarized in Algorithm Algorithm 1 presents comprehensive breakdown of the code flow.
C. Preliminaries
In this section, we introduce a brief background of multi- view graph clustering and GCNs.
hhtps://dl.acm.oogg
The Graph Convolutional Networks (GCNs) leverages the principle of spectral graph theory to facilitate learning on graph-structured data. The core of this method is the utiliza- tion of the normalized graph Laplacian matrix to capture the graph's structural information. The GCNs operates by prop- agating node features across the graph's 's structure, thereby enabling each node to aggregate features from its neighbors,
hhttss//dbllpumiitrieeec
'htpp://wwwwimmhh.com//
1 1 //ww//wwkb
http://wwww...cccc....cccccccccs 1/www//wkb
13

---

Multi-View Graph Clustering via Node-Guided Contrastive Encoding
(a) ACM
Chameleon
(c) DBLP
(d) IMDB
(e)
Texas
Wisconsin
Figure Visualization of learned consensus embedding H all six datasets.
40
(a) epach=200
(b) epach=400
(c) epoch=600
(d) epoch=800
(e) epoch=250
(I) epoch=500
(g) epoch=750
(h) spoch=1000
Figure Visualization of learned consensus embedding the ACM dataset (Figure 4(a), 4(b). 4(c) and 4(d)) and DBLP dataset (Figure 4(e), 4(f). 4(g) and 4(h)) across epochs. At the start of the training stage, the embedded features are non-separable. As the training progresses, the clustering structures the embedded features become more apparent while their centroids gradually separate.
effectively capturing both local and global graph structure.
In this paper, we use GCN without learnable parameters
H (+1) o D A AD- H
(16)
14

---

Multi-View Graph Clustering via Node-Guided Contrastive Encoding
Notations
Mcaning
g
g = (V, graph with node set V and edge set E.
X
E Nxx, the feature matrix of the nodes.
c
The number of clusters.
A
E RNNN, the adjacency matrix with self-loop.
((
Degree matrix in GCN.
I
Identity matrix.
N
[ the number of nodes,
d
The dimension of original node features.
V
The number of views.
("))9""))
The encoder and decoder in the autoencoders.
di
Dimension of the distilled node embeddings.
da
Hidden layer dimension of the autoencoder.
The number of hidden layers.
Z
Distilled and refined node embeddings from (*"().
X pred
Output of the decoder g²(-).
S"
Node correlation matrix for the 1-th view.
S(.)). ). Sim(s-)
Cosine similarity.
Homophily wight for the n-th view.
Y
E (0, 1) Nxe, one-hot encoded pscudo labels.
Ä
Graph joint encoded embeddings for the n--h view.
E
E (0. 13 Nxd. binary random masking matrix.
Pc
Probability of Bernoulli distribution of random mask.
X
Node features with random mask (noisy features).
X"
Recovered node features matrix for the 1e-hh view.
H
Output of 1-th layer GCN.
order
Depth of GCN in NGCF
h
Node-guided joint embeddings of the n-th view.
Indicator function.
Hadamard product.
Ck
Cluster center for the k-tth class of H.
Ca
The Class assigned to node i in Y.
H
Consensus embedding.
p
Cross-view weight modulation parameter
Cross-view fusion wight allocated to h".
eva"
Function to measure congruence between H and h".
CRse
Reconstruction loss on Xpred and X of the 1ith view.
Les, Lea
Contrastive learning loss.
Y)
Learning rate.
Awd
Weight decay regularization parameter.
Table 5. Overall notations.
15


Reviews:
[{"review_id": "ZsN4R6DAmj", "reviewer": "Reviewer_nDQ8", "summary": "This work primarily focuses on integrating homogeneous and heterogeneous information in graph data into a unified framework. Its core modules are an edge and node embedding similarity matrix sensitive to graph homophily, a contrastive learning-guided graph encoding mechanism driven by the recovery of noise-enhanced node features, and a contrastive fusion mechanism across views. The most innovative contribution is the introduction of the second module, which enables the simultaneous learning of homogeneous and heterogeneous information. Extensive experiments demonstrate the feasibility and effectiveness of the model.", "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": "Thank you for your insightful feedback and constructive critiques on our manuscript. Below, we provide a point-by-point response to your comments.\n\n**Q1: Theoretical Validation or Detailed Experimental Evidence of Section 3.1.2**\n\n**A1:** Thank you for your valuable feedback. In the current version, we have provided a detailed algorithmic description and conducted extensive ablation studies to empirically validate the effectiveness of our proposed mechanism. We fully acknowledge the importance of theoretical analysis and plan to incorporate rigorous theoretical examinations (including convergence analysis and generalization capability analysis) in future extensions of this work.\n\nAs shown in the following tables, removing the node recovery component (\"NGCE w/o node recovery\") leads to significant performance degradation across both homogeneous and heterogeneous graphs. \n\n|Methods|ACM|DBLP|IMDB|texas|Chameleon|Wisconsin|\n|--|--|--|--|--|--|--|\n|NGCE (w/o node recovery)|75.0/79.7/92.8/92.8|62.1/62.4/84.8/85.2|3.5/6.7/48.5/40.5|28.4/25.0/55.2/34.9|19.9/15.3/40.8/35.7|36.7/30.5/58.6/43.3|\n|NGCE|80.5/85.0/94.7/94.8|79.1/84.0/93.3/92.8|5.6/12.7/54.6/43.4|47.8/54.9/77.6/46.2|22.6/19.3/42.2/38.4|46.8/46.4/73.7/47.2|\n\nThis table reports clustering performance metrics in the order of NMI/ARI/ACC/F1. These results suggest that the recovery mechanism plays a critical role in capturing both local and global structural patterns, especially in heterogeneous datasets.\n\n**Q2: Typographical Revisions**\n\n**A2:** In response, we have carefully reviewed the entire manuscript and addressed all identified issues to improve clarity, consistency, and overall presentation.\n\n**Q3: Equation (9) Clarification**\n\n**A3:** We have revised the explanation surrounding this equation to provide clearer context and interpretation. Specifically, the first term minimizes the agreement between the reconstructed node features and the features of the masked nodes in the encoder graph, since there is no valid information correlation in these nodes; the second term drives the GCN with graph joint encoding embeddings to retain critical unmasked node information.\n\nThe whole process requires the GCN to identify and preserve the correct unmasked features from the masked non-adjacent nodes in the graph structure, where the graph joint encoding embeddings are forced to learn the essential patterns of node feature distribution in the encoding stage.\n\n**Q4: First-Order Neighborhood Superiority (Figure 2)**\n\n**A4:** We believe that the superior performance under first-order neighborhood aggregation is due to the graph encoding mechanism proposed in our framework. This phenomenon suggests that our learning paradigm enables the encoded graph to directly integrate valuable edges, thereby substantially reducing the necessity for higher-order neighborhood processing in subsequent GNN operations. Specifically, when the order is set to 1 or some other low number, the model effectively captures direct neighborhood relationships within the encoded graph while minimizing noise interference. In contrast, although higher-order aggregation introduces redundancy and can theoretically provide additional information, the induced noise becomes particularly difficult to mitigate in unsupervised learning scenarios due to the lack of explicit supervisory signals. A discussion of this trade-off, along with the inherent limitations of our model, will be provided in the Discussion section.\n\n**Q5: 2024 Baseline Comparisons.** \n\n**A5:** We added comparisons with VGMGC [TNNLS 25], BMGC [ACM MM 24], and SMVC [Neural Networks 24]. Among these, VGMGC and BMGC are open-source and can be evaluated across all datasets, while SMVC, though not yet open-sourced, shares our homogeneous dataset selection. The comparison results are shown in the table below. For open-source baselines, we used the results reported in the original paper where available; otherwise, we evaluated them using default parameters or settings from similar datasets. The following table reports clustering performance metrics in the order of NMI/ARI/ACC/F1.\n\n|Methods|ACM|DBLP|IMDB|Texas|Chameleon|Wisconsin|\n|--|--|--|--|--|--|--|\n|SMVC|72.4/78.0/92.3/92.0|76.1/81.6/92.4/92.0|8.0/7.2/41.3/37.2|-/-/-/-|-/-/-/-|-/-/-/-|\n|BMGC|78.4/83.3/94.1/94.2|80.1/85.4/94.0/93.6|5.5/4.9/44.1/40.7|29.1/15.8/42.5/38.3|9.4/5.9/30.8/30.7|34.0/24.3/51.5/40.8|\n|VGMGC|76.3/81.9/93.6/93.6|78.3/83.7/93.2/92.7|0.8/3.2/52.6/32.8|35.4/26.0/55.2/46.9|22.4/13.4/40.1/39.5|41.6/34.8/56.6/49.6|\n|NGCE (ours)|80.5/85.0/94.7/94.8|79.1/84.0/93.3/92.8|5.6/12.7/54.6/43.4|47.8/54.9/77.6/46.2|22.6/19.3/42.2/38.4|46.8/46.4/73.7/47.2|\n\nThese experimental results show that our method consistently achieves superior performance compared to methods in recent publications.\n\nWe greatly appreciate your rigorous evaluation and suggestions, which have significantly strengthened our manuscript.", "claims_and_evidence": "Yes, the claims are made in the submission supported by clear and convincing evidence.", "methods_and_evaluation_criteria": "Yes, the proposed methods make sense for the problem.", "theoretical_claims": "Yes, the proofs for theoretical claims are correct.", "experimental_designs_or_analyses": "Yes, the experimental designs and analyses are reasonable.", "relation_to_broader_scientific_literature": "Existing MVGC models typically handle heterogeneous and homogeneous graphs separately. The motivation of this work is to integrate heterogeneous and homogeneous graphs into a unified framework. This motivation is innovative.", "essential_references_not_discussed": "N/A.", "other_strengths_and_weaknesses": "Strengths:\n1. The primary motivation of this work is to integrate the learning of heterogeneous and homogeneous graphs within a unified framework. Its innovative intent is distinctly evident. \n2. The work exhibits a clear logical structure.\n\n\nWeaknesses:\n1. In Section 3.1.2, the recovery of noise-enhanced node features is claimed to facilitate the learning of heterogeneous information. However, this lacks theoretical justification. Furthermore, superior clustering performance on heterogeneous graphs in experiments does not necessarily imply that this improvement is attributed to the recovery of noise-enhanced node features. Therefore, the authors should provide further theoretical validation or more detailed experimental evidence.\n2. The manuscript contains numerous typographical errors that need to be corrected.", "other_comments_or_suggestions": "1. In Eq. (9), the statement \"the first term minimizes the agreement between the node and its non-neighbors…\" appears to be grammatically incorrect. What is more, its intended meaning seems problematic.\n2. In Figure 2, the clustering performance is consistently best when the order is 1. The authors should further explain this particular phenomenon.\n3. The comparison algorithms lack references to works published in 2024.", "questions_for_authors": "See weakness and suggestions.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "a56ahoMOxT", "reviewer": "Reviewer_KgQm", "summary": "This paper introduces Node-Guided Contrastive Encoding (NGCE), a novel framework for multi-view graph clustering that integrates homophilic and heterophilic information through node-guided contrastive learning. NGCE aims to outperform existing methods by emphasizing node feature-based information and avoiding explicit decoupling of homophilic and heterophilic components. Experimental results on six benchmark datasets demonstrate significant improvements over baselines.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your insightful feedback and constructive critiques on our manuscript. Below, we provide a point-by-point response to your comments.\n\n**Q1: Delayed Definition of Mathematical Symbols**  \n**A1:** We sincerely apologize for the oversight in deferring symbol definitions to the appendix. In the revised manuscript, all mathematical symbols (e.g., adjacency matrices, node features, and operators) are now explicitly defined when they first appear in the main text. For example, all parameters related to GNNs are now clearly introduced within their corresponding equations.\n\n**Q2: Ambiguity in Equation (11)**  \n**A2:** We thank the reviewer for identifying this ambiguity. The GCN architecture in Equation (11) shares the *same structural design* as the GCN in Equation (8) and operates with *independent parameters* (i.e., no weight sharing). This distinction ensures that the node recovery module learns distinct patterns from the graph encoding process. We have clarified this in the revised manuscript by explicitly stating that in Equation (11).  \n\nWe greatly appreciate your careful evaluation and thoughtful recommendations, which have significantly improved the rigor and clarity of our work.", "claims_and_evidence": "The claims made are clearly explained in the manuscripts.", "methods_and_evaluation_criteria": "Yes, the proposed method provides a novel solution in this field.", "theoretical_claims": "The theory in the manuscript provides further clarification and explanation of the proposed methodology.", "experimental_designs_or_analyses": "The experimental design is relatively reasonable. The experimental results outperform almost all baseline methods, and the experimental analysis is also relatively complete.", "relation_to_broader_scientific_literature": "The proposed NGCE framework introduces novel methodologies to the domains of graph machine learning, multi-view graph contrastive learning, and the handling of heterophily in GNNs.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "Strengths:\n1. To advance existing multi-view graph contrastive learning approaches which primarily focus on homophilic graphs, NGCE introduces node-guided encoding to unify homophilic and heterophilic interactions. \n2. NGCE can improve compatibility with GNN filtering, effectively integrate both homophilic and heterophilic information, and enhance contrastive learning across multiple views.\n3. The paper is well organized and sufficient experiments have been conducted.\n\nWeaknesses:\n1. The paper delays defining mathematical symbols until the appendix, rather than introducing them upon their first appearance, which disrupts readability and comprehension. \n2. Certain equations, such as Eq. 11, are not clearly presented, potentially causing misunderstandings about the computational process. Is that GCN in Eq. 11 set the same as that in Eq. 8?", "other_comments_or_suggestions": "Please refer to the strengths and weaknesses.", "questions_for_authors": "Please refer to the weaknesses.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "nfTsIxasbG", "reviewer": "Reviewer_WwHn", "summary": "This paper presented a novel approach to MVGC called Node-Guided Contrastive Encoding. This method addresses the challenges inherent in GNNs for clustering by effectively using homophilic and heterophilic information within graph data. The proposed framework uses node features to guide the embedding process, thus preserving the interactive nature of graph information.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your insightful feedback and constructive critiques on our manuscript. Below, we provide a point-by-point response to your comments.\n\n**Q1: Time Complexity Concerns**  \n**A1:** We appreciate the reviewer’s attention to computational efficiency. While generating *V* views iteratively introduces additional complexity, this design aligns with state-of-the-art late-fusion multi-view clustering methods (e.g., DualGR), where view-specific processing precedes fusion. As detailed in Section 4.3.4 (Complexity Analysis), NGCE’s complexity remains comparable to prior works, as the incremental cost arises solely from a parallel GNN module (for node-guided encoding, the part from $\\tilde{X}$  to  $\\overline{X}^n$ in Figure 1). \n\n**Q2: Incremental Contribution**  \n**A2:** While NGCE builds on contrastive learning principles, its *node-guided encoding* mechanism represents a novel contribution by unifying homophilic and heterophilic interactions within a single framework. Unlike prior works that treat these as separate tasks or rely on heuristic aggregation, NGCE explicitly models their interplay through adaptive weight learning and noise-augmented recovery (Section 3.1.2). This design enables superior performance on both homogeneous and heterogeneous graphs.  \n\n**Q3: Applicability to Purely Structural Graph and Functionality Without Node Features**  \n\n**A3:** We fully acknowledge your concern regarding the method's reliance on node features, which indeed limits  its applicability in datasets with limited or no node feature  information. In the revised *Limitations* subsection in Discussion section, we clarify that NGCE’s current implementation assumes the availability of node features.  Specifically, we will acknowledge that the current  implementation struggles in scenarios where node features are absent.  However, we believe that this limitation is not insurmountable. There  are potential solutions to extend our approach to such datasets, and we  intend to explore them in future work. Possible strategies include:\n\n- Random Walk-based Feature Generation: Random Walks could be employed to generate node embeddings by capturing structural information from  the graph, an approach often used in graph embedding techniques such as  DeepWalk.\n- Learned Node Features: We could also incorporate a dedicated encoder to generate node features directly from the graph structure, thereby enabling the method to function even in the absence of explicit node  attributes.\n\nBoth strategies might allow us to retain the benefits of our  node-guided contrastive encoding approach while extending its  applicability to a wider range of datasets. We will present these  potential solutions in the *Limitations* subsection to provide a more comprehensive view of possible extensions to our work. \n\n**Q4: Typos and Redundant Definitions**  \n**A4:** In response, we have carefully reviewed the entire manuscript and addressed all identified issues to improve clarity, consistency, and overall presentation.\n\nWe sincerely appreciate your thorough review and constructive feedback, which have greatly improved the quality of our manuscript.", "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 and Graph Learning.", "essential_references_not_discussed": "The paper comprehensively reviews the most relevant literature in the fields of Multi-View Clustering and Graph Learning.", "other_strengths_and_weaknesses": "Strengths\n\n1. The NGCE framework introduces a unique way of integrating node features with graph structure through contrastive learning that combines homophilic and heterophilic information.\n\n2. The use of noise-augmented node feature recovery and adaptive weighting mechanisms demonstrates a well-considered design aimed at improving MVG learning.\n\nWeaknesses\n\n1.The time complexity of the proposed NGCE model may raise concerns, as it appears to generate V views iteratively. \n\n2.Some aspects of the proposed method may appear incremental, particularly the use of graph neural networks in a contrastive learning setting, which has been explored in prior works.\n\n3.The performance of NGCE in purely structural graph clustering scenarios, where node features are absent, remains unexplored.", "other_comments_or_suggestions": "There are some typos, such as the explanation below Equation (2), and a repeated definition of the Hadamard product.", "questions_for_authors": "Note that node-guided encoding in NGCE exhibits strong dependency on node features, could the methodology remain functional when applied to pure graph-structured datasets lacking node features?", "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: All the three reviewers agree that the paper is interesting, the proposed method has made important contribution to the analysis of the homogeneous and heterogeneous graphs and demonstrated better performance in different metrics compared to the existing ones. The rebuttal made various clarifications and explanations on the concerns/comments raised and provided more experimental results.
Decision: Accept (poster)