Hybrid-Collaborative Augmentation and Contrastive Sample Adaptive-Differential Awareness for Robust Attributed Graph Clustering
Authors: TianxiangZhao
Youqing Wang
Jinlu Wang
Jiapu Wang
Mingliang Cui
Junbin Gao
Jipeng Guo
Venue: NeurIPS 2025 poster ()
Keywords: Attributed graph clustering
contrastive learning
hybrid-collaborative representation augmentation
adaptive-differential sample awareness
Primary area: general_machine_learning
TL;DR: The paper proposes RAGC, a novel robust attributed graph clustering method that combines hybrid-collaborative augmentation and contrastive sample adaptive-differential awareness to obtain more discriminative representations.

Abstract: Due to its powerful capability of self-supervised representation learning and clustering, contrastive attributed graph clustering (CAGC) has achieved great success, which mainly depends on effective data augmentation and contrastive objective setting. However, most CAGC methods utilize edges as auxiliary information to obtain node-level embedding representation and only focus on node-level embedding augmentation. This approach overlooks  edge-level embedding augmentation and the interactions between node-level and edge-level embedding augmentations across various granularity. Moreover, they  often  treat all contrastive sample pairs equally, neglecting the significant differences between hard and easy positive-negative sample pairs, which ultimately limits their discriminative capability. To tackle these issues, a novel robust attributed graph clustering (RAGC), incorporating hybrid-collaborative augmentation (HCA) and contrastive sample adaptive-differential awareness (CSADA), is proposed. First, node-level and edge-level embedding representations and augmentations are simultaneously executed to establish a more comprehensive similarity measurement criterion for subsequent contrastive learning. In turn, the discriminative similarity  further consciously guides edge augmentation. Second, by leveraging pseudo-label information with high confidence, a CSADA strategy is elaborately designed, which adaptively identifies all contrastive sample pairs and differentially treats them by an innovative weight modulation function. The HCA and CSADA modules mutually reinforce each other in a beneficent cycle, thereby enhancing discriminability in representation learning. Comprehensive graph clustering evaluations over six benchmark datasets demonstrate the effectiveness of the proposed RAGC against several state-of-the-art CAGC methods. The code of RAGC could be available at https://github.com/TianxiangZhao0474/RAGC.git.

Hybrri-CCllaborative Augmentttinn and Contrastive Sample Adaptive-Differentia Awareness for Robust Attributed Graph Clustering
Tianxiang Zhao!
Youqing Wang' Jinlu Wang²
Jiapu Wang²
Mingliang Cui Junbin Gao Jipeng Guo
CCollege Information Science and Technology, Beijing University of Chemical Technology
Beijing University of Technology
'The University of Sydney Business School, The University of Sydney
(tianxiingzhha, 2021 I 4002088, guojipengl @buct.edu.cn, waag__yuqinge wwt..eaaaaaeuuuu...... wwangjinlu @ comails.bjut.edu... @iapuwang9@gmmil.com gmail..om "junbin.gar @ sydney.edu.au
Abstract
Due to its powerful capability of self-supervised representation learning and clus- tering, contrastive attributed graph clustering (CAGC) has achieved great success, which mainly depends on effective data augmentation and contrastive objective setting. However, most CAGC methods utilize edges as auxiliary information obtain node-level embedding representation and only focus on node-level embed- ding augmentation. This approach overlooks edge-level embedding augmentation and the interactions between node-level and edge-level embedding augmentations across various granularity. Moreover, they often treat all contrastive sample pairs equally, neglecting the significant differences between hard and easy positive- negative sample pairs, which ultimately limits their discriminative capability. To tackle these issues, novel robust attributed graph clustering (RAGC), incorpo- rating hybrid-collaborative augmentation (HCA) and contrastive sample adaptive- differential awareness (CSADA), is proposed. First, node-level and edge-level embedding representations and augmentations are simultaneously executed to es- tablish more comprehensive similarity measurement criterion for subsequent contrastive learning. In turn, the discriminative similarity further consciously guides edge augmentation. Second, by leveraging pscudo-label information with high confidence, a CSADA strategy is elaborately designed, which adaptively identifies all contrastive sample pairs and differentially treats them by an inno- vative weight modulation function. The HCA and CSADA modules mutually reinforce each other in beneficent cycle, thereby enhancing discriminability in representation learning. Comprehensive graph clustering evaluations over six benchmark datasets demonstrate the effectiveness the proposed RAGC against several state-of-the-art CAGC methods. The code of RAGC could be available at httpps: //gi tiu.. wttpaau.coommiiiiannnnaaaaa hwt.///aaa...aag//////////A/
Introduction
Attributed graph representation learning, as an effective method, fully leverages both attribute features and the neighborhood structure among samples [[]. Graph data is widely present in practice. making graph representation learning essential across various fields such as node classification 2 3 4
"Corresponding author: Jipeng
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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node clustering 66 7 9 knowledge graph analysis [0], traffic prediction []], due to its powerful representation capability. Attributed Graph Clustering (AGC), which uses Graph Neural Networks (GNNs) to learn discriminative embedding representation [12 I and partitions nodes into disjoint clusters without label information, has become popular and fundamental task in the field of data mining. However, it also faces numerous challenges [14.
Hybrid- Hybbiid-Collaborative Augmentation
Contrastive Sample Seddattii--ifffeeente Awareness
KMUP
E
Emthedding Representation
EMLP
E
Auag
MLP.
z
Nede kmabedinng Representation
Xang
MLP
Zz
similarity 5
wright modulation Wlw
2 2 (2"+2"
high
H b
Qu
10, P
K-means clostering
pieudo
dynamic samples selection
opochs
Dynamic High Confidence Samples Selection
Figure 1: The overall framework of the proposed RAGC, which mainly consists of HCA and CSADA modules. The HCA module constructs reliable augmented views and comprehensive similarity by hybrid-collaborative augmentation from node-level embedding and edge-level embedding. With dynamic high confidence samples selection strategy, the CSADA module significantly distinguishes the contrastive samples through a powerful weight modulation function.
Recently, contrastive learning, a powerful self-supervised representation learning paradigm that does not rely on label information, has attracted widespread attention and achieved significant progress in various fields, such as computer vision 15] natural language processing [16), feature selection [77. The key idea of contrastive learning is generate supervised signals from the data itself by data augmentation and then learn discriminative representation by optimizing a contrastive objective between positive and negative sample pairs. Building upon the prominent success of contrastive learning, several contrastive AGC (CAGC) methods have integrated contrastive learning into the AGC framework boost clustering performance. Specifically, most existing CAGC methods aim to construct augmented views using carefully designed augmentation operators, encouraging identical samples across different views to align while ensuring distinct samples diverge (18).
Although CAGC methods have achieved satisfactory performance, data augmentation and contrastive objective design remain critical components that significantly impact clustering performance. In graph data augmentation, various manual strategies introduce perturbations to node attributes or structure, such attribute masking [19) edge perturbation [20], noise perturbation (21). Furthermore, to improve the adaptability and flexibility of data augmentation for downstream tasks, several learnable strategies have been proposed 22 23 However, most existing CAGC methods only treat edges as auxiliary information to obtain augmented graph embedding representations and measure contrastive similarity between samples by single embedding representation-Lewe augmentations. while paying no attention to the importance of edge-level embedding representation learning and augmentation. Few existing CAGC methods have explored the collaborative interaction between node-level and edge-level embedding augmentations across different granularity. Moreover, the contrastive objective setting also plays an important role in CAGC methods. Recently, contrastive sample awareness strategies have attracted great attention, enabling more exhaustive contrastive learning and improving discriminative capability. However, most existing CAGC methods only perceive a subsel of contrastive sample pairs in a differentiated manner, often prioritizing specific cases, such as hard negative samples (4 or hard samples (25) 26 27]. Specifically, they struggle to adaptively and effectively distinguish all contrastive samples, especially in differentiating positive-

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easy, posirive-hard, negative-eass, and negative-hard ones. This limitation compromises the quality of embedding representation learning.
To remedy these shortcomings, this study proposes a novel Robust Attributed Graph Clustering (RAGC), which goes beyond single node-level embedding augmentation and partial contrastive sample awareness, offering a more comprehensive approach to contrastive graph clustering. The RAGC seeks leverage hybrid augmentations of node-level embedding representation and edge-level representation through collaborative interaction, while also incorporating comprehensive contrastive sample awareness with adaptive and differential weighting.
As shown in Fig. [ the overall framework of RAGC mainly consists of two key modules: Hybrid- Collaborative Augmentation (HCA) and Contrastive Sample Adaptive- Adaptive-Differentie Differential Awareness (CSADA) modules. In particular, the HCA module simultaneously constructs node-level embedding representation augmentation and edge-level embedding representation augmentation to provide more comprehensive and reliable contrastiveness metric. And, the cross-view contrastive similarity matrix is leveraged refine and optimize the graph structure achieve the multi-level contrastive- ness and collaborative augmentation between node-level embedding representation and edge-level embedding representation and improve robustness against graph structure noise. Furthermore, guided by clustering pseudo labels with high confidence and adaptive confidence factor, the CSADA module thoroughly identifies and perceives the contrastive samples enhance the discriminative capability of representation learning. Specifically, contrastive samples with high confidence are treated differently based on positive-negativy and hard-easy perspectives through a weight modulation function, which adaptively adjusts participation of samples in self-supervised training. By leveraging contrastive similarity and clustering pseudo labels as a bridge, the HCA and CSADA modules mutually promote each other, further enhancing representation learning.
For clarity, the main contributions of this study are summarized follows:
Instead of solely relying node-level embedding, this study further explores edge-level embedding representation augmentation and unifies them to obtain more comprehensive data augmentation and a reliable cross view contrastive similarity across multiple granularity-
levels.
Guided by relatively reliable clustering pseudo-label information with dynamic confidence, contrastive sample pairs are adaptively differentiated by a novel and well-designed weight modulation function. To the best of the authors' knowledge, this study is the first to simultaneously perceive and emphasize positive-easy, positive-hard, negative-easy, and negative-hard samples, all of which contribute to deeper contrastiveness and improve the discriminative ability self-supervised learning.
Extensive experimental results on six benchmark datasets clearly demonstrate the superiority of the proposed RAGC over representative state-of-the-art methods. More importantly, the strong scalability of CSADA strategy in enhancing other CAGC methods is also validated.
Model Formulation
2.1 Notations
For attributed graph -= (V fo......,. represents the node with N nodes from disjoint K classes, is the edge set describing the connection relationships between pairwise nodes, and X ND denotes the node attribute features. The connection relationships in the edge set & can be mathematically formulated as an adjacency matrix A E {0, 1] NxN, where each element A, is defined as follows:
Aij = [1, if (u,, 0y) E otherwise
0,
The diagonal degree matrix is D dliag(d,,. ... .d), where d; = Σ
Aij. The normalized graph
1=1
Laplacian matrix is defined L = I A, where Ā 1-1/2 is the normalized adjacency
3

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Table 1: The explanation of main notations.
Notation
Meaning
X IRND
Original attribute feature matrix
A RNXN
Original adjacency matrix
À RNXN
Modified adjacency matrix with self-connections
Xaug E ERND Angg E ENNN
Node-level embedding representation
Dynamic semantic correlation matrix Identity matrix
IE 10,NN
D, E RNNN
Degree matrices
L RNXN
Normalized graph Laplacian matrix Node-level embeddings in augmented views
Z", Z ERdxd
E", E ER
Edge-level embeddings in augmented views
Z E R
Fused node-level embedding representation Clustering pseudo labels
PE KI,
E 10,1)
Pseudo label semantic correlation matrix High-confidence sample set with M nodes
H V. M
matrix with the refined adjacency matrix of self-connections = A +I++ and D = D + I. For clarity, the notations used in this study are summarized and explained in Table I
2.2 HyyrridCCollabortivs Augmentation
Learning edge representation is beneficial for effectively improving the discriminability embedding representation. Hence, node-level embedding representation and edge representation encoders embed the attributed graph into the various latent spaces, while two-level augmentations are simultaneously employed to construct comprehensive contrastive similarity metric.
Node-level Embedding Augmenter. To achieve simple and effective node-level embedding aug- mentation, representation-fise augmentation-later strategy is adopted. To improve representation generalization ability and robustness to noise, a mixed attribute perturbation augmentation strategy employed, where Gaussian noise and random masking are added to the original attribute features, i.e.,
X = X +N(0OON)) XM X (maak(r)
(2)
where (N(0, and Mmask(() (r) indicate the Gaussian noise with standard deviation ON and the randomly generated mask matrix with mask ratio respectively. After that, multi-order low-passing graph Laplacian filter is performed on both the noisy attribute matrices X and XM. effectively suppressing high-frequency noise and aggregating neighbor information:
x = (I (I- -) XN. X (I- XM
where - L is the graph Laplacian filter, and fn and fm are the order of filters. Furthermore, X N and Ats are fused to obtain the robust and comprehensive node-level embedding representation Xaug for subsequent contrastive augmentation:
1 ( x 2
X aag
(5)
Then, two MLPs encoders are employed on the node-level embedding representation Xauy to generate two augmented views:
Z MLP, (Xaug) ZZ MLP, (Xaug)
(6)
where MLP, and MLP, are two simple and learnable augmenters with the same MLP structure but without shared parameters. After that, augmented node-level embedding representations Z" and Z are further normalized along the row dimension by l2 ly-norm to facilitate the calculation of contrastive similarity:
7 (i.:) = Z (1. (i.:) 12,, Z (i.:) = Z (i,:) IZ (t.:)

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Edge-level Embedding Augmenter. The multi-order graph filter is prone to over-smoothing. To effectively leverage the structural information of the attributed graph. the edge-level embedding representation and augmentations can be obtained using two MLPs encoders:
EMLP& ,A), E EMLP, (A)
(8)
where, similarly, EMLP, and EMLP, & two structure encoders with the same MLP structure but without shared parameters. The E and E² are augmented edge-level embedding representations, which contains different and rich semantic information. Further, the E and E are also normalized along the row dimension:
E E (z,:) - E (i,:)/IIE* (2,:) E (1,:) E² (1,:)/IE" (1,:) ll2
Comprehensive Contrastive Similarity Construction and Collaborative Interaction between Various Augmentations. With node-level embedding augmentations Z", Z" and edge-level embed- ding augmentations E E the comprehensive contrastive similarity matrix across attribute and structure is constructed as follows:
S aZ' (Zm) + (1-a))' (ET)) V., m E {a.
(10)
where a is learnable balance coefficient that adjusts the role between the node-level and edge-level embeddings.
Obviously, the comprehensive similarity matrices S will provide beneficial guidance for contrastive training. In addition, the structural information in similarity matrix Sa.b is more discriminative and can provide adaptive refinement for edge-level embedding representation learning. Eq. (8) is further formulated as follows:
E = EMLP, (Aaug) E EMLP (Aaug)
(11)
where
Aaug == Norm (Z)) + (E")"" + Aaug
(12)
where Norm(.) is the min-max normalization operator. The Aang is dynamic semantic correlation matrix and iteratively updated to achieve structure rectification, and the initial setting is Aaug = A. The node-level embedding representation augmentations Z" and Z' also guide the edge-level embedding augmentations reverse, achieving the collaborative interaction between node-level embedding augmentations and edge-level embedding augmentations.
2.3 Contrastive Sample Adaptive-Diftcae Diffeeentiall Awareness
Contrastive learning usually maximizes the agreement between different augmentations of the same objective sample while minimizing the similarity between the augmented views from different objective samples. For target sample 0 in I-th augmented view, the InfoNCE loss is utilized for self-supervised representation learning, i.e.,
Σ Olvh.e))) milh
[(x)) = - log
(13)
Σ ((elier)) mill
Σ Σ (loh,og) (E
where 0(v), o/7) is the contrastive similarity, defined as similar way in Eq. 100 However, St.. contains edge-level embedding augmentations, so it is more comprehensive similarity. Further, is evident that the classical InfoNCE loss treats all contrastive sample pairs equally limiting the discrim- inability self-supervised representation learning. To deepen contrastiveness, contrastive samples with high- nigh-confidence clustering structure are given greater emphasis and effectively distinguished by dynamic weighting strategy.
Dynamic High Confidence Samples Selection. In contrastive learning, focusing on high confidence samples with clear clustering structure helps improve the boundaries of representation learning. After node-level embedding representation augmentation, a comprehensive, clustering-oriented representation of node-level embedding obtained by linearly fusing Z and z
1 IZ a Z 2
1
Z
(14)
5

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Then, the K-means clustering algorithm is performed on Z to extract clustering information, including pseudo labels P E {I.... K}* and clustering centers (K,.... _K}. To select high confidence samples more efficiently, the confidence score CONF; is defined based on the distance between the embedding and the corresponding center:
CONF; = a K
(15)
where Kr, is the clustering center corresponding sample Z, Pp, and a is the softmar activation function to normalize the distance. The high confidence sample set constructed by selecting top M samples with the highest confidence scores:
) the distance function,
H = {us] top (CONE, M)}
(16)
where M [N -)] is the number of high confidence samples, [.] is rounding function, and T is a dynamic confidence factor. In practice, the confidence parameter T is initially set to a large value, and then gradually decreases as the training progresses. This ensures that an increasing number of samples are selected and focused on, which is beneficial for contrastive training. With iterative training, the discriminability of the embedding representation Z and clustering structure improve. Therefore, more high confidence samples are prioritized in contrastive learning, further enhancing self-supervised representation learning in a reinforcing cycle.
In addition, the label semantic correlation matrix Q E {0, 1) NxN is constructed based on clustering pseudo labels P as follows:
Qu 11 (0. P
P; P==P,
(17)
Qij effectively reveals the pseudo label correlation between nodes v; and vy. Specifically, when QU L, indicates that nodes v2 and v belong to the same cluster with high probability, i.e. they are more likely to be positive sample pairs. Conversely, when Q2 = 0, it indicates that the nodes 2s and 0y have different pseudo labels, implying that they are more likely to be negative sample pairs.
daptiiv-- Adaptive-Differentia Differential Weight Modulation Function for Contrastive Sample. Different contrastive sample pairs play significantly different roles in self-supervised training. For example, some samples are easily confused and require deliberate attention, which helps enhance the discriminative ability of representation learning. To adaptively distinguish contrastive sample pairs, novel weight modulation function is designed and defined as:
1, Ut Uy $ H el (L-Norm(st,"))
e (or U1 UU E H. Qij
(18)
Us Uy E H. Qij where B E 1) and 7 E [1 are adjustable weight factors. Fig.
visualizes the weight
modulation function under various cases. Some desirable properties of W (v. oy can be summarized
as follows, all of which contribute to enhancing contrastive learning.
1) For high-confidence contrastive samples, W(r), u(") 1 is always satisfied, ensuring strong attention to contrastive samples with a clear clustering structure. In contrast, samples with an unclear clustering structure should not be emphasized, as it may lead to an inaccurate label semantic correlation matrix Q which could negatively impact contrastive learning.
2) For positive sample pair (i.e., Qij 1). the greater the similarity, the easier it is to promote agreement between them. Hence, positive hard sample pairs with low similarity are up-weighted, while positive easy sample pairs with high similarity still receive relatively high weight. And, the weight assigned to positive hard sample pairs is always greater than the weight of positive easy ones. For negative sample pair (i.e., Qiy 0), the greater the similarity, the more difficult it is to push them apart. Hence, negative hard sample pairs with high similarity are deig-weighted, ensuring that they are forced to separate much as possible.
3) For contrastive similarity, positive sample pairs are assigned higher weights to strengthen the aggregation of similar samples. In addition, under the same similarity, negative sample pairs are assigned relatively lower weights than positive ones, thereby pushing apart negative samples more effectively during optimization. Hence, appropriately adjusting 3 E (0, and y E [1,5] allows

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control over the weight difference between positive and negative sample pairs, enhancing the flexibility of the weight modulation mechanism in dealing with various applications. Specifically, reducing and increasing 7 sufficiently amplifies the weight difference between positive and negative sample pairs with moderate similarity, thereby strengthening the ability of RAGC to capture complex boundaries and improve discriminative representation learning.
In summary, the CSADA module adaptively distinguishes contrastive sample pairs by the well- designed weight modulation function W (ut, oy"), effectively handling positive-hard, positive-easy, negative-harr hard, and negative-eart easy sample pairs.
275
250
225
200
100
00
02
04
0.
08
1.
Figure 2: Visualization of weight modulation function W Wod, ugr)) with different weight adjustment factors.
2.4 Objective Function
By calculating the view-wise contrastive similarity function St. and the weight adjustment function W (e ) for target sample v; in /-th view, the contrastive sample dlaptive-differentie awareness guided self self-supervised training loss can be defined as:
Σ ((llas)s mel!
[(v)) -log
(19)
(W m
Σ
+ W(ef JEi
By incorporating a comprehensive contrastive similarity metric St. and an effective weight adjust- ment mechanism, the RAGC enforces discriminative learning across hositive-hard, positive-easy, negative-hard, and negative-easy sample pairs. The overall training loss of the RAGC method is formulated as follows:
N
Σ
Σ
C(v))
(20)
2N
[E(a,b]
i=1
For clarity, the detailed training process of RAGC is described in Algorithm 1
3 Experiment
In this section, the superiority and effectiveness of the proposed RAGC are validated through extensive experiments. Detailed experimental settings shown in Appendix B and additional results shown in Appendix C
3.1 Experimental Setting
Following the key baseline in 126]. the proposed RAGC is evaluated on six challenging graph benchmark datasets, including CORA (88) CITESEER (CITE) 28), AMAP (29) BAT EAT 21 and UAT (21). The detailed statistics of these datasets are briefly summarized in Appendix B. In experiment, RAGC is compared against 11 state-of-the-
baseline methods, which are introduced in the Appendix B.2 Moreover, to reduce the impact of random initialization, the parameters
7

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Algorithm Training process of RAGC.
Input: Attributed graph 9: Cluster number K; Iteration number It; Standard deviation of Gaussian
noise ox; Mask ratio r; Filter orders l, bm; flype-paraametent T, 9,
Output: Clustering label matrix P.
1: Construct the node-level embedding representation Xang using Eqs.
2: Initialize A Ang
A.
3: for iler= = 1 to Tt do
4: Obtain two augmented views of node-level embedding representation X aug using Eqs. (6)-
5: Obtain augmented views of edge-level embedding representation using Eqs.
6: Update the augmented structure matrix Auug using Eq. (12)
7:
Calculate contrastive similarity St. using Eq. (TO).
8:
Perform K-means on comprehensive node-level embedding Z to obtain clustering pscudo labels P and construct dynamic high-confidence sample set H using Eqs. (4))- T6).
9: Obtain label semantic correlation matrix Q based on pseudo labels P using Eq. (77
Calculate the weight modulation function W vn") to distinguish contrastive sample pairs using Eq. (18).
11: Train the entire network by minimizing C in Eq. 20)
12:
end for
13: Calculate the final clustering result P by performing K-means on Z.
initialized with different random seeds and all methods run 10 times, and then the experimental results report the mean value and corresponding standard deviation for all clustering metrics.
3.2 Performance Comparison
The quantitative experimental results of the all AGC comparative methods on the benchmark datasets shown in Table 2 Notably, except for few cases, the proposed RAGC achieves optimal clustering performance across all six datasets, clearly demonstrating its superiority and effectiveness. Specifically, the performance improvements of RAGC are significant on several datasets. For example, on the BAT dataset, RAGC outperforms the sub-optimal HSAN method by 2.65%, 2.53%, 2.44% and 2. 2.33% in terms of ACC, NMI, ARI and Fl metries, respectively. Similarly, for the CORA dataset, the RAGC exceeds the sub-optimal HSAN by 1.67%, 1.41%, 2.32% and 1.80% on ACC, NMI, ARI and F1 metrics, respectively.
Obviously, the proposed RAGC significantly outperforms classical generative- based, adversarial- based, and existing contrastive AGC methods. This effectiveness stems from its augmentation that integrates node-level and edge-level embeddings, and a contrastive sample adaptive- differential awareness strategy that distinguishes between hard-easy and nositive-negative sample pairs. These modules enhance the discriminability and boundary awareness of the learned represen- tations, leading to improved clustering results. Experimental comparisons, including with strong baselines like HSAN, confirm RAGC's effectiveness in contrastive learning for graph clustering. A more detailed analysis can be found in the Appendix C.
3.3 Ablation Study
The ablation experiments are conducted to evaluate the impact of the key modules in the RAGC method. Specifically, three ablation variants of RAGC are defined as follows: 1) (w/o) D: This ablation variant represents RAGC with static high confidence samples selection, where the confidence coefficient remains fixed in the training process. 2) (w/o) H: This ablation variant represents RAGC without the HCA module, where a simple low-pass filtering is utilized to obtain node-level embedding representation and the corresponding augmented views are generated by MLPs encoders. 3) (w/o) C: This ablation variant is RAGC without the CSADA module, where the classical infoNCE contrastive loss is utilized for self-supe training.
From the experimental results of the ablation variants Fig. several notable observations can be drawn. 1) The ablation results clearly validate the effectiveness of each core component in RAGC. Removing any key strategy leads to performance degradation, highlighting their compatibility and necessity. 2) Notably, the HCA module contributes most significantly by enabling collaborative

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Table 2: The performance comparison on six datasets. All results are reported with (mean + std) under ten runs. The red and blue values indicate the best and the suboptimal results, respectively.
Generative and Adversarial AGC Methoos
Classic CAGE Methods
Hard Sumple Aware CMGC Methods
Dattsset Metric
DAEGC SDCN
DFCN
ARGA
AGE
NCLA
CCGC
GL
GDCL
ProUCL
HSAN
RAGC
ACC
70.4560.66 35 60.62.8 36.330040 40 71 21,34+0.25 73, 73.50+1.4
51.0941.25 .22 73 88-1..20 20
74.9111.8
7753-0.47
57.13+1.23
77.071..55
78.74-0.72
CORA
NMI
ART
49.630043 07. 7863.24 04 6722 10 1a.71
52.8920.69 14 11.2811.91 19.3640.87 51 31.0680.52
57. 1,25 31. 11.800078 56 45.151001 16466683
50 2416
36.66a1 165 1 53. 53.80a2.25
48.05
56,0000.36
30.71
41.0221.34
57 27.52.2.70 70
59.2141.00 03
60.6220.34
39,8440.88 60
F1
68.2740.57 34 37..220).0 26 16e0.50 69.2740050
30 69 (9.68e1159
51, 31,12+1,12 12 T0 98+2.79
52.58-0.77
45.68+1.29
75 [1 40
76.91+0.76
ACC
64.5441.39
96 00.5000
61,0780449
69.73m0024
59.2822.3
59.540004
05.9220.90
15:
21.3080042
CITE
NMI
36,4180.886 38, 28.7129..2
43 235000020
34,9089.71
40.9320055
20.08880.89
44.33200.99
43.50x1135
39.5220:38
39,59900.39
45.00
45.06650.24
45.3249.51
ART
37,78+1.22 .24 40, 17+0044
25 5.5000 30 34. 72
45.31=044
33,37H0.55
45 (5.68+1880 80 44. 85
41.07=095
36. 16116
0. 12
46.51+0063
62.20M1132
63 24.62600.2
(4.30e0.20
58.23601.11
67.45=00.27
52.674ll.44
02 02.7122.06 (5.01=9).99
61.12=0.70
57.8961.98
03.01=1.29
622.49=1.15
ACC
75:06+0:25
51.44+0.81
76 76.83e0.23
69.2842.50
75.08+0.68
18+6.8
77.24+0.87
43.75=0078
51.53+0.38
02:00:3:.3
788.29+0.3 82
AMAP
NMI
ART
56.12:0.24
65.2540045 44.85510.83 66.2221121
31. 31.2121.23 58. 38.0.880.. 74 44, 1816.1
58, 36.3662.76
65, 65.58:0.61
55 15.89
63.63a1.07
30s1.59
67. 07.4110-18
57. 99.9966 66 58. 14.0.4.
67.1220.92
57.
57.522:0228
21.57a0.51 34,18:0,89
38.56g0..99
58, 33.01:00.40 48
67.21
59.53&1.33 .3
67.50..0.64
59,
69.87140.54
50.6611.49
11,250031 64,3041
71,74
2200511.08
1840.57
73:0242.34
38 31.9740.44
72.0340.46
72.6742.
ACC
52,7800000
53.05544665 55.7360006
67.86st0
56 56.0800.76 76 47.4841164
75.04
75.50ml1377
45.42=0054
55. 55.75t0.79
77.15
79.77+1 .9
BAT
NMI
2144200335
25.7485.71
48.7750.51
49, 94
36.04a
14 24.36&1.54
50.2362243
50.5%a01500
51.70gb0.45
42 28, 28.69980::22
53.21 53.211
25.7461.17 70
18.1840.29 04+4.97
7..660022
26. 13
24.1449995
47.45=1.5
19.33-0.55
54.64+2.244
02.254000
46.45e5.90
50,9060.12
12 67.02e1.15
55.0H0030
42.25H0034
74.90e1.80
75.40e0).85
39.94e01557
56,00+00.90
77. (7.12
79.66e1.337
ACC
35
39.0761.51
29.37750 19 $2.13860000
47, 47.2085132
20,0681.22
57, 19200.6
57.22251.7 73
33.40a50.15 18 43.36880.77
20.09233.34
53.49330:45
FAT
NMI
ARI
05 56.000
05.0340.08
08. 831..3....
06.91 25.0
90g0.4
22.4811.21
17.29.0.50
1:21
16.5740.46
23,7440
21,4810.64
21.0611.80
180 53, 85.8550..7 33.6740.34
27.71
26.2
04.31.0:29 15.0330.95
13:22a0033
23,9320.45
33.25.0.:4 44
06.8840.55
18.27:40.6
34.79g0.25
F1
34.7220.16
16 33 12.423.10 42
02.95
52,7560.07
45 50
31,2560,96
57, 57.0990094
57.5241967
25:02=0::1
42.5520..5
57.26640.28
53.66700:5
ACC
52.29H0449
52. 25 53.61 +0.09
49, 45
42.57=0042
45, 15
56 34t1..11 54. 7.ml 422
48, 16.7000000
45, 55.3555
56.0446.67
58,49=1.07
UNT
21,3300.44
16.6
25.44+0.31
24.4910.57
|5s1.99 25.22552300000
10=00:0:0
22.04+2.23
26
11
33.48s1.00
ART
20.50+0.51
63++1.4 87+0
16.5740.31
20. 50+0.70
34+0.78
52+2.00
19.44-1
21.76-0.01
14.74+1.90
27.21+11.1
F1
30.53e00.64 45 35.554 25. 79,00.0
50.26660.16
50. 30.15500.3 30.56+40.25
55 24e1.60 53.61=2.61
45.00=0000
39.30ee182
54,20le1.84 84
57.40l=1.57
node-level and edge-level augmentation, ensuring more reliable contrastive similarity. 3) The CSADA module also plays a vital role by enhancing boundary perception through adaptive differentiation of contrastive samples. The scalability and effectiveness of the CSADA module on other CAGC methods are further validated in Appendix C22 4) Additionally, the dynamic confidence factor facilitates progressive learning by expanding the set of gegh-confidence samples, further boosting representation discriminability.
(a) ACC
(b) ARI
(c) NMI
(d) F1
Figure 3: The clustering results of three ablation variants and RAGC on the six used datasets, where the proportion between best result achieved by RAGC and each ablation variant is shown.
3.4 Robustness to Noise
To evaluate robustness to noise, this section presents performance comparison between RAGC and several representative CAGC methods, including SCGC 12T, DCRN 29). and CCGC 330, under various noisy conditions. To be specific, Gaussian noise (O, σN)) is added to the attribute features with varying standard deviations: 0.1, 0.2, and 0.3. The experimental results, presented in Table 3 reveals the following key observations. 1) The proposed RAGC consistently outperforms all the other comparisons across all metrics, even under varying levels of noise disturbances. 2) Although the performance of all methods declines the noise ratio increases, RAGC exhibits the smallest average degradation ratio across all metrics and datasets, demonstrating its superior robustness to noise. For example, the performance of RAGC decreases by 11. 11.66, while DCRN experiences a 19.03% drop. The robustness of RAGC to noise is mainly attributed to its comprehensive HCA data augmentation and discriminative contrastive setting.
3.5 Visualization Analysis
To intuitively demonstrate the advantages of RAGC in discriminative representation learning, the raw attribute feature and embedding representations learned by several representative AGC methods are

---

Table 3: The performance comparison of SCGC 21. DCRN 29 CCGC B0 and RAGC with
different noise levels. Negative values indicate the performance degradation percentages compared to corresponding methods without noise.
Arg.
ACC
NMI
ART
F1
ACC
NMI
ART
ACC
NMT
AR1
Fi
(-3)
(:5)
(-67
67.15
(:13) 39.81 (-14) 59.01 (-9)
50.60 (-11) 20.37 (-27) (-27) 46,64 (-16)
SCGC
0.2
67.63 (-8) 47.91 (:15)
42.16
61.68 (-13)
55.11 (-22)
27.52 (339) 23.42 (-49) 49.48 (9.48
50,08 (:11) 20.08 (:26) 16.75 (:32) (8134(-13) 20.61
(7,44(:9)
62.58
(6))
(:30
(-27) (7176
0.1
57.68 (-7) 41.62 32.91 (11)
(-145(-1)
16.81 (-20) 33.00 (-28) (-27) 53.97 (-6)
43.28
30,51 (-15) 11.88 (-31) (6157
(-.76
40.79
(-10) (2246(22)
48.81
(-233
28,92 (:37) 27.31 (:30) 52.27
(-119
15.82
12:34
(-29)
(-17)
-1908
0.3
(-12)
34.73 (23) 23.56 (129) 44,27 (-11)
(5.52
(6.33 (333
(-12)
42.77
(:34) 15.06 (:37) (:
(1100000)300000111 (-10)
0.1
(0.30.(55
52.91 (-61 (-15 65.37
(3.84(-9)
37.85 (:15) (-24) 56.8 (-9)
52.82
23.85 (-15) 18.11 49.46
COGC
0.2
64.78
49.02 (-13) (-27) 59.02 59.02.(-17)
(-17)
51.81
(-26) 27.84 (:37) (-55) 44.84 (-28)
12,44 (-7) 22.78 (-21) 19.75 (-23) (-13) -21.36
(-176
44.73 (211) 34,58 (-34) 56.67 (-20)
(5.04 21.51 (-51) (-69)
(:36)
(2.26
21.01 (-25) (0240 (-,43(114)
16.84::2)
55.41 (:) (5)68 (-24
69.19()3) 41.81 (-8) 43.06 (1117
(-40
(-113 26.51 (-10) 54.01
OURS
0.2
73.27 (-7) 52.50 (-13) 49.47 (-17) 72.41 (-6)
65.35 (-8) 68 (:19) 37.46 (-19) 57.6
(77))((7) (:7)
(5.7)
25.76 (-176 25 (-8) (-719
-11.36
0.3
(-130 48.60 (19) 45.05
69.49
(-17)
29.52 (-35) 29.58 (-36) 51,32 (-18)
(4,40 24.97 (-12) 22.45 (-17) 52.38
visualized using t-SNE 31 As shown in Fig. 4 and Appendix C.4 different clusters marked with distinct numbers and colors. can be observed that the distribution of nodes with raw attribute features appears irregular. Among all AGC methods, RAGC exhibits the strongest discriminability in embedding representation, as evidenced by nodes within the same cluster being more compact and boundaries between different clusters being relatively well-defined.
raw
(b) DCRN
(c) CCGC
(d) Graphl.camer
(c) DAEGC
(f) RAGC
Figure 4: The 2-1) visualization CORA dataset. The 2-D visualization of the AMAP dataset is provided in Appendix C.4
4 Conclusions
In this study, a novel deep contrastive clustering method, termed RAGC, was proposed for the attributed graph clustering task, primarily comprising the HCA and CSADA modules. Specifically, RAGC takes advantage of edge-level embedding representation and performs hybrid-collaborative data augmentation by integrating both node-level and edge-level embeddings. A comprehensive contrastive similarity constructed, which in turn provides reverse guidance for edge-level embedding augmentation. Furthermore, a novel weight modulation function dunction-oriented contrastive strategy was designed to adaptively distinguish sample pairs according their own characteristics, including contrastive similarity, clustering label confidence, and pseudo label correlation. This approach enhanced boundary perception and discriminative capability self-supervised representation learning. Extensive experiments on six benchmark datasets demonstrated the promising clustering performance of RAGC and the scalability of the key CSADA module in CAGC methods. Although RAGC has demonstrated outstanding performance, there are still potential challenges when dealing with highly sparse and dynamic graphs. Exploring clustering for such graph data a promising direction for future research.
Acknowledgment
This research was supported by the National Natural Science Foundation of China under Grant 62403043, 62225303, and 62433004; in part by the Beijing Natural Science Foundation under Grant 4244085; in part by the Postdoctoral Fellowship Program CPSF under Grant GZC20230203; in part by the China Postdoctoral Science Foundation under Grant 2025T1 10467 and 2023M740201; in part by the Interdisciplinary Research Center of Beijing University of Chemical Technology under Grant XK2025-06.
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A
Related Studies
In recent years, deep attributed graph clustering has attracted significant attention, aiming to learn node-level embedding representation and classify nodes into disjoint clusters according distribution of embedding representation. Existing AGC methods can usually be classified into three classes: generative, adversarial and contrastive [18].
to feature
A.1 Generative and Adversarial Attributed Graph Clustering
Generative and adversarial AGC methods usually utilize Graph Convolutional Network (GCN) 32 and Graph Attention network (GAT) [33] learn node-level embedding representation, with the core difference between them lying in their representation learning objectives. Generative AGC methods focus on recovering graph information (either attribute or structure) from the learned embedding representation 34 For example, Deep Attention Embedded Graph Clustering (DAEGC) [35 and Parallelly Adaptive Graph Convolutional Clustering (PAGCC) [36] reconstruct the graph structure, to enhance clustering performance. On the other hand, adversarial AGC methods improve the discriminability of embedding representation by an adversarial game between a discriminator and generator 33 38 39]. Furthermore, to alleviate the over-smoothing problem and obtain more comprehensive embedding representation, some methods effectively pass attribute representation through auto-encoder to GNNs by delivery operator in layer-by-layer manner, such as Structural Deep Clustering Network (SDCN) [40] and Deep Fusion Clustering Network (DFCN) [41). To unify representation learning and clustering, sele-supe training strategies are widely utilized. These strategies typically minimize the Kullback-Leible (KL) divergence between the initial label distribution and the confidence augmented distribution, ensuring more effective clustering.
A.2 Contrastive Attributed Graph Clustering
Although generative and adversarial AGC methods have achieved notable success, most of them rely on certain prior knowledge, such as feature distribution or label distribution, making their performance relatively sensitive to these assumptions. In contrast, contrastive learning, a self- supervised representation learning paradigm, has been rapidly extended to AGC. It constructs self-supervision signals by maximizing the similarity between the embeddings of positive samples while minimizing the similarity between the negative ones. Contrastive Multi- Multi-View Representation Learning on Graphs (MVGRL) 42 generates augmented structure by a graph diffusion network and maximizes the mutual information between cross- views through the InfoMax contrastive loss. Similarly, Self-supervieed Contrastive Attributed Graph Clustering (SCAGC) 43 constructs two augmented graphs by adding noise attribute and applying random edge perturbation structure, then performs contrastive learning at both the node-level and the clustering label-level. Similar to the augmentation strategies in 443. Dual Correlation Reduction Network (DCRN) [29] further reduces redundant correlation at both the feature level and the sample level to alleviate the representation collapse problem. To eliminate the need for complex and manual data augmentation, several Icarnable augmentation strategies have been developed. Simple Contrastive Graph Clustering (SCGC) [1]] first smooths graph signal using low- www-passing Laplacian filter and then utilizes garameter-unshane MLPs to generate augmented views, and further constructs Node Clustering with Fully Learnable Augmentation (GraphLearner 23] dynamically constructs an augmented graph through rich learnable structure and attribute augmenters in a self-cycle way and utilizes normalized temperature-scall cross-entropy loss to pull positive samples closer while pushing negative samples apart.
oriented contrastive loss. Graph
However, most existing the methods treat all contrastive samples equally, limiting the discriminability of contrastive learning. Recently, some studies focus on hard samples, recognizing their crucial role in improving both the generalization and discriminability of the model. Structure-enbanced Heteroge- neous Graph Contrastive Learning (STENCIL) [24 focuses on hard negative samples and enriches model training by randomly mixing up negative samples with highest similarity. Similarly, Xia et al. [44 establishes more suitable measure criterion for hard negative samples through probability estimators and focuses on them by weight adjustment or node mixing strategy. Furthermore, to hard
mitigate interference from false negatives, Niu et. al 25 propose an affinity uncertainty-bot negative mining approach for graph contrastive learning, which evaluates the hardness of negative samples according to collective affinity information. Beyond negative sample pairs, Liu et al. [26)
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also extend the focus to hard positive samples by a unifying Hard Sample Aware Network (HSAN), strengthening the boundary perception capability.
Obviously, graph data augmentation and contrastive objective play a crucial role in contrastive AGC methods. However, most existing CAGC methods fail to fully leverage edge information. Specifically, they only utilize edge information to obtain node-level embedding representation and achieve single augmentation. The edge-level embedding representation learning and augmentation are ignored, preventing the natural modeling of collaborative interaction across multiple levels. In addition, existing methods struggle to sufficiently perceive contrastive samples, failing to differentiate them from the perspectives of hard- posiiive, hard-negative, easy-positiin and easy-negative Adaptively perceiving and significantly distinguishing these samples is crucial for improving the discriminative capability of representation learning.
B Experimental Setting
B.1 Datasets
Following the key baseline in 126 the proposed RAGC is evaluated on six challenging graph
benchmark datasets, including CORA 28, CITESEER (CITE) (28), AMAP (2),, (1 EAT
21 and UAT 21 The detailed statistics of these datasets are briefly summarized in Table 4
B.2 Baselines
In the experiment, RAGC is compared against 11 state-of-the-art baseline methods, including:
four generative and adversarial AGC methods: DAEGC 35 SDCN 40
DFCN 41 and
Adversarially Regularized Graph Auto-encoder (ARGA)
37
four classic CAGC methods: Adaptive Graph Embedding (AGE) 28 Neighbor Contrastive
Learnable Augmentation (NCLA) 45).
Cluster-guide Contrastive Graph Clustering Net-
work (CCGC) 30), GraphLearner (GL)
233
three hard sample aware CAGC methods: Graph Debiased Contrastive Learning with Joint Representation Clustering (GDCL) [46). ProGCL [44), HSAN (26).
Please refer to Section A or the original papers for a detailed description of these methods. For fair comparison, the original clustering results of all comparison methods are directly taken from their respective papers.
Table 4: The statistics of all used datasets and parameter settings of proposed RAGC method.
Statistics
Parameters
Dataset
Sample
Dimension
Edge
Class
B
Y
Ir
CORA
2708
1433
5429
7
0.9
2
le-3
CITESEER
3327
3703
4732
0.9
le-3
AMAP
7650
745
119081
8
0.1
2
5e-5
BAT
131
81
1038
4
0.9
1
le-3
EAT
399
203
5994
4
0.7
5
1e-4
UAT
1190
239
13599
4
0.8
5
le-4
B.3 Parameter Setting
During the training process, the number training epoch is set to 400. The detailed settings of weight factors 3, 7 and learning ratio Ir are shown in Table In the HCA module, both the node-level embedding encoders and edge-level embedding encoders are both single-layer MLPs with unshared parameters. The embedding dimension is set to 1500 for CORA, CITESEER, BAT and EAT datasets, and set to 1000 for AMAP and UAT datasets, respectively. In the attribute augmenter, the standard deviation ON of Gaussian noise is 0.001 and the mask ratio of the mask matrix is 0.005.
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B.4 Metrics
To comprehensively evaluate the clustering performance of all AGC methods, four widely used clustering metrics are utilized, including Accuracy (ACC), Normalized Mutual Information (NMI), Average Rand Index (ARI) and macro Fl-score (F1). Each of these metrics is positively correlated with clustering performance. All methods are conducted ten times and the average values along with their corresponding standard deviations of all clustering metrics are reported.
B.5 Computing Resource Details
The experimental environment is server equipped with Intel(R) Xeon(R) Gold 6348 CPU, NVIDIA A800 PCLe 80GB GPU, 100GB RAM, and the Py Torch deep learning platform. The training time per run for each dataset is less than 3 minutes.
C Additional Experiments
In this section, additional experiments are conducted to further verify the robustness and effectiveness of the proposed RAGC. These include detailed analysis of the performance comparison experiment (Section C.Ip. an investigation of the scalability of the CSADA module (Section C.2 sensitivity analysis of parameters 3, 7, ON, and r (Section C.3 as well as comprehensive visualization results (Section
C.1 Performance Comparison
The quantitative experimental results of the all AGC comparative methods on the benchmark datasets are shown in Table 2 Notably, except for few cases, the proposed RAGC achieves optimal clustering performance across all six datasets, clearly demonstrating its superiority and effectiveness. Specifically, the performance improvements of RAGC are significant on several datasets. For example, on the BAT dataset, RAGC outperforms the sub-optimal HSAN method by 2.65%, 2.53%, 2.44% and 2.53% in terms of ACC, NMI, ARI and Fl metrics, respectively, Similarly, for the CORA dataset, the RAGC exceeds the sub-optimal HSAN by 1.67%, 1.41%, 2.32% and 1.80% on ACC, NMI, ARI and metrics, respectively.
Further, several fine- fine-grained analyses are drawn from the following aspects:
1) It is clear that RAGC always achieves better performance all six datasets compared to the classical generative-based and adversarial-based AGC methods. For example, RAGC achieves an average improvement of 17.28%, 9.1%%, 15. 78% and 21.08% over DFCN in terms of ACC, NMI, ARI and F1, respectively. The primary reason is that classical generative and adversarial based AGC methods learn node-level embedding representation under the guidance of prior knowledge, making their discriminability sensitive to these assumptions. They lack specialized contrastive strategies to achieve information alignment and fully leverage self-supervised information from the discriminative latent space, leading to poor clustering performance. In most cases, contrastive AGC methods outperform classical generative-base based and adversarial-baa AGC methods, further validating the effectiveness of the contrastive learning strategy.
2) Among all contrastive AGC methods, RAGC remains superior, with its performance advantage being even more pronounced. As an example, on the CORA dataset, RAGC outperforms the CCGC method by 4.86%, 4.1 4.17%, 7.33% and 5.93% in terms of ACC, NMI, ARI and F1, respectively. The main reason for this superior performance is that RAGC enhances the discriminability of embedding representation effectively by distinguishing contrastive sample pairs, with particular emphasis on hard samples. In addition, hard sample aware contrastive AGC methods (such as GDCL, ProCGL, and HSAN) achieve better performance on some datasets. However, they still underperform compared to the proposed RAGC on all datasets, demonstrating that RAGC is more effective in learning discriminative embedding representation. Especially compared the important baseline HSAN, on all datasets, RAGC achieves an average improvement of 1.66%, 1.25%, 1.53% and 1.51% across all datasets in terms of ACC, NMI, ARI, and F1, respectively. This superior performance primarily due to RAGC's hybrid-collaborative augmentation, which integrates both node-level embedding representation and edge-level embedding representation, resulting more comprehensive and discriminative contrastive similarity. In addition, the designed contrastive sample delapiive-differentie
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CSSC HAAN HAAN-CSADA
SGSL HEAR
2042
(a) CORA, AMAP, BAT
(b) CITE, EAT, UAT
SCGC K:S..C5ADM
COO S05C
31223
(c) CORA, AMAP, BAT
(d) CITE, EAT, UAT
Figure 5: The experimental results of HSAN 26 and SCGC with the proposed CSADA module on all datasets.
awareness strategy allows RAGC effectively distinguish sample pairs, especially positive-hard, positive-easy, negative-hard, and negative-easy ones. This significantly enhances its boundary perception ability in representation learning, leading to improved clustering performance.
In conclusion, these experimental results and analyses evidently validate the effectiveness of the proposed RAGC method in attributed graph clustering task.
C.2 Scalability of the CSADA module
To further validate the scalability and compatibility of the proposed CSADA strategy, it is transferred to other contrastive DGC methods, including SCGC [2]] and HSAN [26). Specifically, the data augmentation strategy and similarity construction across augmented views remain with the original settings in (26 21), and only the contrastive setting is replaced by the proposed CSADA strategy. As shown in Fig. 5) in most cases, the clustering performance of these methods significantly improves when combined with the proposed CSADA strategy. This demonstrates that CSADA not only compatible with existing CAGC methods but also exhibits strong scalability.
C.3 Parameter Sensitivity Analysis
Several key parameters influence the performance of the RACG method, including the weight factors 3, y the CSADA module, as well as the noise standard deviation oN and mask ratio r in the HCA module. The performance sensitivity analysis of RAGC with respect to these parameters are examined as follows.
C.3.1 Sensitivity Analysis of 3 and
The factors and y control the weight magnitude of contrastive samples. The search ranges of these weight factors and are {0.1, 0.5, 0.7, 0.9) and 21,2,3, 4, 5). respectively. As shown in
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(a) CORA
(b) CITESEER
(c) AMAP
(d) BAT
(c)
EAT
(f) UAT
Figure The clustering results RAGC with different on six datasets.
(a) CORA
(b) CITESEER
(c) AMAP
(d) BAT
EAT
( UAT
Figure 7: The clustering results of RAGC with different six datasets.
Fig. and Fig. 7 all clustering metrics across different datasets exhibit commendable performance and excellent stability when and y across these parameter variations. The experimental results show that the proposed RAGC insensitive to 8 and demonstrating its strong robustness to these hyperparameters.
C.3.2 Sensitivity Analysis of parameters ON and
The candidate ranges for noise standard deviation and mask ratio in the HCA module are NN {0.0001, 0.001, 0.01, 0.1, 1} and (0.0005, 0.005, 0.05, 0.5, 0.7, 0.8), respectively. Fig and Fig. 9 show the variations in ACC metrics with respect to and It can be observed that the performance of RAGC remains relatively stable when aN varies in relatively wide range {0.0001, 0.001, 0.01, 0.1). indicating its robustness to moderate noise perturbations. Despite notice- able performance fluctuations when r varies within the given range, RAGC still maintains relatively excellent performance when E (0.0005, 0.005, 0.05). This suggests that moderate disturbance (such as noise or feature mask) can enhance the generalization ability and robustness represen- tation learning. However, excessive noise and feature masks may cause semantic drift in attribute
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70
CITESCER
ACC11))
85
20
BAT
50-
50.2
45
logos
(a) CORA, AMAP, BAT
(b) CITESEER, EAT, UAT
Figure 8: The sensitivity analysis of standard deviation in Gaussian noise.
BAT
CORA AMAD
USI
EXT
ACCE00)
ACC/80
5x 10"7 5x
Sx Lond
0.7
0.8
3K
5H 5x 10
03
(a) CORA, AMAP, BAT
(b) CITESEER, EAT, UAT
Figure 9: The sensitivity analysis of the mask ratio r in attribute mask matrix.
information, increasing the difficulty of representation learning, which in turn hinders discrimination and degrades clustering performance.
C.4 Visualization
(a) raw
(b) DCRN
CCGC
(d) GraphL.arner
DAEGC
RAGC
gg)
(h) DCRN
(i CCGC
(j) GraphLearner
(k) DAEGC
()) RAGC
Figure 10: The 2-D visualization datasets. The first row and second correspond CORA and AMAP datasets, respectively.
26


Reviews:
[{"review_id": "uAoGwn9dY7", "reviewer": "Reviewer_zM6C", "summary": "The paper explores the robust attributed graph clustering and discusses two problems faced by existing works, i.e., insufficient data augmentation and rough differential perception of contrastive sample pairs in contrastive learning. To tackle these issues, a novel robust attributed graph clustering (RAGC), incorporating hybrid12 collaborative augmentation (HCA) and contrastive sample adaptive-differential awareness (CSADA), is proposed in this work, which integrates CSADA and HCA for better feature extraction capacities. The paper indicates its novelty and signifcance, which is also demontrated via a series of experiments.", "questions": "1. How about the adaptability of the work to heterogeneous graphs? I recommend to discuss this issue in brief.\n2. The augmentation strategies for nodes and edges are from different feature sources, which might result in some problems of conflicting objectives. Please have a discussion on this issue.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "## Pros\n1. The work is overall well-written with clear problem statement and motivations. The method is well illustrated.\n2. The method design is technically solid, by employing CSADA as a reasonable and fine-grained extensions in differentiation awareness between positive and negative sample pairs.\n3. The experiments are sufficient.\n\n## Cons\n1. Some details to be further explained. For example, the reason for adopting exponential weighting strategies.", "was_revised": true, "final_justification": "This paper proposes a novel contrastive attributed graph clustering, RAGC, which mainly focuses on the issues in effective data augmentation and contrastive objective setting. This work exhibits relatively good innovation, particularly in the proposed contrastive sample adaptive-differential awareness. Although, large-scale scalability should be further considered, which is important for graph clustering. Therefore, I provide the above recommended score.", "rebuttal": "**Reply**: Thank you for your thoughtful and detailed review. We appreciate your recognition of our contributions and the advantages of the proposed method. We will carefully address your issues below.\n\n**Cons1**: *The reason for adopting exponential weighting strategies should be further explained.*\n\n**Reply**: Thank you for your insightful comment. In our CSADA module, we adopt an exponential weighting strategy to enhance the contrastiveness difference among the four types of contrastive sample pairs. This design is motivated by two key considerations:\n\n- First, the exponential functions allow the weights of high-confidence samples to grow beyond the fixed baseline weight setting ($W=1$) assigned to low-confidence pairs. This ensures that truly informative samples significantly contribute to the contrastive objective, effectively amplifying reliable signals and suppressing the influence of noisy or uncertain examples.\n\n- Second, the exponential form offers a smooth yet discriminative weighting mechanism based on sample similarity, enabling adaptive contrastive awareness. As shown in Fig. 2 and Eq. (18), the exponential function allows easy samples (e.g., high-similarity positive pairs and low-similarity negative pairs) to retain relatively high weights, while simultaneously adjusts the contribution of hard samples through controlled weighting. This property ensures that the model focuses on both reliable and informative pairs, thereby facilitating more effective contrastive optimization and enhancing robustness.\n\nOverall, the exponential weighting strategy not only supports fine-grained differentiation across the four contrastive categories, but also enhances the ability to perform confidence-aware learning in an adaptive and theoretically grounded manner.\n\n**Q1**: *How about the adaptability of the work to heterogeneous graphs? I recommend to discuss this issue in brief.*\n\n**Reply**: Thank you for your insightful comment. Although our method does not explicitly incorporate heterogeneous node or edge types, its architectural design exhibits strong potential for application to heterogeneous graphs. Specifically, the Hybrid-Collaborative Augmentation (HCA) module jointly leverages node-level and edge-level embeddings through a flexible similarity fusion mechanism, which does not assume uniform node semantics and can naturally adapt to scenarios with diverse node types and relation patterns. Moreover, the CSADA module performs adaptive weighting based on pseudo-label confidence and sample similarity, without relying on type-specific assumptions. This design enables our model to capture fine-grained structural and semantic information, making it inherently compatible with heterogeneous graph characteristics such as multi-type interactions and complex topology.\n\nHere, we have evaluated the proposed method on datasets such as BAT and EAT, involving heterophilic structural characteristics. From a semantic perspective, heterophily graphs can be viewed as a special type of heterogeneous graphs, where the heterogeneity stems from label interactions rather than node or edge types. Compared with the representative HSAN method, our proposed RAGC achieves average improvements on the BAT and EAT datasets of $2.20$% in ACC, $2.04$% in NMI, $1.93$% in ARI, and $1.97$% in F1. The excellent performance achieved by our model on them provides supporting evidence for its potential to generalize to broader heterogeneous graph scenarios. We thank you again for this valuable suggestions. In the future, we would try to extend the proposed RAGC to general heterogeneous graph clustering.\n\n**Q2**: *The augmentation strategies for nodes and edges are from different feature sources, which might result in some problems of conflicting objectives. Please have a discussion on this issue.*\n\n**Reply**: Thank you for your valuable suggestions. In this study, indeed, the node and edge augmentation strategies are from different feature spaces, may result in potential objective conflict. To address this, we designed the Hybrid-Collaborative Augmentation (HCA) module based on multi-source information. Specifically, we construct a contrastive similarity matrix that fuses structural and attribute information, and introduce a learnable balance coefficient $\\alpha$ to dynamically weigh node-level and edge-level augmentations (see Eq. (10)). Moreover, while using structural information to filter out high-frequency noise in attributes, we further guide the edge-level representation updating through both attribute and structural cues. This allows node representations to reversely influence the edge augmentation process, enabling collaborative consistency between the them. Ablation studies (see Section 3.3) in the experimental section also demonstrate that removing the HCA module significantly degrades performance, which validates the effectiveness of the hybrid augmentation strategy with collaborative interaction. \n\nTherefore, the augmentation strategies from different sources are effectively aligned through the carefully designed collaborative interaction mechanism in RAGC, achieving joint augmentation of attribute and structure information. This design improves objective consistency and enhances the discriminability and robustness of RAGC in graph embedding representation learning."}, {"review_id": "WCjzObWGAI", "reviewer": "Reviewer_ryRm", "summary": "This study proposes a novel graph contrastive clustering framework, RAGC, consisting of two crucial modules, HCA and CSADA. This proposed RAGC method simultaneously utilizes node embedding representation and edge embedding representation for comprehensive contrastive learning, and distinguishes different types of positive and negative sample pairs through an adaptive weighting mechanism, thus enhancing the discriminability and robustness of representation learning and clustering results. The experimental settings are sufficiently reasonable and it shows better performance than existing mainstream methods.", "questions": "Q1: The numerical significance of Fig.3 is unclear when expressing the ablation results.\n\nQ2: The dynamic confidence selection mechanism gradually expands the set of high-confidence samples during the training process, is this strategy still applicable when the sample distribution is extremely unbalanced at the beginning of training or when there is a high proportion of noisy samples?\n\nQ3: In CSADA module, confidence parameter $\\tau$ is adaptive and varies with the  training epoch. What are the advantages of this setting?\n\nQ4: Why did CSADA use positive/negative and easy/hard divisions rather than finer grained or other division criteria when it differentiated the sample into four categories for weighting?", "limitations": "Yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths\n\nS1: The study introduces edge-level augmentation to fully utilize the structural information with a complementary and collaborative way, which aims at improving the completeness of representation learning and contrastive learning;\n\nS2: The sample weighting mechanism takes into account the differences between positive and negative samples as well as easy and difficult samples, which significantly improves the contrastiveness of self-supervised representation learning;  \n\nS3: The CSADA module has strong generalizability and can be potentially integrated into other contrastive learning frameworks with migration and extension value.\n\nWeaknesses\n\nW1: The scalability of this method for large-scale data needs further verification.", "was_revised": true, "final_justification": "All my concerns are addressed. Thus, I keep my positive score.", "rebuttal": "**Reply**: Thank you for your thoughtful and detailed review. We appreciate your recognition of our contributions and the advantages of the proposed method. We will carefully address your issue below.\n\n**W1**: *The scalability of this method for large-scale data needs further verification.*\n\n**Reply**: Thank you for pointing out this important issue. We acknowledge that the current experiment only be conducted on medium-scale datasets, primarily due to limitations in our experimental hardware resources. However, the scalability has been fully considered in the model design. Specifically, we employ the low-frequency filtering combined with lightweight MLP-based augmentation, which avoids complex and computationally intensive operations, thereby effectively reducing computational complexity. Additionally, the K-means based pseudo-label generation process in our method is highly parallelizable, facilitating adaptation to large-scale data processing. Once again, we sincerely appreciate your review and valuable feedback.\n\n**Q1**: *The numerical significance of Fig.3 is unclear when expressing the ablation results.*\n\n**Reply**: Thank you for pointing out the issue regarding the clarity of the numerical physical meaning in Fig. 3. In this figure, we adopted a radar chart format to intuitively illustrate the relative performance distribution of RAGC and its three ablatiton variants (i.e., **(w/o) D**, **(w/o) H**, **(w/o) C**) across multiple clustering metrics (ACC, NMI, ARI, F1) on six datasets, where D: Dynamic High Confidence Samples Selection, H: HCA module, C: CSADA module. The radar chart reflects the proportion of the optimal result accounted for by each ablation variant and complete RAGC across different metrics, thereby highlighting the individual contributions and synergistic effects of each component. It is worth noting that since radar charts are primarily used for trend analysis and comparative visualization, the exact numerical values are not explicitly annotated in the figure. We will consider adding annotations or supplementary explanations in the ablation study section to improve the readability and rigor of the figure. Thank you again for your helpful suggestion.\n\n**Q2**: *The dynamic confidence selection mechanism gradually expands the set of high-confidence samples during the training process, is this strategy still applicable when the sample distribution is extremely unbalanced at the beginning of training or when there is a high proportion of noisy samples?*\n\n**Reply**: Thank you for your attention to the novel dynamic sample selection mechanism. In RAGC, we adopt a progressive strategy that starts with a small set of high-confidence samples. Specifically, in the early training stage, a relatively large $\\tau$ value is used to select only a few top-confidence samples for hard-aware contrastive learning, ensuring the stability and reliability of early training. As the representation learning capability improves, the threshold gradually decreases, allowing more confident samples to be involved and thereby enhancing generalization. This design helps to alleviate the adverse effects of sample distribution imbalance or noisy labels at the initial stage. Additionally, in our contrastive framework, low-confidence samples are assigned a fixed weight of $W = 1$, which further reduces the risk of noise-induced misleading updating. As shown in Section 3.4, the proposed RAGC demonstrates strong robustness in the presence of noise. This robustness is largely attributed to the joint effect of the dynamic sample selection strategy and the contrastive sample weighting mechanism, together mitigating issues caused by distribution imbalance and label noise in the early training phase.\n\nNevertheless, we acknowledge that this strategy may still face challenges when confronted with extremely poor data quality, and thus we would consider this important direction for future research.\n\n**Q3**: *In CSADA module, confidence parameter $\\tau$ is adaptive and varies with the training epoch. What are the advantages of this setting?*\n\n**Reply**: Thank you for your questions. In the CSADA module, the design of gradually decreasing the confidence threshold $\\tau$ over training epochs offers several advantages. First, by setting a larger $\\tau$ value in the early stages of training, only a small number of high-confidence samples are selected, which helps mitigate the negative impact of inaccurate pseudo-labels and improves the stability and robustness of early training. Second, as the representation ability of model improves, $\\tau$ is gradually reduced, leading to an expansion of the high-confidence sample set. This forms a progressive learning process that moves from easy to hard and from few to many, thereby enhancing the ability to distinguish complex samples. At the same time, incorporating more samples into training allows the model to capture richer semantic and structural information, further improving effectiveness of contrastive learning. Finally, this mechanism works synergistically with the weighting adjustment function, enabling adaptive training dynamics at different stages and enhancing both the representation learning capacity and generalization performance.\n\nTherefore, the dynamic sample selection mechanism not only provides a stable and progressive learning path, but also plays a key role in improving model performance and adapting to complex data structures.\n\n**Q4**: *Why did CSADA use positive/negative and easy/hard divisions rather than finer grained or other division criteria when it differentiated the sample into four categories for weighting?*\n\n**Reply**: Thank you for your question. In the CSADA module, we adopt a four-category weighting strategy based on the positive/negative and easy/hard distinction, which is motivated by both the core objectives of contrastive learning and practical feasibility. On the one hand, the positive or negative relationship between samples determines whether they should be pulled together or pushed apart in the representation space, which is fundamental to contrastive learning. On the other hand, the easy or hard level reflects the difficulty of representation learning from a particular sample pair. Combining these two aspects allows us to identify four representative categories of contrastive pairs that effectively cover the most influential training cases for the model. Compared to existing hard-sample aware schemes, our approach maintains strong expressiveness while achieving better stability and generalization, and reduces the risk of overfitting or being misled by noisy pseudo-labels. Experimental results across multiple datasets also confirm the effectiveness of this contrastive design and its scalability on other graph contrastive clustering methods. Therefore, we believe that this positive/negative and easy/hard four-type categorization sufficiently captures the key contrastive patterns and serves as an efficient and reliable choice for graph contrastive learning."}, {"review_id": "5qFqPBGaAY", "reviewer": "Reviewer_uEFh", "summary": "The paper develops a RAGC framework to systematically improve representation discrimination in the contrastive graph clustering task by combining Hybrid-Collaborative Augmentation and Contrastive Sample Adaptive-Differential Awareness. The HCA module augments both node-level and edge-level features to achieve multi-granularity information fusion. The CSADA module dynamically adjusts the importance of different contrastive samples according to confidence level of pseudo-label and semantic similarity, thereby realizing differential learning between positive, negative, easy, and hard samples. Experiments verify the superior performance of RAGC on multiple datasets.", "questions": "1. In the HCA module of the model, why was the parameter-unshared MLP chosen to implement the data augmentation? If it is an empirical choice, it needs to be explained. Are there other, more efficient structures for enhancing the representation of graph data?\n2. The experiments were limited to homogeneous graph data (e.g., citation networks), and the generalization ability of the method on heterogeneous should be verified.\n3. In the HCA module, how do the node-level embedding augmenter and edge-level embedding augmenter collaborate?\n4. The CSADA module relies on pseudo-labels for sample weighting, but do different pseudo-label initialization strategies have an impact on the final clustering performance? The authors are requested to further explain the specific methodology and selection basis of the current pseudo-label initialization, and to indicate whether the process has better stability under various initialization.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "The study proposes targeted improvements in both node-edge dual augmentation and contrastive sample differential perception, with good innovations and technical contributions. The experimental part is fully designed and validated, and the corresponding results are convincing over several representative methods. In addition, this paper also verifies the generalization of key module in other graph contrastive clustering methods, which is very interesting and valuable. More details of existing weakness can be found in the Questions section.", "was_revised": true, "final_justification": "Most of my concerns have been addressed, and I have updated my scoring accordingly. And,  I recommend acceptance of this paper.", "rebuttal": "**Reply**: Thank you for your thoughtful and detailed review. We appreciate your recognition of our contributions and the advantages of the proposed method. We will carefully address your concerned issues below.\n\n**Q1**: *In the HCA module of the model, why was the parameter-unshared MLP chosen to implement the data augmentation? If it is an empirical choice, it needs to be explained. Are there other, more efficient structures for enhancing the representation of graph data?*\n\n**Reply**: Thank you for your question. The MLP module performs simple nonlinear transformations on the low-pass filtering representations to generate diversified augmented views. Specifically, we design un-shared MLPs as augmenters to learn different contrastive representations, thereby achieving the effects of traditional data augmentation methods (e.g., attribute perturbation or structural modification) in a more flexible manner. This implicit augmentation approach avoids the complexity of directly modifying node attributes or graph structures, while preserving semantic consistency. Moreover, as a pure feature transformer, the MLP operates independently of the graph structure, which decouples it from the graph convolution operator and avoids the intricate entanglement often seen in conventional graph augmentation methods. This enhances the overall flexibility and generalizability of the framework. While other methods, such as Graph Attention Networks (GAT), could in theory also capture structural information, they typically require additional neighborhood aggregation or parameterized augmentation strategies, introducing more computational complexity. In contrast, the generality of MLP makes it suitable for various types of graph data, such as citation networks and traffic networks.\n\nIn summary, the use of MLP achieves a favorable balance among efficiency, generalization, and performance, making it a theoretically sound and practically effective design choice.\n\n**Q2**: *The experiments were limited to homogeneous graph data (e.g., citation networks), and the generalization ability of the method on heterogeneous should be verified.*\n\n**Reply**: Thank you for your valuable suggestion. Although our method does not explicit design for heterogeneous node or edge issue, the overall design of our framework is inherently adaptable to heterogeneous graphs. In particular, the HCA module performs node-level and edge-level augmentation through a unified similarity fusion mechanism that does not depend on node or edge homogeneity, allowing it to naturally accommodate varying semantic and structural relationships across different types. Similarly, the CSADA module conducts confidence-aware contrastive weighting without assuming type-specific information, making the entire contrastive learning process type-agnostic and structurally flexible. These architectural properties provide a solid theoretical foundation for the potential generalization to heterogeneous graphs.\n\nIn experiment, we have evaluated the proposed method on datasets such as BAT and EAT, involving non-homophilous structural characteristics. From a semantic perspective, heterophily graphs can be viewed as a special type of heterogeneous graphs, where the heterogeneity stems from label interactions rather than node or edge types. Compared with the representative HSAN method, our proposed RAGC achieves average improvements on the BAT and EAT datasets of $2.20$% in ACC, $2.04$% in NMI, $1.93$% in ARI, and $1.97$% in F1. The excellent performance achieved by our model on them provides supporting evidence for its potential to generalize to broader heterogeneous graph scenarios. We thank you again for raising this valuable point. In the future, we will attempt to extend the proposed RAGC to general heterogeneous graph clustering.\n\n\n**Q3**: *In the HCA module, how do the node-level embedding augmenter and edge-level embedding augmenter collaborate?*\n\n**Reply**: Thank you for your question. In the HCA module, the node-level and edge-level augmenters collaborate through a joint similarity fusion mechanism. Specifically, we first perform separate augmentations on node attributes and graph structure to obtain node-level embeddings ($\\mathbf Z^a$, $\\mathbf Z^b$) and edge-level embeddings ($\\mathbf E^a$, $\\mathbf E^b$). These embeddings are then integrated within a unified contrastive framework by constructing a fused similarity matrix $\\mathbf S^{l,m} = \\alpha \\mathbf Z^l \\left(\\mathbf Z^m\\right)^T+(1-\\alpha)\\mathbf E^l \\left(\\mathbf E^m\\right)^T$, which allows both node-level and edge-level information to contribute to a shared contrastive objective. Furthermore, we dynamically update the edge structure representations using attribute information (as described in Eqs. (11)–(12)), enabling the edge-level augmenter to receive feedback from node-level embeddings during each training iteration. This facilitates mutual interaction and structural refinement. In this framework, the node-level augmenter provides semantic guidance, while the edge-level augmenter imposes structural constraints. They work collaboratively and promote each other in the representation space, effectively enhancing the discriminative capability.\n\n**Q4**: *The CSADA module relies on pseudo-labels for sample weighting, but do different pseudo-label initialization strategies have an impact on the final clustering performance? The authors are requested to further explain the specific methodology and selection basis of the current pseudo-label initialization, and to indicate whether the process has better stability under various initialization.*\n\n**Reply**: Thank you for your valuable suggestion. In this study, we chose K-means clustering as the initialization method for pseudo-labels mainly because it is widely used in unsupervised scenarios, easy to implement, and computationally efficient. Compared to other clustering algorithms such as spectral clustering or DBSCAN, K-means is more lightweight and easier to integrate with the graph neural network training process. Additionally, in the CSADA module, we adopt a dynamic confidence mechanism, where only a small number of high-confidence samples are selected for weighted contrastive learning during the early training phase. This helps to mitigate the impact of noisy pseudo-labels at initialization. To further validate the stability of this approach, we performed 10 independent runs on all datasets and reported the mean and standard deviation of clustering metrics (see Table 1). The results demonstrate that our model maintains stable performance under different K-means initializations, with only minor fluctuations.\n\nIn summary, we believe that K-means offers advantages in terms of efficiency, stability, and ease of use, making it a suitable pseudo-labeling strategy for our framework."}, {"review_id": "Pg0SW2Yq12", "reviewer": "Reviewer_PbCi", "summary": "In the paper, the authors propose an unsupervised graph clustering method RAGC to improve the clustering performance, through combining two modules Hybrid-Collaborative Augmentation (HCA) and Contrastive Sample Adaptive-Differential Awareness (CSADA). The HCA module combines the dual collaborative augmentation of node-level and edge-level, and the CSADA module utilizes some dynamic prior information to differentiate the importance of contrastive sample pairs with an elaborate weight function from four key perspectives, eventually improving the discriminability of self-supervised graph embedding representation learning. The experimental results show significantly performance than existing methods on benchmark datasets. The theoretical analysis is sound and experimental verification is convining.", "questions": "Q1: The CSADA module is dependent on the accuracy of pseudo-labeling in the contrastive sample weighting process, but the paper lacks a systematic analysis of the impact of pseudo-labeling errors on model performance. It is recommended to supplement the relevant analysis so as to enhance the completeness and persuasiveness of the paper.\n\nQ2. The dynamic pseudo-label selection mechanism is one of the innovations of this study, but how exactly does it dynamically change and converge during the training process?\n\nQ3. Sensitivity experiments on the weight adjustment parameters β and γ show that they are robust over a range, but how are the parameter ranges chosen? Please explain the selection principle, or provide a theoretical or empirical evidence.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The strengths:\nS1. To my knowledge, this is the first work to systematically categorize and distinguish the contrastive samples from four key criteria.\n\nS2. The work enhances the granularity and effectiveness of contrastive representation learning, and the  design is reasonable and interesting for general contrastive learning.\n\nS3. The experiments are convincing. The overall quality of the paper is high and has potential for acceptance.\n\nThe weakness: \nW1. This paper shows a relatively good readability, but there are still some writing and layout issues. \n\nW2. The paper does not provide a detailed analysis of the impact of the quality of pseudo-label information on the performance of RAGC.", "was_revised": true, "final_justification": "Following the rebuttal period and the response from the authors, I believe my rating remains appropriate and will keep it as is.", "rebuttal": "**Reply**: Thank you for your thoughtful and detailed review. We appreciate your recognition of our contributions and the advantages of the proposed method. We will carefully address your issue below.\n\n**Q1**: *The CSADA module is dependent on the accuracy of pseudo-labeling in the contrastive sample weighting process, but the paper lacks a systematic analysis of the impact of pseudo-labeling errors on model performance. It is recommended to supplement the relevant analysis so as to enhance the completeness and persuasiveness of the paper.*\n\n**Reply**: Thank you for your valuable suggestion. To mitigate the potential impact of pseudo-labeling errors on contrastive sample weighting, we designed several specific mechanisms into the RAGC model. On one hand, the CSADA module adopts a dynamic confidence-based weighting contrastive sample selection strategy, where only a small number of high-confidence samples are used for weighting during the early stages of training, thereby reducing the influence of inaccurate pseudo-labels on contrastive learning. On the other hand, as training progresses, pseudo labels are dynamically updated and gradually corrected, which improves the overall robustness of the model. Additionally, to further assess the impact of pseudo-label errors, we conducted 10 repeated experiments and reported the mean and standard deviation of clustering metrics in the comparison study (see Table 1). The results show minimal performance fluctuations, demonstrating the stability of our mechanism under different pseudo-label initialization conditions. In addition, the noise disturbance of the graph will reduce the quality of pseudo labels. We tested the robustness of proposed RAGC method to noise under different noise conditions (Gaussian noise $\\mathcal N(0, \\sigma_N)$ with $ \\sigma_N \\in $ {0.1, 0.2, 0.3} ), as shown in Section 3.4 and Table 2. The following key observations could be concluded: 1) The proposed RAGC consistently outperforms all the other comparisons across all metrics, even under varying levels of noise disturbances. 2) Although the performance of all methods declines as the noise ratio increases, RAGC exhibits the smallest average degradation ratio across all metrics and datasets, demonstrating its superior robustness to noise. For example, the performance of RAGC decreases by 11.36\\%, while DCRN experiences a 19.03\\% drop. This indirectly verifies the robustness of our method to pseudo labels.\n\nWe sincerely appreciate your suggestion and will consider adding further analysis and discussion to enhance the completeness and persuasiveness of the paper.\n\n**Q2**: *The dynamic pseudo-label selection mechanism is one of the innovations of this study, but how exactly does it dynamically change and converge during the training process?*\n\n**Reply**: Thank you for your question. Our dynamic pseudo-label selection mechanism is implemented through a gradually decreasing confidence threshold $\\tau$ combined with the iterative update of pseudo-labels. In the early stages of training, a high value of $\\tau$ is used to select only a small set of high-confidence sample pairs for weighted contrastive learning, thereby reducing the impact of pseudo-label noise. As training progresses, $\\tau$ is progressively reduced following the update rule $\\tau = \\max(\\tau \\times 0.1, \\tau \\times 0.95)$, and eventually stabilizes at $\\tau \\times 0.1$. This allows the coverage of high-confidence samples to gradually expand over training. Meanwhile, pseudo-labels are dynamically updated in each training epoch using K-means clustering, ensuring consistency with the current node representations and improving both representation quality and the reliability of contrastive learning.\n\n**Q3**: *Sensitivity experiments on the weight adjustment parameters $\\beta$ and $\\gamma$ show that they are robust over a range, but how are the parameter ranges chosen? Please explain the selection principle, or provide a theoretical or empirical evidence.*\n\n**Reply**: Thank you for your question. The parameter ranges $\\beta \\in (0,1)$ and $\\gamma \\in [1,5]$ are carefully chosen to enable more discriminative weighting of the four types of contrastive sample pairs in the CSADA module. As illustrated in Fig. 2 and Eq. (18), the weighting functions are designed to dynamically adjust sample weights based on their similarity scores. Specifically, $\\beta$ controls the weight differentiation between hard and easy positive pairs, i.e., hard positive pairs with lower similarity receive increased weights, while easy positive pairs with higher similarity still maintain relatively high weights. $\\gamma$, on the other hand, governs the negative sample weighting, i.e., hard negative pairs with high similarity are down-weighted to ensure they are effectively pushed apart in the embedding space. As shown in Fig. 2, the current parameter ranges effectively achieve this intended behavior. Values outside these ranges tend to result in indistinguishable weighting across samples, thereby undermining the purpose of sample differentiation. Additionally, sensitivity analysis experiments conducted across various values confirm that the selected intervals for $\\beta$ and $\\gamma$ offer both robustness and adaptability, ensuring stable performance of the model."}]

Author rebuttal:

Meta-review: This paper proposes a novel robust attributed graph clustering (RAGC), which designs hybrid-collaborative augmentation from both node and edge levels and achieves the interactions between them. More importantly, the sample adaptive-differential awareness mechanism is innvatively proposed to differentially treat contrastive sample pairs  by an innovative weight modulation function, which is scalable in general contrastive learning.  

The response from authors well addresses the concerns from reviewers, and after the rebuttal, four positive scores (three accept and one borderline accept) are received. All reviewers recognized its innovative idea, interesting theoretical method, and persuasive experimental results and thus reached an agreement to accept it.  Hence, I recommend it for acceptance.
Decision: Accept (poster)