Federated Graph-Level Clustering Network with Dual Knowledge Separation
Authors: Xiaobao Wang
Renda Han
Ronghao Fu
Di Jin
Venue: ICLR 2026 Poster (2026)
Keywords: Clustering
Deep Graph Learning
Unsupervised Learning
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Abstract: Federated Graph-level Clustering (FGC) offers a promising framework for analyzing distributed graph data while ensuring privacy protection.
However, existing methods fail to simultaneously consider knowledge heterogeneity across intra- and inter-client, and still attempt to share as much knowledge as possible, resulting in consensus failure in the server.
To solve these issues, we propose a novel **F**ederated **G**raph-level **C**lustering **N**etwork with **D**ual **K**nowledge **S**eparation (FGCN-DKS). 
The core idea is to decouple differentiated subgraph patterns and optimize them separately on the client, and then leverage cluster-oriented patterns to guide personalized knowledge aggregation on the server.
Specifically, on the client, we separate personalized subgraphs and cluster-oriented subgraphs for each graph. Then the former are retained locally for further refinement of the clustering process, while pattern digests are extracted from the latter for uploading to the server.
On the server, we calculate the relation of inter-cluster patterns to adaptively aggregate cluster-oriented prototypes and parameters. Finally, the server generates personalized guidance signals for each cluster of clients, which are then fed back to local clients to enhance overall clustering performance.
Extensive experiments on multiple graph benchmark datasets have proven the superiority of the proposed FGCN-DKS over the SOTA methods.

Published as a conference paper at ICLR 2026
FEDERATED GRAPH-LEVEL CLUSTERING NETWORK WITH DUAL KNOWLEDGE SEPARATION
Xiaobao Wang', Renda Han', Ronghao Fu?, Di Jin
1 School of Artificial Intelligence. Tianjin University, Tianjin, 300000, China
2 College of Computer Science and Technology, Jilin University, Changehun, 130000, China
3 School of Computer Science and Technology, Tianjin University, Tianjin, 300000, China
{ [wangxiaobao, jindi J ju. a.j.edd... edu. cn, rd. rd.hhcomppter.oog furhê j jlu. edd.....oom cn
ABSTRACT
Federated Graph-level Clustering (FGC) offers promising framework for ana- lyzing distributed graph data while ensuring privacy protection. However, exist- ing methods fail simultaneously consider knowledge heterogeneity across intra- and inter-client, and still attempt to share as much knowledge as possible, result- ing consensus failure in the server. To solve these issues, we propose a novel Federated Graph-level Clustering Network with Dual Knowledge Separation (FGCN-DKS). The core idea is to decouple differentiated subgraph patterns and optimize them separately the client, and then leverage cluster-oriented patterns to guide personalized knowledge aggregation on the server. Specifically, on the client, separate personalized subgraphs and cluster-oriented subgraphs for each graph. Then the former are retained locally for further refinement of the cluster- ing process, while pattern digests extracted from the latter for uploading to the server. On the server, we calculate the relation of inter-cluster patterns to adap- tively aggregate cluster-oriented prototypes and parameters. Finally, the server generates personalized guidance signals for each cluster of clients, which are then fed back to local clients enhance overall clustering performance. Extensive ex- periments on multiple graph benchmark datasets have proven the superiority of the proposed FGCN-DKS over the SOTA methods.
INTRODUCTION
Federated Graph Learning (FGL) (Liang et al. 2023 2024b Liu et al. 2024a b Li & Guo 2025
has recently emerged powerful paradigm for privacy-preservie preserving machine learning (Liao et al. 2026 2025b a), enabling multiple clients to collaboratively train models without exposing their raw graph data. With the explosive growth of graph-structured data in domains such personalized recommendation (Wu et al. 2021), decentralized fraud detection (Chen et al.) 2024), and scientific discovery (Zhang et al. 2023 Liang et al. 2024c), research on FGL has gained increasing attention.
Among the various tasks in this domain, cluster- ing (Zhang et al. 2024 Bo et al. 2020) plays a fundamental role by discovering latent patterns federated settings,
Neve-Level
Graph-Leve
Datasets
hro
NS
hro
hry
Cite
23.7
SM
45,2
54.5
without label supervision. clustering can be performed at different granu- larities, which leads two distinct paradigms: node-level and graph-level clustering. In feder- ated node-level clustering (Liang et al. [2244a] Liu ct al. 2023 2025b), clients hold subgraphs drawn from the same global graph, where distributions relatively homogeneous, allowing the server to easily achieve consensus. In contrast, federated graph-level clustering (FGC) (Liang al. 2024c)
PubMed
18.6
SM-BIO
69.1
58.3
Photo
4.4
SN
43.6
39.6
Table 1: Mubti-subgraph/grrahh heterogene- ity in node- and graph-level tasks, calculated by graph kernel. Here, hro, hr, denote inter- and intra-client heterogeneity, respectively. NS refers to non-lID settings (i.e., the strategy of assigning different private datasets to clients).
"Corresponding author

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Published as a conference paper at ICLR 2026
requires clients to cluster entirely different non-IID graphs. This introduces severe intra-client het- erogeneity (inconsistent graph patterns within each client) and inter-client heterogeneity (domain shifts across clients), making server consensus much more challenging (see Table [ Recent meth- ods such as FedGCN (Liu et al. 2025a) and FedPKA (Wu et al. (025) follow the paradigm of maximizing global knowledge sharing that works for graph-level tasks, but they overlook the unique challenges of multi-graph heterogeneity, As a result, they often suffer from consensus failure when applied to graph-level clustering.
Inspired by FedPer (Arivazhagan et al. 2019). which separates model parameters across layers to enable personalized training in FL, we extend this idea to graph structure by exploring how graphs can be decomposed into different components for FGC. Guided by Invariant Graph Learning (IGI.) (Sui al. 2024, Li et al. 2022b), we further attempt to separate each graph into common and personalized subgraphs: common parts are shared with the server to support global consensus, while personalized parts are kept locally to protect unique knowledge, as shown in Fig- [ (a). This design directly matches our goal: common subgraphs contain stable cross-domain patterns (see Fig. (b)), whereas variant subgraphs represent client-oriented information. However, deploying IGL in federated settings is highly challenging. On each client, multiple graphs with diverse distributions coexist, so the extraction of common components must be carefully controlled in granularity to benefit both local clustering and global consensus. On the server, client heterogeneity prevents simple weight aggregation. 'Tee global model must move beyond naive consensus and accurately identify representative patterns across participants, guiding a more optimal aggregation process.
Based on the above challenges, we propose Federated Graph-Level Clustering Network with Dual Knowledge Separation (FGCN-DKS). The key idea is decouple graph knowledge within and across clients, so that local clustering benefits from personalization while the server achieves consensus. On each client, an invariant subgraph separator divides graphs into cluster-oriented common subgraphs and client-specific personalized subgraphs. Only common knowledge digests are uploaded to the server, while personalized subgraphs remain local. On the server, a Common Knowledge Sharing Strategy (CKSS) aggregates invariant pattern digests by computing cluster-level affinities and capturing semantically con- sistent components. The resulting cluster-level signals are sent back to clients, enabling finer-grained con- sensus. Finally, clustering is conducted two stages: K K-means is initialized with common representations that are extracted from common parts and refined with personalized representations for local adaptation. In
Krowwedge
Knowledge
Oure
Exsting Aporoacns
Commo Babyoot
CB
Dar Ooen
AeCtent Penosie bagett
Glent
(b)
Clustrt Cuarer
(a) Compared with the existing FGL methods, our approach only shares knowledge that is beneficial to global con- sensus. (b) Graphs within the same cluster share certain common substructures, and there also inter-cluster sharing across different clients.
Figure 1:
summary, our contributions are threefold:
New Perspective. We provide the first systematic study of federated graph-level cluster- ing (FGC) under both intra-client and inter-client heterogeneity, revealing why existing paradigms of maximizing global knowledge sharing fail in this more challenging setting.
New Method. We propose FGCN-DKS, a dual knowledge separation framework that sep- arates invariant and variant subgraphs on clients and performs cluster-level consensus ag- gregation on the server, directly addressing the identified challenges.
Strong Results Extensive experiments demonstrate that FGCN-DKS consistently outper- forms state-of-the-art baselines in graph clustering performance.
RELATED WORK
2.1 INVARIANT GRAPH LEARNING
Learning graph representations that remain stable under distributional shifts has become a central theme in -ut-of-distribution (OOD) generalization. Early work, such GIL. (Li et al. 2022a
2

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Published as a conference paper at ICLR 2026
introduces subgraph generator and invariant learning module to extract label substructures, infer- ring latent environments via variant subgraphs and enforcing consistency across them. Building on this, CIGA (Chen et al. 2022) employs an cermmation-thhooree objective to identify subgraphs whose embeddings maximize intra-class invariance under diverse graph interventions. At the clus- ter level, CIT (Xia et al.) 2023) ensures that cluster embeddings remain consistent despite structural perturbations, promoting robust GNN representations. Beyond task-specific frameworks, several peneral-purpose techniques further the cause of invariance in graphs. MARIO (Zhu al.) (024) integrates an Information bottleneck with adversarial augmentations in graph contrastive learning to distill invariant features. CGCL (Chen et al.) 2025) enforces cross-view reconstruction consis- tency between augmented graph views, enhancing OOD robustness for link prediction. IGM (Jia) jet al., 2024) synthesizes new environments via env-Mixup and inv-Mixup on variant and invariant subgraphs, obviating the need for manual environment labels. More recent advances continue to push the task. InfoIGL (Mao et al. 2024) leverages a multi-level contrastive learning grounded in the Information Bottleneck principle to isolate invariant graph features. MPHIL (Shen et al. 2025) introduces hyperspherical invariant representations with multi-prototype matching and sepa- ration losses, directly tackling semantic entanglement across unknown environments. Despite these advances, existing methods assume centralized access to fully labeled data, which is incompatible with federated settings where clients neither share raw data nor possess label supervision.
2.2 FEDERATED GRAPH LEARNING
FGL has emerged to enable collaborative model training across multiple clients while preserving data privacy. A straightforward extension of FedAvg (Li et al. 2019) to GNN demonstrates that naively averaging GNN parameters can yield reasonable performance but suffers under the non-IID issue. Subsequently, FedPer (Arivazhagan et al., 2019) adapts personalization layers in GNNs, en- abling clients to fine-tune private parameters while sharing common backbone. FedProx (Li et al.) 2020) generalizes and re-parametrizes FedAvg, providing convergence guarantees when learning from non-lID datasets. To address heterogeneity, FedGraphNN (He et al. 202Ii introduces client- specific adaptation layers and a global graph aggregator, improving convergence in graph classi- fication and node prediction tasks. Building on this, FedSage (Zhang al., 2021) and FedGAT (Ambekar et al.) 2024) incorporate sampling-basee based neighbor selection and attention mechanisms, respectively, to reduce communication overhead and align local and global feature spaces. In par- allel, FedStar (Tan et al. (202)) addresses client label heterogeneity by aligning local embeddings via contrastive regularization. More recent research, FedGCN (Liu al., (025a), as a first FGC framework, is proposed, which optimizes prototypes between multiple clients and guides the lo- cal model learn. Subsequently, FedPKA (Wu al., 2025) mitigates non-IID heterogeneity and knowledge drift by confidence seniddence-guided knowledge aggregation and adaptive prototype adjustment for personalized FL.. However, existing methods still cannot effectively solve the consensus failure is- sue caused by large knowledge differences. In contrast, FGCN-DKS effectively alleviates it through client internal knowledge decoupling and cluster-oriented personalized aggregation between clients.
METHODOLOGG
In this section, present the proposed Federated Graph Learning framework called Federated Graph Clustering Network with Dual Separation (FGCN-DKS) in detail, which collaboratively solves the issue of consensus failure both within and across clients. Its core idea is to decouple knowledge that either promotes or hinders consensus, and then share the cluster-oriented, high- affinity components to regulate the guidance signals for each cluster accurately. As illustrated in Fig. 2 FGCN-DKS consists of three key modules: local pattern separation mechanism, common knowledge sharing strategy, and two-stage K-means clustering. The overall process detailed in Algorithm I.
3.1 NOTATIONS
We consider a non-lID federated setting with No clients, where each client é E (I....,NN) N.) holds a private graph dataset containing N₂ clusters and NG graphs, denoted as g = |, All datasets in the federated setting contain N₂ clusters. For each client, the node feature matrix represented as X E Nxx and the normalized adjacency matrix is represented A (0, NxN. where N is
==
3

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Common Subgraph Learning
2-Stage Clustering
Graph Karnel C₁
Server
...
Eq
CR2
+
Guide
2
Clustering Result
1/
Foodback
(A,X)
Cp... Cv2
M
VP
Personalized Subgraph Learning
Rensoomied Ponurbatiore
Inpul
NN
Ea 14
XX, A)
Buparater
(3) Eq (4)
(A.
Structuee Separator
Clustering Reeult
② Environment Construction
3 Subgraph Separation
K-means Clustering
Client Share Knowledge
Server Feedback Knowledge
Figure 2: The framework of FGCN-DKS. We decouple the graph into invariant subgraphs and vari- able subgraphs, guided by clusters and clients, respectively. The invariant component is optimized in cluster-oriented coordination with global sharing, while the variable component further refines the clustering objectives. The two promote each other to produce clearer cluster boundaries.
the number of nodes, and d is the dimension of node attributes. The total number of edges is denoted as [E). . detailed list of symbols provided in the Appendix A
3.2 LOCAL PATTERN SEPARATION MECHANISM
In this section, attempt to decouple two distinctive subgraph patterns (i.e., common subgraph and personalized subgraph). Then, the knowledge stemming from the former uploaded to the server for sharing, while the knowledge stemming from the latter is retained locally. To facilitate this, de- fine a series environments by cluster, where each cluster represents a distinct distribution of graph data. The goal is learn the invariant signal that characterizes the common pattern of each cluster while distinguishing the variant signal that reflects the personalized pattern of graphs. Specifically, for each original graph Gs, generate E No perturbed views of its graphs (g/-)) Je=1 through randomized structure and attribute perturbations to simulate distributional shift for each client. Each (k) perturbed set & (9 J==1 defines environment with graph structure A (A)
Subgraph Separation To disentangle invariant and variant parts from each graph, we introduce node attribute separator t and graph structure separator V which generate the structure mask M and node attribute mask M for each graph G; as:
M = ({{A (T) X), M" V-AA X).
(1)
Applying these masks yiclds two complementary adjacency matrices and node feature matrices, as
A A, Ā=
M O A.
= OX, x= M
(3)
where @ denotes the Hadamard product. Thus, two subgraphs for any graph are obtained: Č [X, }} and n = (X, A}. We then employ dual projector Fo and Fo based on GNN to extract node invariant features H and variant node features H,
H = Fo(A,
(4)
where Ô and Ô are parameters of Fg and Fec. respectively. Finally, graph-level representations Z and Z are obtained via a READOUT function, as Z READ(H). To encourage the projector to derive decoupled representations that are both cluster-discriminatiee and environment-ineaaee we first enforce samples belonging the same cluster to share similar invariant subgraphs. Given the set Pt= = {i c(i) }} for cluster k we minimize the pairwise variance within each group:
Linv = Σ ci=1
No
2
(ef) z
12.
(5)
P
ijEPP
4

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Published as a conference paper at ICLR 2026
To prevent the collision of invariant subgraphs from different clusters, which would hinder the cap- ture of sufficiently distinguishable cluster features, we design Lav to increase the distance between invariant subgraphs from different clusters. Let = =i.5) d(i) # c(j) denote inter-cluster pairs, the Ldiv can be calculated as:
Laiv W Σ
Σ E (i.)EN 0(z (2)) (
(6)
where .) is inverse distance function. This term explicitly encourages inter-cluster separa- tion in the embedding space. To enforce invariance under environmental shifts, we minimize the variation of each graph's invariant representation across different environments, as:
Lenv EN, Σ -
E
(c) z,
2
Σ
E 0 (Z 2()),
where 2; = EE= (c) This objective encourages the encoder to focus on information that is sta- ble across distributional shifts, enhancing generalization to unseen environments, while effectively separating the invariant and variant components, ensuring the model retains the stable structure of the graph while capturing the patterns of variation. Finally, the overall optimization objective C in
each client is as:
(8) where Lise is the node representation reconstruction loss. /3 and y are two hyperparameters that control the ratio of the loss. By doing so, separate each graph into two distinct subgraaph patterns (i.e.. variant subgraph and variant subgraph). The theoretical and experimental effectiveness of the subgraph separation process are presented in Appendix and Appendix C respectively. Subse- quently, these common subgraph structures G represented as C are uploaded and serve as irrecov- erable digest information on the server to reflect inter-cluster affinity, facilitating the achievement of personalized consensus. Meanwhile, the invariant subgraphs are kept the client, offering crucial guidance for clustering while safeguarding privacy. This design strikes balance by enabling the global model parameters to maintain coherence in local knowledge while simultaneously adapting to local distributional variables.
L= Line + + Laiv + Lene + Lmse-
3.3 COMMON KNOWLEDGE AGGREGATION STRATEGY
In this section, we design Common Knowledge Sharing Strategy (CKSS), aiming to aggregate negotiated-friee friendly knowledge at a finer level of granularity, mitigating the impact of weak correla- tions on the target and enhancing the overall quantity of global consensus. First, the server receives the common prototype, parameters, and pattern digests from the clients. Next, we employ cluster- oriented common pattern digests derived from subgraphs capture the relation of stable structural semantics across clients. Finally, we leverage these relations to guide the aggregation of parameters and prototypes, achieving personalized knowledge consensus for different clients.
Cluster-oriented Information Aggregation Since the pattern digests reflect the underlying mani- fold structure of the cluster, we utilize the cluster-oriented pattern digest uploaded from each client to compute potential relationships using graph kernels, such as RW (Kang et al., 2012), WL (Liu) al. 2025b). SP (Borgwardt al., 2020). LT (Johansson et al., 2014). and others. These graph kernels effectively capture the similarity between cluster patterns, aligning local information within each cluster with the global structure, while ensuring privacy protection. Specifically, the similarity between cluster i and j is given by k(C, C2). The pairwise affinity matrix S is then computed as: S.j = A(C,, Cý), where k(.,-) is the graph kernel method and C, is the pattern digest from i-th cluster. In this way, we obtain the initialized affinity matrix of all clusters. However, relying solely on this initialization relationship to propagate knowledge is insufficient; we also need to incorporate additional information to ensure more robust aggregation process. Therefore, further intro- duce historical information to define a stability coefficient a to quantify the stability of relationships between clusters multiple iterations,
[ (
c A(C. -,,-"")
Cij
(C !1) ),))
where t is the communication epoch. A smaller an indicates a more stable relationship between clusters. Then the affinity matrix can be updated as
S(t) = (1 - A) S + X. En oi =(C(") c,
(10)
5

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Published as a conference paper at ICLR 2026
where À is hyperparameter controlling the relative weight between historical and current simi- larity information. This smoothing trick ensures that the similarity matrix evolves gradually over iterations, avoiding over-reliance single-round updates, and stabilizing the convergence process. Subsequently, the server performs personalized aggregation based on the cluster affinity to obtain a consensus guide signal. The consensus prototype PatofE for cluster and the consensus parameters @ glo/m for client m are calculated as:
Pyto!! - S1 P
glo/m = = Σ
No. -EnEs.,.e, Suy H..
(11)
JES... u=1
where Sn denotes cluster set from client m. is noteworthy that this alignment scheme differs from traditional methods, which require equal cluster quantities for proportional division. Instead, it leverages the inherent affinity of clusters through pattern relationships, guiding clients to delineate clearer clustering boundaries.
This strategy allows each client to benefit from similar peers in the same latent space, while avoid- ing negative transfer from unrelated distributions. Compared to the naive average strategy, method explores the relationship between patterns, allowing clients to be guided by more personal- ized knowledge with greater affinity, enabling them exert greater clustering advantages.
3.4 TWo STAGE K-MEANS CLUSTERING
When the personalized consensus knowledge is generated and fed back to the local models for optimization, we further exploit the disentangled representations learned through in- variant training by introducing a two-stage clustering. This process first captures cluster-oriented stable patterns and then refines client-oriented personalized information. Specifically, we first perform clustering over the invariant representations Z using a standard K-means algorithm. Since these representations are learned to be robust against environment-specifie perturbations, the initial clustering (()) provides reliable global se- mantic grouping. Then, we further refine the initial clusters by leveraging the variant representations Ż, which are specifically designed to encode environment-sensittve instance-level information. Within each initial cluster c( we perform secondary cluster- ing or similarity-based refinement to enhance the granularity and expressiveness of the final partitioning. This variant-aware refinement step enables the model to adaptively adjust for intra-cluster diversity, thereby improving clustering fidelity and interpretability. Overall, this commmon-to-personalieee clustering paradigm enables robust yet flexible representation-dree cross-enviromment consistency. while the variant component captures local distinctions, jointly facilitating high-quality cluster assignments even under distributional shifts.
Algorithm 1 Algorithm Pseudo of FGCN-LKS
Require:
Initial model parameters { { J. Node fea-
ture X, Adjacent matrix A; Client Number No-
Ensure: Clustering Result R. 1: on each client for c= - N2 do 3: Generate E perturbed graphs { to con- struct environments.
4:
Obtain invariant mask M and M by Eq. (2).
5:
Separate two type subgraphs A and Á by Eq. (3). Extract dual embeddings and Z by Eq. (4). Upload common prototype p. pattern digest C and invariant encoder parameters O to the server.
6:
end for
9: on the Server
10: Collect C. P and from each client to the server.
II: Calculate affinity matrix S by Eqs. (9) (10).
No 12: Personalized aggregate [ and ] gen- erate consensus knowledge by Eq. (11).
13: Feedback parameters and prototype to each client.
14: Execute 2-stage K K-means clustering.
15: return R.
grouping mechanism. The invariant component ensures
3.5 EFFICIENCY ANALYSIS
Compared with the standard parameter averaging in FedAvg, our framework introduces only a slight increase in global computation through guiinet consensus aggregation. FedAvg performs weighted average with complexity Odd). whereas our method additionally computes cluster-level affinities from pattern digests at O (2N2, N2xx), x),, where N₂ d and is any linear kernel in practice. The

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Published as a conference paper at ICLR 2026
subsequent personalized aggregation requires only d, complexity. Therefore, the increase in computational complexity is acceptable given the corresponding performance gains.
SM (7)
S2"(2)
SM-BIO (9)
Models
ACC
NMI
ARI
F1
ACC
NMI
ARI
F1
ACC
NMI
ARI
FedSage"
4
12.2+1.3
7.640.6
50.2+1.0
53.3+1.9
14.&+14
11.6+28
49.3+2.0
57.4+2.2
5.242.1
4.2=2.7
49.940.5
GCFL"
61.1418
8.742.4
9.422.4
49.642.3
52.142.3
12.5+2.3
13.2+2.3
52.341.6
60.1218
4.742.4
3.242.3
47.3&1.5
FedStar"
58.92244
12.0x1.2
0.110.8
49.742.8
51.712.7
13.7+2.8
12.4a1.9
50.742.3
59.5&1.6
5.3&1.5
3.8:20
51.712.2
LG-FGAD
8
18.8+1.9
3.411.1
62.9406
37.942.5
9.642.9
0.4+0.7
26.343.5
59.641.5
9.0+1.4
7.841.7
56.042.6
FGAD!
66.4224
20.242.6
4.343.2
63.8226
41.241.9
5.812.4
0.541.4
35.841.6
63.5&1.0
14.7a1.1
2.1:2.0
60.7+1.5
AGDifft
70.2:1.
19,3+2.9
13.633.9
67.3+28
42.3+1.9
7.5+1.2
8.6+20
37.2+1
61,342.5
1066119
3.400.2
57.2+1.6
GLOC:
86.242.8
8.643.4
5.444.2
53.744.1
43.512.0
9.712.4
3.5.1.5
40.712.1
57.5
6.71188
4,642.0
41.611.5
UDGCt
53.643..
9.742.5
8.633.4
53442.3
50.142.4
10.4+2.5
9.3+1.
48.4+2.3
55.6+18
89:14
6.840.4
50.4+1.0
DGLCI
60.8+15
14.3+1.2
10.7+1.4
52.2+144
55.5+1.5
11,6228
12.3+1.7
52.1+2.1
58.0+1.9
12.3+1.4
11,6+1.7
53.5+1.5
DCGLCt
63.1+1.7
17.5+1.
17.621.7
584:2.0
59.6+1.9
13.7+2.0
15.62188
56.822.3
60.4+1.6
13:2:1.1
15,8119
56.6+1.2
FedGON
8
23.1+1.6
113.
5
66.6+2.3
30,4+6.6
34.1+5.3
50.8+2.4
69.240.6
14.0=2.7
17,5+3,1
59.140.9
FedPKA
77,0+0.2
26.8+3.8
31,2+3.3
67.3+2.0
67.5+1.5
25.742.3
72.6=2.4
55.5+1.5
70.8+1.
15,4+2.7
19.6+33
60.6+2.1
OURS
79.2+0.5
28.3+1.1
34.6#0.9
72.3+1.1
70.240.4
34.2+1.7
36.8s1.2
60.4+1.9
73.8+2.2
17.7=2.4
21.342.0
61.3+1.7
SM-BIO-SY"
SN-SY' (2)
(3)
FodSage"
57.6+19
20.6+119 9
17.6+2.4
46.7=18
15.6+1.1
7.6+1.0
3.4+2,7
2.9+1 8
19,6+088
22.7=0.4
12,5+1
18:2+0.8
GCFL"
59.1+2.
14.4+2.2
13.7+2.8
52.3+19
19.340.6
4.5+2.3
1.2+1.1
8.7
27.9+1.6
27.5+2.2
13.1+19
27.4+1.3
FedSturs
57.9226
15.742.4
16.143.0
52.3+2.2
19.0a2.9
4.142.5
2.3
7.9222
22.7+1.
20.3+1.7
10.342.1
20.243.2
LG-RGAD
58.400
7.640.4
6.440.8
54.620.7
19.111.4
6.710.6
3.3:1.0
7/211
27.4
31.424.0
9.6:3.2
24.713.3
FGAD/
62.2+133
14.642.6
3.022.9
56.740.8
16.420.5
7.4
2.7.0.3
8.3
26.021.1
31.9212
7.3+1.1
25.241.1
AGDiIT
6144113
15.642.8
13.5a1.
50.43.00
15.812.0
4.312.0
3.42 0.2
9.622.8
23.6E1.4
27.5
8.720.9
22811.4
GLOC:
54.243.5
10.8+1.3
7.6+0.9
53.5=1.6
16.3+2.6
3,842.1
3.2+2.0
10.0+2.3
22.8+1.2
20.451.3
10.611
14.2+1.0
UDOC
55.642.
12.742.4
11.412.6
54.142.2
17.5+1.2
8.122.2
6.413.55
9.722.9
20.412.3
10.522.3
82:1.
14.711.8
DGLC1
57.8+200
14.4+1.
10.751.6
54.3+1.2
18.2+1.0
9,14144
7.S+1.1
8,6
29.5+2,4
21.6113
14,5+14
22.1+117
DCGLCC
60.1+14
15.6+1.7
13.1+1.2
59.7+1.
17.5+1.2
8.2+1.4
6.5+2.0
28.8+2.0
24.3+1.1
18.641.2
FedGON
68.64133
13.5+2.1
17.2+3.6
89,4:388
18.343.1
4.845.0
2.3+2.6
11,243
34,62288
34.8=2.4
19.342.
31.6+2.9
FedPKA
70.1+099
17,2+08
22.2+1.1
61.5+23
16.4+2.6
5.7+2.3
5.9+2.0
8.2+2.5
36.4+111
34,4+1.6
20.3+1.2
33,5+.3
OURS
73.6+1.4
22.7+1.2
23.5=1.9
64.4=1.7
23.5&1.5
13.4&1.0
8.7116
15.6+1.2
39.2+1.3
37.1+16
34.5+13
35.241.3
Table 2: Performance comparison across different FGL methods under six non-lII settings. de- notes supervised methods adapted for unsupervised learning. f denotes anomaly detection methods adapted for clustering. & denotes centralized deep graph-level clustering methods adapted for FGL.
4 EXPERIMENTS
In this section, we conduct extensive experiments evaluate the effectiveness and robustness of FGCN-DKS. We first introduce the experimental setup, including datasets, baseline methods, and implementation details. Then, we present the comparison results with the SOTA approaches, fol- lowed by ablation studies to examine the contribution of each component. Finally, we provide additional analysis further to validate the efficiency and generalizability of our methods.
4.1 EXPERIMENT SETTINGS
Benchmark Datasets We evaluate FGCN-DKS on 16 public datasets from the TUDataset collec- tion, spanning small molecules, bioinformatics, computer vision, and social networks (Liang et al. 2025 These datasets are organized into six non-IID settings: same-domain (SM, SN, CV) and cross-domain (SM-BIO, SM-BIO-SY, SN-SY), aligned following FedGCN (Liu et al. 2025a). De-
tailed dataset information and non-lID settings are provided Appendix D
Evaluation Metrics To comprehensively assess the performance of FGCN-DKS, we adopt four standard unsupervised clustering evaluation metrics: Accuracy (ACC) (Cai et al. 2022, 2024a). Normalized Mutual Information (NMD) (Liang et al. [2024b), Adjusted Rand Index (ARI) (Cai ct al. 2024b), and Fl Score (Tu et al. 2024). Details of these metrics are given in the Appendix
Baseline Methods To evaluate the effectiveness of FGCN-DKS, we consider two types of base- lines. The first includes the SOTA FGC method FedGCN, FedPKA, and several representative FGL methods adapted FGC, such as FedSage (Zhang et al. 2021). GCFL (Xie et al.) 2021), FedStar (Tan et al. (023), LG-FGAD (Cai et al., 2024c). FGAD (Cai et al. 2024d), and AGDiff (Cai et al. 2025). The second comprises advanced centralized Deep Graph-level Clustering (DGC) methods,
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including GLCC Juu et al. 2023), UDGC (Hu et al. 2023), DGLC (Cai et al. 2024a), and DCGLC Caa et al. 2024b). As these models rely on full data access, we adapt them to the FGL scenario by local traming and parameter aggregation, ensuring fair comparison. The description of the baselines
and the implementation details of FGCN-DKS are provided in Appendix
4.2 COMPARISON EXPERIMENTS
Comparison with FGL Methods We compare FGCN-DKS with advanced FGL methods to assess the performance. As illustrated Table @ the experimental results lead to the following observa- tions: Our approach delivers superior performance, primarily because invariant learning effectively disentangles the two structural patterns and aggregates them globally in cluster-oriented manner. This process refines cluster-relevant signals while preserving the consistency of invariant represen- tation learning. Compared with supervised FGC methods and unsupervised anomaly detection ap- proaches, our method achieves superior performance. Supervised methods rely on label guidance, and without labels, they lack a reliable signal to define meaningful cluster boundaries, leading to degraded clustering quality, while unsupervised anomaly detection focuses identifying rare, dis- tinctive graph patterns rather than general clustering. Moreover, compared with SOTA FGC meth- ods, our approach still demonstrates significant advantage, indicating that merely sharing abundant parameters and prototypes does not necessarily lead to more effective performance improvement.
Comparison with Centralized DGC Methods To further assess the performance of FGCN-DKS, we compare it with some representative centralized DGC methods. The experimental results are shown in Table 2 and the following conclusions are obtained: Compared with existing advanced methods, FGCN-DKS significantly improves performance, which is mainly attributed to the lack of ability of existing methods to perceive cluster-directed signal to adjust learning strategies. The inherent paradigm will cause consensus failure due to large differences in optimization directions between parameters. contrast, our method cleverly separates the two structural patterns and uses the cluster summary prototype to guide the server to learn with different strategies, overcoming the difference in semantic granularity and improving the overall performance of the model.
Comparison with Supervised FGL Methods To further demonstrate the superior performance of FGCN-DKS, we conduct comparison with several supervised methods by providing them with a par- tial set of labels. The experimental results shown in Fig. 3 which leads to the following conclusions: Compared with supervised methods, our method still shows strong performance despite the lack of labels. This is mainly attributed to the fact that our method can effectively separate cluster-driven knowledge and personalized features locally and use different strategies to aggregate cluster- friendll guidance sig- nals, improving the global performance.
FedSage
GCRL
FedStar
FeeGCN
75
50
25
0 SM
SN
SM-BIO
SM-BIO-SY
settings
Figure 3: Comparison experiment results on the supervised methods with few labels un- der five non-IID settings.
4.3 MODULE ABLATION STUDIES
To provide a clearer and more systematic understanding of how each component contributes to the overall performance of our framework, we organize the ablation settings into four representative variants. The first adopts only the minimal client and server settings, forming a basic baseline with- out any advanced mechanisms (Basic). The second removes the subgraph pattern separation module and the two-stage k-means refinement, while retaining the basic local learning strategy and keep- ing the server unchanged (-Local). The third replaces CKSS with the standard FedAvg aggregation while preserving the complete local inference and learning pipeline (-Server). The final activates the full proposed framework, where all modules and optimization mechanisms are jointly enabled (Ours). This structured decomposition allows fine-grained quantification of the importance of each design choice. The experiment results are shown in Table 3 which reveal several notable observations. First, performing knowledge separation solely on the client side already yields consis- tent improvements across all datasets. This indicates that mitigating local knowledge heterogeneity plays crucial role in obtaining clearer representations of both shared and personalized graph pat-
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Variants
SM
SM-BIO
SM-BIO-SY
SN
ACC
ARI
ACC
NMI
ARI
ACC
NM1
ACC
NMI
ARI
Basic
61.7+11
19.5=16
14.6=14
59,3+21
15,2+16
13.8-11
56.3+29
7.7=24
13.3+19
29.5-24
18.6+18
16,3+14
-Local
64.6114 22.4
16
61.6120
17.9
16.2-17
58,4129
8.9
15.7
32.4
20.4
19.7
-erver
68.2+1.
23.9=11
32.0=16
69.5
17.4
19.2-16
67.2=11
16.5212
19.6
37.7=10
33.5
22.7
Ours
79.2+0. 28.3=14 34.6=09
73.8+22
17.7+24 21.3-20
73.6+14
22.7+11
23.5+1.
39.2-13 37.1 24.5+13
Table 3: Module ablation study results on SM, SM-BIO, SM-BIO-SY, and SN non-III settings.
Ours
FedGCN
FedPKA
FedAvg
Clients
Time (s)
Cost (KB)
Time (s)
Cost (KB)
Time (s)
Cost (KB)
Time (s)
Cost (KB)
16.8
32.3
15.93
30.5
20.6
42.1
14.6
28.7
2 35.5
67.3
30.8
61.8
41.5
85.4
29.1
57.5
3
53.0
96.7
44.8
93.6
64.4
131.6
45.6
86.8
Table 4: Communication overhead comparison under the CV non-IID setting.
terns. Second, using CKSS alone brings only moderate gains. This limitation arises because CKSS fundamentally relies on reliable common subgraph patterns extracted through local separation; with- them, the server struggles to accurately estimate inter-client affinities, reducing the effectiveness of global consensus modeling. Finally, when both modules operate jointly, they reinforce each other, leading to substantial improvements clustering performance. These results collectively demon- strate that local knowledge disentanglement and global consensus optimization are complementary and jointly necessary for achieving high-quality federated graph-level clustering.
0.8
0.7 Malle
0.4
06 Vaae
0.5
0.3
0.2
02
02
022
0.1
0.0
PAce
Acc
c,, Ratio
1:10
MMl
ARi
Marrics
Ratio
1:10
NiA!
ARI
Metrics
10
2 Ratio
1:10
NM
ARi
Marrics
2 Ratio
1:10
ARI
NMM
Metrics
SM
SM-BIO
SN
CV
Figure 4: Hyper-parameters and 9 sensitivity analysis results under four non-lID settings with varying a38 ratios in the range of [1:10, 10:1], reporting ACC, NMI, ARI and Fl values.
4.4
SENSITIVITY ANALYSIS
To investigate the effects of each loss component in Eq. (8. we perform a sensitivity analysis by varying the weighting hyperparameters a and 3. The experimental results are shown in Fig. 4 and the following conclusions are obtained: FGCN-DKS achieved optimal balanced performance at 1:1 ratio. Increasing the ratio slightly improved NMI and ARI, but led to decline in ACC and F1. Conversely, decreasing the ratio exhibited the opposite trend.
4.5 COMMUNICATION OVERHEAD ANALYSIS
To further evaluate the practicality of the proposed framework in federated environments, we con- duct communication overhead analysis. As shown in Table 4 our method incurs slightly higher communication time and communication payload than FedGCN. This increase mainly results from transmitting shared structural patterns, and the overall additional cost remains negligible relative to the full model parameters. Compared with FedPKA, our framework shows clear advantages both communication time and communication payload. FedPKA requires frequent model gradient changes, which substantially increases its communication burden. In contrast, our design effectively reduces unnecessary transmissions while preserving model performance. We also compare ap- proach with the standard FedAvg baseline. Although additional structure patterns are transmitted, their size is small. The resulting communication overhead remains marginal and does not affect

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FedGCN
Local
FedPKA
Ours
40
ACC (%)
NMI (%)
(%)
Loss
80
30
30
60
20
20
40
70
10
10
60
0
0 0
5 10 Epoch
15
20
10 Epoch
15
20
5
10 Epoch
15
20
0
5
10
20
Epoch
Figure 5: Convergence curves ACC, NMI, ARI clustering metrics and loss values under SM non-IID setting, compared with FedPKA, FedGCN federated graph-level clustering methods.
the overall efficiency of the model. Meanwhile, this lightweight increase brings notable perfor- mance gains. Overall, the communication analysis indicates that our method achieves competitive efficiency while maintaining strong performance across heterogeneous federated settings.
4.6 CONVERGENCE STUDIES
To assess the stability and convergence behavior of FGCN-DKS, we track the trajectories of ACC, NMI, ARI, and loss values across communication rounds and compare them with FedGCN and FedPKA. As shown in Fig. 5 our model converges smoothly and rapidly with stable performance on all metrics. Although FedPKA shows relatively strong sarly-stage performance due its com- munity division mechanism, it fails to maintain improvement and ultimately does not converge. In addition, only local training also converges, but remains clearly inferior without server coordination. The training loss decreases steadily with only minor fluctuations, indicating robust optimization dy- namics under federated settings. Overall, these results confirm that FGCN-DKS achieves reliable and stable convergence throughout the training process.
4.7 CLIENT-WISS WISE PERFORMANCE COMPARISON
FedGCN
Local
OURS
To further evaluate the client-level effectiveness of FGCN- DKS, we conduct a client-wise performance comparison, as shown in Fig. 6 The results show that our FGL method con-
100
90
sistently improves the accuracy all clients, demonstrating strong robustness under heterogeneous data distributions. Al-
70
though FedGCN enhances the overall performance to some ex- tent, it does so while reducing the accuracy of several clients, indicating an unbalanced aggregation effect. In contrast, our approach yields both global performance gains and stable client-level improvements, thereby achieving a more reliable and uniformly beneficial optimization across participants.
2
7
9
10
SM-BIO-SY
Setting Clients
Figure 6: Client-wise performance comparison experiment results un- der SM-BIO-SY non-IID setting.
CONCLUSION
In this paper, we propose FGCN-DKS, a federated clustering framework that effectively addresses the challenge of consensus failure caused by knowledge heterogeneity. By improving invariant learning and common knowledge shared strategy, our method decouples on two levels: (1) shared subgraph patterns and personalized subgraph patterns, and (2) Cluster-oriented consensus pattern and client-driven prior knowledge negotiation. Through this elegant design, we upload only the shared subgraph pattern digests to the server for consensus optimization, focusing on the most ben- eficial parts for clustering, while the personalized subgraph patterns are retained locally to refine the clustering process by the 2-stage K-means clustering process. Regardless of the distribution pattern the clients, approach achieves superior performance compared existing sate--o--hh-an arrt methods. In the future, we plan to address this challenge at the node level, enabling more flexible clustering without being overly constrained by inherent priors.
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6 ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China (No. 62302333, 92370111, and 62272340) and the Open Research Fund from Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ) (No. GML-KF-24-16)
REPRODUCIBILITY STATEMENT
We provide all essential details, including datasets, pseudocodes, hyperparameters, and environment settings, to facilitate the reproducibility of our experiments.
REFERENCES
Siddharth Ambekar, Yuhang Yao, Ryan Li, and Carlee Joe-Wong Fedgat: A privacy-preservingg fed- crated approximation algorithm for graph attention networks. arXiv preprint arX1v:2412.16144, 2024.
Manoj Ghuhan Arivazhagan, Vinay Aggarwal, Aaditya Kumar Singh, and Sunav Choudhary, Fed- erated learning with personalization layers. arXiv preprint arXiv:1912.008/8 2019.
Deyu Bo. Xiao Wang, Chuan Shi, Meiqi Zhu, Emiao Lu, and Peng Cui. Structural deep clustering network. In Proceedings of the Web Conference, pp. 1400-1410, 2020.
Karsten Borgwardt, Elisabetta Ghisu, Felipe Clinares-óópez Leslic O'Bray, and Bastian Rieck. Graph kernlls: State-of-the-ar and future challenges. Foundations and Trends@ in Machine Learning, 13(5-6):531-71,, 2020.
Jinyu Cai, Jicong Fan, Wenzhong Guo, Shiping Wang, Yunhe Zhang, and Zhao Zhang Efficient deep embedded subspace clustering. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1-10, 2022.
Jinyu Cai, Yunhe Zhang, and Jicong Fan. Self-discriminative modeling for anomalous graph detec- tion. arXiv:2310.06261, 2023.
Jinyu Cai, Yi Han, Wenzhong Guo, and Jicong Fan. Deep graph-level clustering using pseudo-label- guided mutual information maximization network. Neural Computing and Applications, 36(16); 9551-9566, 2024a.
Jinyu Cai, Yunhe Zhang, Jicong Fan, Yali Du, and Wenzhong Guo. Dual contrastive graph-level clustering with multiple cluster perspectives alignment. In Proceedings of the International Joint Conference Artificial Intelligence, 2024b.
Jinyu Cai, Yunhe Zhang, Jicong Fan, and KionKiong Ng. Lg-fgad: An effective federated graph anomaly detection framework. In Proceedings of the International Joint Conference Artificial Intelligence, pp. 7760-3769, 2024c.
Jinyu Cai, Yunhe Zhang, Zhoumin Lu, Wenzhong Guo, and See-kiong Ng. Fgad: Self- boosted knowledge distillation for an effective federated graph anomaly detection framework. arXiv:2402.1 12761, 2024d.
Jinyu Cai, Yunhe Zhang, Fusheng Liu, and See- Kiong Ng. Leveraging diffusion model as pseudo- anomalous graph generator for graph-level anomaly detection. In Proceedings of the Forty-second International Conference on Machine Learning, 2025.
Chuan Chen, Ziyue Xu, Weibo Hu, Zibin Zheng, and Jie Zhang. Fedgl: Federated graph learning framework with global self-supervision. Information Sciences, 657:119971 19976, 2024.
Jie Chen, Hua Mao, Wai Lok Woo, Chuanbin Liu, and Xi Peng. Cross-view graph consistency learning for invariant graph representations. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pp. 15795-15802. 2025.

---

Published as a conference paper at ICLR 2026
Yongqiang Chen, Yonggang Zhang, Yatao Bian, Han Yang. MA Kaili, Binghui Xie, Tongliang Liu, Bo Han, and James Cheng. Learning causally invariant representations for out- out-of- distributton generalization graphs. Advances in Neural Information Processing Systems, 35:22131-22144 2022.
Chaoyang He, Keshav Balasubramanian, Emir Ceyani, Carl Yang, Han Xie, Lichao Sun, Lifang He, Liangwei Yang, S Yu Philip. Yu Rong. al. Fedgraphnn: A federated learning benchmark system for graph neural networks. In Proceedings of the Workshop on Distributed and Private Machine Learning, 2021.
Mengling Hu, Chaochao Chen, Weiming Liu, Xinyi Zhang, Xinting Liao, and Xiaolin Zheng. Learn- ing uniform clusters on hypersphere for deep graph-level clustering. arXiv e-prints, pp. arViv- 2311, 2023.
Tianrui Jia, Haoyang Li, Cheng Yang, Tao Tao, and Chuan Shi. Graph invariant learning with subgraph co-mixup for out-of-distribution generalization. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 8562 8570, 2024.
Fredrik Johansson, Vinay Jethava, Devdatt Dubhashi, and Chiranjib Bhattacharyya. Global graph kemelss using geometric embeddings. In Proceedings of the 31st International Conference on Machine Learning, volume 32, pp. 694-704 704-702,270 2014.
Wei Ju, Yiyang Gu, Binqi Chen. Gongbo Sun, Yifang Qin, Xingyuming Liu, Xiao Luo, and Ming Zhang. Glee: A general framework for graph-level clustering. In Proceedings of the AAAI con- ference on artificial intelligence, number 4, pp. 4391-4399 2023.
U Kang, Hanghang Tong, and Jimeng Sun. Fast random walk graph kernel. In Proceedings of the 2012 SIAM international conference on data mining, pp. 828-838 SIAM, 2012.
Haoyang Li, Ziwei Zhang, Xin Wang, and Wenwu Zhu. Learning invariant graph representations for distriiiitti generalization. Proceedings of the 36th International Conference on Neural Information Processing Systems, pp. 11828 18441, 2022a.
Haoyang Li, Ziwei Zhang, Xin Wang, and Wenwu Zhu. Learning invariant graph representations for diitribbuttinnnoonnnn generalization. Advances Neural Information Processing Systems, 35: 11828-1 1841, 2022b.
Shangyang Li and Jiayan Guo. Subgraph federated learning with information bottleneck constrained generative learning. ACM Transactions on Knowledge Discovery from Data 19(6):1-23, 2025.
Tian Li, Anit Kumar Sahu, Manzil Zaheer, Maziar Sanjabi, Ameet Talwalkar, and Virginia Smith. Federated optimization in heterogeneous networks. In Proceedings of the Machine Learning and Systems, volume 2, pp. 429-450, 2020.
Xiang Li, Kaixuan Huang, Wenhao Yang. Shusen Wang, and Zhihua Zhang. On the convergence of fedavg non-iid data. arXiv preprini arXiv: 1907.0090 2019.
Ke Liang, Yue Liu, Sihang Zhou, Wenxuan Tu, Yi Wen, Xihong Yang, Xiangjun Dong, and Xin- wang Liu. Knowledge graph contrastive learning based on relation-symii cattiion--ymmtricaall structure. IEEE Transactions Knowledge and Data Engineering, 36(1):226-238, 2023.
Ke Liang, Lingyuan Meng. Hao Li, Meng Liu, Siwei Wang, Sihang Zhou, Xinwang I Liu, and Kunlun He. Mgksite: Multi-modal mowledge-driveed site selection intra and inter-modal graph fusion. IEEE Transactions Multimedia, 2024a.
Ke Liang, Lingyuan Meng, Meng Liu, Yue Liu, Wenxuan Tu, Siwei Wang, Sihang Zhou, Xinwang Liu, Fuchum Sun, and Kunlun He. A survey of knowledge graph reasoning on graph types: Static, dynamic, and modal- IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024b.
Ke Liang, Sihang Zhou, Meng Liu, Yue Liu, Wenxuan Tu, Yi Zhang, Liming Fang, Zhe Liu, and Xinwang Liu. Hawkes-enhanced pratial-temporll hypergraph contrastive learning based on crim- inal correlations. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 8733-8741, 2024c.
12

---

Published as a conference paper at ICLR 2026
Ke Liang, Lingyuan Meng, Hao Li, Jun Wang, Long Lan, Miaomiao Li, Xinwang Liu, and Huaimin Wang. From concrete to abstract: Multi-view clustering on relational knowledge. IEEE Transac- tions Pattern Analysis and Machine Intelligence, pp. 1-18, 2025.
Tianchi Liao, Lele Fu, Lei Zhang, Lei Yang, Chuan Chen, Michael K Ng. Huawei Huang. and Zibin Zheng. fiwacy-preserving vertical federated learning with tensor decomposition for data missing features. IEEE Transactions on Information Forensics and Security, 20:3445-3460. 2025a.
Tianchi Liao, Binghui Xie, Sheng Huang Lele Fu, Bowen Deng, Chuan Chen, and Zibin Zheng. Federated domain generalization with decision insight matrix. In Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, pp. 5689-5697, 2025b.
Tianchi Liao, Ziyue Xu, Qing Hu, Hong-Ning Dai, Huaiwei Huang, Zibin Zheng, and Chuan Chen. Fedbrb: A solution the small-to-large scenario in device-heter heterogenety federated learning. IEEE Transactions Mobile Computing, 25(3):303630550 2026.
Jingxin Liu, Jieren Cheng, Renda Han, Wenxuan Tu, Jiaxin Wang, and Xin Peng. Federated graph- level clustering network. In Proceedings of the AAAI Conference on Artificial Intelligence, vol- ume 39, pp. 18870-18878, 2025a.
Jingxin Liu, Renda Han, Wenxuan Tu, Haotian Wang, Junlong Wu, and Jieren Cheng. Federated node-level clustering network with cross- cross-subgraph link mending. In Proceedings of the Forty- second International Conference on Machine Learning. 2025b.
Meng Liu, Ke Liang, Dayu Hu, Hao Yu, Yue Liu, Lingyuan Meng. Wenxuan Tu, Sihang Zhou, and Xinwang Liu. Tmac: Temporal multi-modal graph learning for acoustic event classification. In Proceedings of the 31 ACM International Conference on Multimedia, pp. 3365-3374, 2023.
Meng Liu, Yue Liu, Ke Liang, Wenxuan Tu, Siwei Wang, Sihang Zhou, and Xinwang Liu. Deep temporal graph clustering. In Proceedings of the 12th International Conference on Learning Representations, 2024a.
Rui Liu, Pengwei Xing, Zichao Deng, Anran Li, Cuntai Guan, and Han Yu. Federated graph neural networks: Overview, techniques, and challenges. IEEE Transactions on Neural Networks and Learning Systems, 2024b.
Wenyu Mao, Jiancan Wu, Haoyang Liu, Yongduo Sui, and Xiang Wang. Invariant graph learning meets information bottleneck for out-of-distribution generalization. arXiv preprint arXiv:2408.01697, 2024.
Xu Shen, Yixin Liu, Yili Wang, Rui Miao, Yiwei Dai, Shirui Pan, and Xin Wang. Raising the bar in graph ood generalization: Invariant learning beyond explicit environment modeling. arXiv preprint arXiv:2502. 2025.
Yongduo Sui, Caizhi Tang, Zhixuan Chu. Junfeng Fang, Yuan Gao, Qing Cui, Longfei Li, Jun Zhou, and Xiang Wang. Invariant graph learning for causal effect estimation. In Proceedings of the ACM Web Conference 2024, pp. 2552-25622 2024.
Yue Tan, Yixin Liu, Guodong Long, Jing Jiang, Qinghua Lu, and Chengqi Zhang, Federated learning on non-iid graphs via structural knowledge sharing. In Proceedings of the AAAI conference on artificial intelligence, volume 37, pp. 9953-9961, 2023.
Wenxuan Tu, Renxiang Guan, Sihang Zhou, Chuan Ma, Xin Peng, Zhiping Cai, Zhe Liu, Jieren Cheng, and Xinwang Liu. Attribute-missing graph clustering network. In Proceedings of the AAAI Conference on Artificial Intelligence, number 14, pp. 15392-15401, 2024.
Chuhan Wu, Fangzhao Wu, Yang Cao, Yongfeng Huang, and Xing Xie. Fedgnn: Federated graph neural network for privacy-preserving recommendation. arXiv preprint 1XXx:2100200425: 2021.
Junlong Wu, Haotian Wang, Jingxin Liu, Wenxuan Tu, Renda Han, Jieren Cheng, and Xiangyan Tang. Fedpka: Federated graph-level clustering network with personalized knowledge aggre- gation. In Proceedings of the International Conference on Intelligent Computing, pp. 27-38. Springer, 2025.
13

---

Published as a conference paper at ICLR 2026
Donglin Xia, Xiao Wang. Nian Liu, and Chuan Shi. Learning invariant representations of graph neural networks via cluster generalization. Advances in Neural Information Processing Systems, 15:45602-456133 2023.
Han Xie, Jing Ma, Xiong, and Carl Yang. Federated graph classification over non-iid graphs. Advances in neural information processing systems, 14:18839-18888 18852, 2021.
Ke Zhang, Carl Yang, Xiaoxiao Li, Lichao Sun, and Siu Ming Yiu. Subgraph federated learning with missing neighbor generation. Advances in Neural Information Processing Systems, 34:6671-
6682, 2021.
Taolin Zhang, Chengyuan Mai, Yaomin Chang, Chuan Chen, Lin Shu, and Zibin Zheng. Fedego: privacy-preserving personalized federated graph learning with ego-graphs. ACM Transactions on Knowledge Discovery from Data, 18(2):1-27, 2023.
Yunhe Zhang, Yan Sun, Jinyu Cai, and Jianping Fan. Deep orthogonal hypersphere compression for anomaly detection. In Proceedings of the Twelfth International Conference on Learning Repre- sentations, 2024.
Yun Zhu, Haizhou Shi, Zhenshuo Zhang, and Siliang Tang. Mario: Model agnostic recipe for improving ood generalization of graph contrastive learning. In Proceedings of the ACM Web Conference 2024, pp. 300-311, 2024.
A NOTATIONS
All notations used in the proposed FGCN-DKS are summarized in Table 5
B GRAPH DECOMPOSITION INTO INVARIANT AND VARIANT SUBGRAPHS
PROBLEM SETUP AND NOTATION
Let G = (V, E) be an undirected graph with node set and edge set E, where each node v E V has feature vector X,, Rd We assume that the graph G can be decomposed into two components: invariant subgraph Gin and a variant subgraph Gvars such that:
(12) where Giny is the invariant subgraph that represents the part of the graph that remains unchanged across different datasets or transformations. Gvar is the variant subgraph that represents the part of the graph that is sensitive changes in the data, such variations across different experiments, graphs, or time steps.
G = Ginv G
Our goal is provide a formal decomposition of the graph into these two subgraphs and to prove that this decomposition is meaningful in terms of graph properties.
B. DECOMPOSITION METHODOLOGY
The decomposition process follows these steps:
Identification of Invariant Components: We first identify the subgraph Giny by looking for the parts of the graph that are consistent across all observed instances. This is done by comparing the graph's s structure and node features across different datasets or views.
2. Identification of Variant Components: The remaining graph, G consists of the com- ponents that change depending on external factors. These components are identified by measuring the variation in the graph's 's structure node features time across differ- ent instances.
3. Formalizing the Decomposition: The graph G is decomposed into two disjoint subgraphs Gim and Gvar, such that:
G = Gim U Grar. Gime G = 6.
(13)
The invariant subgraph captures the stable, core relationships in the graph, while the variant subgraph contains the dynamic or fluctuating parts.
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Notations
Meaning
Notations
Meaning
N
Number of nodes
NG
Number of graphs from each client
Ne
Number of clients
N₂
Number of clusters from each client
Ny.
Number of clusters from all clients
Number environments
d
Dimensions of node attribute
d'
Dimensions of node embedding
Node attribute matrix
Graph adjacency matrix
M
Graph structure mask matrix
M
Node attribute mask matrix
X
Invariant node attribute matrix
A
Invariant graph adjacency matrix
X
Variant node attribute matrix
Variant graph adjacency matrix
H
Invariant node embeddings
H
Variant node embeddings
Invariant graph-level embeddings
Variant graph-level embeddings
P
Common prototype
Personalized prototype
P alo
Consensus prototype
+
glo
Consensus parameter matrix
Invariant model parameter matrix
Variant model parameter matrix
Y
Weight hyper-paramend
Weight pyyerr-praamee
S
Affinity matrix
Stability coefficient
S
Cluster set
Cluster node set
small lower bound constant
Weight hyper-parameler
Table 5: Basic notations for the proposed FGCN-DKS.
INVARIANT AND VARIANT SUBGRAPHI PROPERTIES
For the decomposition to be valid, we must ensure that the invariant subgraph captures only those parts of the graph that are consistent across multiple views or datasets. We define the following properties for the invariant and variant subgraphs:
Invariant Subgraph (Giny: The invariant subgraph contains the edges and nodes that remain unchanged across different instances. Formally, for any two graphs G = E)) and G2 (V2, E2) with the same node set V, the edges in Gnv must satisfy:
Fun C E1 E2, VE1, E2 E 11,
(14)
This ensures that the edges in Giny are consistent across all graphs or datasets.
Variant Subgraph (Gvar): The variant subgraph contains the edges and nodes that differ between graphs. This can be formally defined as:
Ever
E
Fanv; V=
ViN:
(15)
where Evar and Var are the edges and nodes in Gvar that do not appear in Gine
MATHEMATICAL FORMULATION OF DECOMPOSITION
The decomposition can be viewed as an optimization problem, where the objective to minimize the difference between the original graph and the sum of the invariant and variant subgraphs. This can be formulated as follows:
min Gun
(IG - (Giny + G1 + (l)
(16)
where: Giny and Gvar are the invariant and variant subgraphs, respectively. The first term ensures that the sum of the subgraphs approximates the original graph. The second term is a regularization term that penalizes the size the invariant subgraph, ensuring that only contains core, stable components.
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Table 6: Effectiveness of subgraph separation under various non-IID settings (%)
Non-IID Settings
IC
DR
AVG-IC
SM
88.7
90.2
54.8
SM-BIO
85.6
84.5
30.9
SN
90.1
83.2
56.4
PROOF OF DECOMPOSITION VALIDITY
We now provide a proof that the decomposition of the graph into invariant and variant subgraphs is valid, i.., the decomposition maintains key structural properties of the original graph.
theorem Let G = (V, E) be a graph that can be decomposed into an invariant subgraph Gav and variant subgraph Gvar. Then, the decomposition is valid if and only if:
G = Gine U Gvar
and G O G = 0.
(17)
Proof. We begin by noting that the invariant subgraph Giny must consist of nodes and edges that are consistent across all instances of the graph. Therefore, Ginv captures the stable relationships in the graph. On the other hand, the variant subgraph Gvar consists of the edges and nodes that differ between instances.
Since the decomposition is performed by removing the invariant components from the original graph, we have:
Gvar G \ Ginv-
(18)
Additionally, by construction, the invariant and variant subgraphs disjoint, meaning that:
Ginv n Gyar 0.
(19)
Thus, the graph G is indeed the union of Giny and Gvara required.
Therefore, the decomposition is valid, and we have:
G Gin U Gyars Ginv O Gvar 0.
(20)
CONCLUSION
In this section, we have formalized the decomposition of graph into invariant and variant sub- graphs. The invariant subgraph captures the stable structural relationships across multiple instances transformations, while the variant subgraph captures the parts of the graph that vary. We have proven that the decomposition valid, and we have provided an optimization framework for learn- ing such decomposition. This decomposition is useful in various applications, such raph-based anomaly detection, graph classification, and multi-vies view learning, where the goal to separate stable and namamic components of the graph.
C EFFECTIVENESS ANALYSIS OF SUBGRAPH SEPARATION
To evaluate the effectiveness of our subgraph separation mechanism, we employ three complemen- tary metrics: Invariance Consistency (IC), which quantifies the similarity of invariant subgraphs ex- tracted from different clients; Distinctiveness Ratio (DR), which measures the separability between invariant and variant subgraphs; and the average IC of raw graphs (AVG-IC), which indicates the baseline similarity across clients without separation. As reported in Table our method consistently achieves high IC and DR values across various non-llD settings, even when the raw cross-client similarity (AVG-IC) is considerably lower. These results demonstrate that the separation mecha- nism substantially enhances cross-client pattern affinity and reveals shared structural semantics that are less apparent in the original graphs. Overall, the findings confirm that our approach effectively identifies robust and meaningful common patterns despite substantial distributional shifts.
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D DETAILS OF DATASETS AND NON-IID SETTINGS
In this manuscript, the statistical information of the benchmark datasets used is provided in Table 7 Based on these datasets, we construct a series of non-iid (Non-Independent and Identically Dis- tributed) settings, which are consistent with FedGCN. The non-III settings refer to the strategy of distributing different datasets across clients, where each client possesses a private, exclusive dataset. Detailed information on this setting is shown in Table 8 The Ground Truth for the datasets involved also provided, serving as the evaluation standard. All the Ground Truth information includes the true labels for cach dataset, which will be used for subsequent model evaluation and comparison.
MUTAG dataset originates from chemical experiments and is primarily used for predicting the mutagenicity (toxicity) of molecules. Mutagenicity is an important indicator in drug de- velopment and environmental safety, making this dataset highly relevant in drug discovery and molecular property prediction.
BZR dataset is derived from drug screening experiments, aiming to predict whether a small molecule can bind to the benzodiazepine receptor and exhibit biological activity. Ben- zodiazepine drugs are associated with anti-anxiety, sedative, and muscle relaxant effects, making this dataset valuable for research in drug design.
COX2 dataset originates from the field of drug design, with the goal of predicting whether a small molecule can inhibit Cyclooxygenase-2 COX-2 is an enzyme involved in inflam- matory responses, and its inhibitors are commonly used in anti-inflammatory, analgesic, and anticancer drug development.
DHFR dataset is key metabolic enzyme involved in DNA synthesis, repair, and cell pro- liferation. This dataset is used predict whether small molecule can inhibit the activity of DHFR, which is crucial in the development of anticancer and antimicrobial drugs (such as methotrexate).
PTC MR is subset of the Predictive Toxicology Challenge, with data from carcinogenic- ity testing of compounds in experimental animals (in this case, male rats). The goal is to predict whether a chemical molecule toxic, which is particularly valuable in drug safety evaluation and environmental chemical screening.
AIDS dataset comes from the National Cancer Institute's (NCI) drug activity screening program. It used to predict whether a small molecule can effectively inhibit HIV replica- tion. Each molecule has been experimentally screened, and the labels indicate its inhibitory effect on HIV, with active molecules potentially offering antiviral properties.
BZR MD dataset originates from the inhibitory activity data of benzodiazepine receptors obtained via molecular dynamics simulations. Compared to the BZR dataset, BZR MD) involves more complex molecular simulation information and is typically used in higher- level drug screening and design, especially for evaluating drug molecules in environments combining simulation and real-world data.
DD dataset comes from the drug-drug interaction (DDI) prediction task. In clinical phar- macology, drug-drug interactions are important issue that can affect the efficacy of drugs or cause severe side effects. The DD dataset aims to predict potential interactions between different drugs, aiding in drug development and clinical medication safety assessments.
PROTEINS dataset derived from the protein structure prediction task. The goal is to predict whether a protein, based on its amino acid sequence and structure, is an enzyme. Enzymes are vital molecules involved in catalyzing biochemical reactions, and this dataset is significant for drug design, disease research, and biological studies.
SYNTHETIC dataset is a synthetic benchmark dataset primarily used for model validation and experimentation. It is typically used to test the effectiveness of new algorithms or methods, rather than solving specific biological or chemical problems. Due to its synthetic nature, the SYNTHETIC dataset provides a relatively simple and controlled environment for evaluating the performance of graph classification models diverse and structured data.
COLLAB dataset originates from social network analysis and is mainly used to study cooperation and non-cooperation relationships between users in social networks. The goal
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is predict whether the structure of social network graph is cooperative one. Social network amalysis is highly important in modern society, with broad applications in user behavior prediction, advertising, and social platform development.
IMDB-MULTI dataset is derived from the IMDB movie database and is primarily used for movie recommendation system classification tasks. The goal is to predict the category of movie based its attributes and social relationships (such actors, directors, and labels). This dataset is especially suited for research on multi-label classification problems in social network analysis and recommendation systems.
Letter-high dataset is standard dataset for letter graph classification, used in computer vision for graph classification tasks. Each sample is an graph of a letter, and the goal is to recognize the letter through the pixel information in the graph. This dataset is typically used to test models in graph representation and classification tasks, especially graph classification algorithms within the computer vision field.
Letter-low dataset is standard dataset for classifying lowercase letter graphs, used in computer vision for graph classification tasks. Each sample is an graph a lowercase letter, and the goal is to recognize the letter through the pixel information in the graph. This dataset commonly used test graph classification algorithms, particularly how graph neural networks (GNN) handle graph data.
Letter-med dataset is standard dataset for classifying medium-sized letter graphs, used in computer vision for graph classification tasks. Each sample an graph of medium-sized letter, and the goal is to recognize the letter through the pixel information in the graph. This dataset is frequently used to test model performance in graph classification tasks, especially in how graph neural networks (GNN) process graph data with graph structures.
Datasets
Domain
Classes
Graphs
A.Nodes
A.Edges
MUTAG
188
17.93
19.79
BZR
405
35.75
38.36
COX2
467
41.22
43.45
SM
2
DHFR
756
42.43
44.54
PTC.MR
344
14.29
14.69
AIDS
2000
15.69
16.20
BZR MD
306
21.30
225.06
DD
1178
284.32
715.66
BIO
2
PROTEINS
1113
39.06
72.82
SYNTHETIC
2
300
100.00
196.00
SY
SYNTHIE
4
300
95.00
172.93
COLLAB
5000
74.49
2457.78
SN
3
IMDB-MULTI
1500
13.00
65.94
Letter-higg high
2250
4.67
4.50
Letter-low
CV
15
2250
4.68
3.13
Letter-med
2250
4.67
3.21
Table Dataset statisties.
E DETAILS OF THE EVALUATION METRICS
Clustering Accuracy (ACC) ACC computes the optimal mapping between predicted clus- ter labels and ground-truth labels using the Hungarian algorithm. Formally, let yi be the
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non-IID Settings
Datasets
Domains
SM
SM-BIO
SM-BIO-SY
SN
SN-SY
CV
MUTAG
SM
BZR
SM
V
COX2
SM
V
DHFR
SM
PTC_MR
SM
AIDS
SM
BZR_MD
SM
DD
BIO
PROTEINS
BIO
SYNTHETIC
SY
SYNTHIE
SY
COLLAB
SN
IMDB BIBB-BIRARY
SN
Letter-low
Letter-med
SN
Letter-high
SN
Table 8: The non-IID benchmark settings.
ground-truth label and ú, the predicted cluster label for instance i, then:
ACC
max TEP
Σ [(: T(;)),
(21)
where и ranges over all possible label permutations and I(.) is the indicator function.
Normalized Mutual Information (NMI) NMI measures the mutual dependence between the predicted labels and true labels, normalized by their entropies:
NMI 2 T(Y:
(22)
H + H(Y)
where ((; Ý) is the mutual information and H-)) denotes entropy. NMI ranges from (no mutual information) to 1 (perfect correlation).
Adjusted Rand Index (ARI) ARI evaluates the similarity between the predicted and true clusterings by comparing all pairs of instances. adjusts for random chance:
RI ER
ARI
(23)
max RI) E[
where RI is the Rand Index and E| its expected value under random labeling.
Macro-F1 Score (F1) The Fl score balances precision and recall across all classes. We compute the macro-averaged F1:
C 2 Prec. Rec,
F1 C
(24)
Prec. Rec,
where C is the number ground-trus truth classes, and Prec,, Rec, are the precision and recall for class
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F OUR METHOD IMPLEMENTATION AND BASELINE DESCRIPTIONS
F.1 HARDWARE ENVIRONMENTS
All experiments are conducted on a Windows operating system equipped with an Intel Core 13900K CPU and an NVIDIA GeForce RTX 4090 GPU.
F.2 SOFTWARE ENVIRONMENTS
We implement the proposed method using Py PyTorch 2.4.0 with CUDA 12.1.
F.3 IMPORTANT PARAMETERS
The model is trained using the Adam optimizer with batch size of 256 for 10 epochs per com- munication round, and total of 20 communication rounds. The learning rate set to 0.001 with standard weight decay of 5e-4. The graph encoder is built with 4 layers of Graph Isomorphism Networks (GIN), each configured with a hidden feature dimension of 10. The hyperparameter is fixed at 0.5. The SP kernel is chosen the kernel function.
F.4 ADAPTATION SCHEME
The adaptation scheme for all comparison methods follows that of FedGCN, For supervised fed- erated graph-level learning baselines, labels are removed, and the same clustering loss used in our approach is applied. For federated graph anomaly detection methods, samples grouped accord- ing to their anomaly scores.
F.5 EVALUATION METRICS
To ensure reproducibility, each experiment is conducted 5 times with different random initializa- tions. We report the mean and standard deviation of the following clustering metrics: Accuracy (ACC), Normalized Mutual Information (NMI), Adjusted Rand Index (ARI), and score.
All baseline methods adapted to the unsupervised federated learning setting perform graph- level clustering, ensuring a fair and consistent comparison with our proposed approach. Detailed descriptions of each baseline are shown below
FGAD (Cai et al. 2024d) LGAD proposes effective framework for federated graph anomaly detection to address key challenges in collaborative learning. The framework introduces anomaly generator that perturbs normal graphs to create anomalous graphs, which are then distinguished from normal ones by a trained anomaly detector. To preserve the personalization of local models and mitigate the adverse effects of non-IlI problems, student model is employed to distill knowledge from the trained anomaly detector (teacher model). Furthermore, novel collaborative learning mechanism is introduced ensure the preservation of local model personalization while significantly reducing communication costs between clients.
LG-FGAD (Cai et al., 2024c) LG-FGAD introduces a self-adversarial generation mod- ule that generates anomalous graphs, which are then distinguished from normal graphs by trained discriminator. To enhance anomaly awareness, the framework maximizes and minimizes mutual information from both local and global perspectives. To address the challenges posed by non-III problems in collaborative learning, a dual knowledge distilla- tion module is proposed. This module performs knowledge distillation over both logits and embedding distributions, with only the student model engaging collaboration, thereby preserving the personalization of each client's model.
AGDifT Cai et al.) 2025) AGDiff leverages the latent diffusion framework to introduce subtle perturbations into graph representations, generating seeudo-anomalour graphs that closely resemble normal graphs. By jointly training classifier distinguish these gen- erated anomalies from normal graphs, AGDiff learns more discriminative decision bound- aries. The key innovation of AGDiff lies in the shift from focusing solely modeling
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Table 9: Performance Comparison clients with non-identical numbers of clusters.
Methods
ACC
NMI
ARI
F1
FedGCN
54.5
17.6
13.4
40.7
OURS
62.1
20.7
14.8
54.4
normality explicitly generating and learning from pseudo-graph anomalies, enabling it to capture complex anomalous patterns that may be overiooked by other methods.
GLCC (Ju et al. 2023) The GLCC: A general framework for graph-level clustering (GLCC) framework designed to enhance graph-level clustering tasks by leveraging trastive learning principles. This method focuses on learning discriminative representations of graph-level features through a contrastive loss function, which encourages the network to distinguish between similar and dissimilar graphs. GLCC incorporates both local and global graph structures the learning process, thereby improving the clustering quality by optimizing the embedding space. The framework uses contrastive objective to maximize the similarity between similar graph pairs while minimizing the similarity between dissim- ilar ones, ensuring better generalization and robustness in graph clustering applications.
UDGC (Hu et al. 2023 Learning Uniform Clusters on Hypersphere for Deep Graph- level Clustering (UDGC) addresses the challenges of graph-level clustering, which involves grouping multiple graphs into clusters, task that has received less attention than node-level clustering. Graph-level clustering is important in real- wol-world applications like molecule property prediction and community detection in social networks. However, this task is difficult due to the insufficient discriminability of graph-level representations, which often leads to cluster collapse in deep clustering methods.
DGLC (Cai et al. 2023) DGLC is graph-based clustering approach that leverages dual- level learning improve the quality of clustering in graph data. incorporates both global and local structural information from graphs. and optimizes the clustering process by si- multaneously considering intra-graph and inter-graph relations. This method enhances the clustering accuracy by using self-supervised mechanism to adaptively capture graph-level representations and achieve better performance in various graph-based tasks.
DCGLC (Cai et al., 2024b) DCGLC extends the DGLC framework by introducing dual contrastive learning mechanism. This approach focuses on improving graph-level clus- tering by integrating contrastive learning with graph-level features, thereby enhancing the model's ability distinguish between clusters. DCGLC employs both positive and nega- tive samples for contrastive learning, encouraging the model to learn more discriminative and robust representations. This method further optimizes the clustering process, improv- ing its scalability and accuracy in diverse applications graph data.
G ADDITIONAL EXPERIMENTS ON CLIENTS WITH NON-IDENTICAL NUMBERS CLUSTERS
To further demonstrate the advantages of proposed method, conduct additional experiments on clients with non-identical numbers clusters. Specifically, the non-IID setting includes MU- TAG (2 clusters), COLLAB (3 clusters), and Letter-low (15 clusters). We compare our method with FedGCN under this non-lID setting. As shown in Table 9 our method consistently outper- forms FedGCN. This improvement is primarily attributed to the ability of our method perceive the distinct cluster structures between clients and align the personalized optimization parameters accordingly for different clusters.
21


Reviews:
[{"review_id": "v0md4JdWCV", "reviewer": "Reviewer_5r3P", "summary": "The paper proposes a novel federated graph-level clustering algorithm. The algorithm decouple knowledge at both the local and server levels, thereby improving the quality of global consensus. The motivation is clearly presented, the overall presentation is of high quality, and the experimental results demonstrate superior performance compared with existing methods.", "questions": "Q1. The convergence analysis mentions the FedPKA method, but it is missing from the comparative experiments. Although this method was not published in a top-tier conference, could it be that the authors accidentally omitted it?\n\nQ2. Why was FedSage compared in the experiment? This method seems to be applicable to node-based tasks rather than graph-level tasks?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "S1. Unlike traditional approaches that enhance consensus by increasing shared data, this framework adopts an alternative strategy by reducing the amount of data involved in consensus, which not only facilitates more efficient agreement but also contributes to better privacy protection.\n\nS2. The article demonstrates high quality in writing, presentation, and overall organization, and it is easy to follow and understand.\n\nS3. Compared with other methods, this approach is better suited for real-world federated scenarios. Theoretical analysis is further provided to demonstrate the convergence of the proposed method.", "weaknesses": "W1. The convergence analysis should include the loss variation during training.\n\nW2. Performance comparisons should be performed across all clients in a non-iid setting to demonstrate that the federated approach can improve overall performance without sacrificing the performance of individual clients.\n\nW3. Comparing it to supervised methods seems less meaningful; replacing it with the experiments described above better demonstrates the advantages of the method.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "eFhJ2wIhX2", "reviewer": "Reviewer_YqnG", "summary": "This manuscript introduces a novel framework for federated clustering, centered around the idea of decoupling knowledge both within and across clients to enhance clustering performance. This manuscript is well-written, logically structured, clearly articulated, and experimentally robust, addressing an innovative problem. The experiments demonstrate significant improvements compared to advanced methods.", "questions": "1. The calculation of the heterogeneity of intra-client graphs is unclear. Is the author referring to the heterogeneity of all graphs within the client, or the heterogeneity of graphs within different clusters on the client?\n2. Does this method have the capability to address the issue of inconsistent numbers of clusters across different clients?\n3. Is this federated client configuration self-defined, or does it follow the setup used in prior work?\n4. What exactly does the prototype refer to? I hope the author can explain it further.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "1. The proposed method is novel, as it introduces for the first time the dual decomposition of knowledge into cluster-oriented and client-oriented dimensions.\n2. The experimental setup is robust and reliable and thoroughly demonstrates the superiority of the proposed framework.\n3. The authors cleverly integrate invariant learning into the federated graph-level clustering framework, which I find very insightful. It suggests that a similar strategy could potentially be used to improve federated graph classification as well.", "weaknesses": "1. The adaptation of other methods, such as federated graph learning and federated anomaly detection, to federated graph clustering should be further explained.\n2. Communication overhead experiments should be included to further validate the superiority of the method.\n3. The fonts in the architecture diagram are consistent. It is recommended to further unify them to New Times Roman or Microsoft YaHei.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "gtpyM1gPFw", "reviewer": "Reviewer_q64Q", "summary": "This paper addresses the challenging issue of Federated Graph-level Clustering, where heterogeneity across clients, both intra- and inter-client, can cause difficulties in achieving a meaningful consensus on the server side. The authors propose a novel framework called FGCN-DKS. The core idea involves two levels of decoupling: 1) On the client side, each graph is split into an \"invariant\" subgraph and a \"variant\" subgraph. Only the digest of the invariant part is shared. 2) On the server side, a Common Knowledge Sharing Strategy is employed to perform a personalized aggregation of client models, guided by the similarity between clients' cluster pattern digests. A two-stage clustering process on the client leverages both shared and local representations.", "questions": "1.Given the complexity of the framework, could the authors provide a more detailed ablation study to isolate the contribution of each key component? \n\n2.Could the authors quantify this communication cost and compare it to standard federated learning approaches like FedAvg, which transmit model parameters?\n\n3.How can the \"quality\" of this separation be directly evaluated, beyond just its impact on downstream clustering accuracy? Is there a way to ensure that the invariant subgraphs capture truly common, cross-client patterns?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 1, "strengths": "1.The paper effectively identifies the key issue of heterogeneity in federated graph clustering, distinguishing it from the more common challenges seen in node-level federated learning.\n\n2.The comprehensive experiments across multiple datasets and non-IID settings lend strong support to the method's robustness and generalizability.", "weaknesses": "1.The framework introduces multiple new components and hyperparameters, making it complex and difficult to analyze or tune effectively. It is unclear which specific component contributes most to the performance gains, making it challenging to pinpoint areas for improvement or fine-tuning.\n\n2.The many moving parts in the system make it difficult to attribute performance improvements to specific components. \n\n3.While the dual knowledge separation and two-stage clustering approach is novel, the system’s complexity may limit its practicality and ease of adoption. Simplifying some aspects could make it more accessible.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "rrWtemwohx", "reviewer": "Reviewer_zKZU", "summary": "This paper proposes a new method for federated graph-level clustering. Compared with existing federated graph-level clustering methods, this method solves the heterogeneity problem of multi-source data through dual knowledge separation. The article is clear in expression, motivation is clear, and the experimental design is complete.", "questions": "1. The paper mentions using a graph kernel method to measure network heterogeneity. To facilitate understanding and replication, could the authors please specify which specific graph kernel or types of kernels they used? Also, could they explain the rationale for choosing this particular kernel function to quantify heterogeneity?\n2. The authors need to clarify how and to what extent label information is used in the unsupervised training phase and the downstream task evaluation phase.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "1. The experimental setup is comprehensive, with comparisons made against both supervised and unsupervised methods. Ablation analysis demonstrates the superiority of the proposed approach.\n2. As the novel method for federated graph-level clustering, this approach significantly enhances performance by separating different subgraphs and utilizing cluster-guided prototype aggregation.\n3. Research on federated graph-level clustering remains scarce, and this study effectively fills that gap.", "weaknesses": "1. The authors should further elaborated The non-IID setting in the appendix for additional clarification.\n2. The authors should include experiments on federated communication costs.\n3. Some minor errors should be further corrected, such as changing \"leverage\" to \"leverages.\"", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:

Decision: Accept (Poster)