With the rise of vertical segmentation in real-world data, federated graph-level clustering has gained significant attention in recent years. However, the inherent missing attributes in graph datasets held by certain clients lead to suboptimal local parameter updates and misaligned global parameter consensus. This results in knowledge shifts during negotiation to ultimately impair overall clustering performance. This issue remains largely underexplored in the current advanced research. To bridge this gap, we propose a novel deep learning network called Federated Graph-level Clustering Network with Attribute Inference (FedAI), which utilizes high-confidence prior knowledge from each domain and multi-party collaborative optimization to achieve efficient reasoning of unknown features. Specifically, on the client, high-confidence graph samples are projected into a latent space. We then extract and upload irreversible path digest information and attribute-oriented inference signals from them. On the server, we first identify affinity relationships hierarchically via the improved graph kernel method. We then infer the features of clients lacking node attributes through a prior structure-guide recovery operator, facilitating inter-client knowledge transfer for better clustering. Experimental results on 15 cross-dataset and cross-domain non-IID graph datasets demonstrate that FedAI consistently outperforms existing methods.

In the federated clustering task, structural heterogeneity across clients inevitably impedes effective multi-source information sharing. To solve this issue, Personalized Federated Learning (PFL) has emerged as a potentially effective solution for image and text clustering. Unlike Euclidean data, graph-structured data exhibits diverse and fragile local patterns, which widely exist in real-world scenarios. Multi-graph data analysis in the federated learning setting is challenging and important, yet remains underexplored. This motivates us to propose a novel PERsonalized Federated graph-lEvel Clustering neTwork (PERFECT), which generates a specialized aggregation strategy for each client by uploading key model parameters and representative samples without sharing private information. Specifically, for each client, we first reconstruct privacy-preserving representative samples in a min-max optimization manner and then upload these samples to the server for subsequent personalized parameter aggregation. On the server, we first extract graph-level embeddings from the uploaded data, and then estimate affinities among multiple learned embeddings to formulate a personalized aggregation strategy for each client. Subsequently, to help each local model better identify the cluster boundaries, we utilize clustering-wise gradient to update the key components in the personalized model parameters from the server. Extensive experimental results have demonstrated the effectiveness and superiority of PERFECT over its competitors.

Node-level federated graph clustering allows multiple unlabeled subgraph holders to collaboratively train on node-level tasks without sharing private information. Existing methods usually assume that the node attributes are complete and have achieved promising progress. However, in the Federated Graph Learning (FGL) scenarios, this assumption is overly strict due to failures in data collection devices. Consequently, most existing FGL frameworks struggle to extract useful features from attribute-incomplete graphs for clustering, yet the issue remains underexplored. To bridge this gap, we propose a causally-aware attribute completion for Incomplete Federated Graph Clustering (IFedGC), which constructs a reliable global causal structure that incorporates clustering-friendly information to guide attribute completion for each subgraph. Specifically, in the attribute completion step, we first construct the causal structure to extract the causal relationships between initialized features, and then upload them to the server. Subsequently, we integrate multiple uploaded causal structures into a global causal one to achieve cross-client attribute completion. Moreover, to support reliable clustering, we first collect the high-confidence cluster centroids from each subgraph using a Graph Neural Network (GNN) model and subsequently aggregate these centroids on the server. The above two steps are seamlessly integrated into a unified FGL framework to obtain a clustering-oriented causal structure, which is sent back to the client to promote high-quality attribute completion for better clustering. Extensive results on five benchmark datasets demonstrate the effectiveness and superiority of IFedGC against its competitors.

Federated graph-level clustering (FGC) provides an effective solution for analyzing decentralized graph data with privacy protection. Existing methods typically assume that all clients have the same number of clusters. This assumption simplifies the learning task and has achieved preliminary success. However, this assumption rarely holds in practice, as clients often exhibit substantial heterogeneity in both data distributions and semantic granularity. As a result, cluster-specific knowledge becomes misaligned during server-side aggregation, which ultimately degrades the overall clustering performance. To address this challenge, we propose a novel Federated Graph Clustering under Inter-Client Cluster Number Discrepancy (FedCND) framework, which aligns inter-client heterogeneous distributions by decoupling graph data into public and private patterns. Specifically, after initial local training and clustering on each client, we design a public learner and a private learner to model public and private graph data, respectively. Only anonymized, cluster-level public information is uploaded to the server, while private information remains local. On the server, cluster-level public prototypes are aggregated based on affinities between reconstructed cluster-level graphs, enabling privacy-preserving prototype alignment across clients with heterogeneous cluster numbers and mitigating interference from misaligned information during global aggregation. Finally, private subgraphs derive client-specific prototypes through local relearning, which are subsequently fused with globally oriented public prototypes for better clustering. Extensive experiments demonstrate that the proposed FedCND achieves an average of 4.9% accuracy improvement against current state-of-the-art methods.

Federated graph learning (FGL), which excels in analyzing non-IID graphs as well as protecting data privacy, has recently emerged as a hot topic. Existing FGL methods usually train the client model using labeled data and then collaboratively learn a global model without sharing their local graph data. However, in real-world scenarios, the lack of data annotations impedes the negotiation of multi-source information at the server, leading to sub-optimal feedback to the clients. To address this issue, we propose a novel unsupervised learning framework called Federated Graph-level Clustering Network (FedGCN), which collects the topology-oriented features of non-IID graphs from clients to generate global consensus representations through multi-source clustering structure sharing. Specifically, in the client, we first preserve the prototype features of each cluster from the structure-oriented embedding through clustering and then upload the learned multiple prototypes that are hard to be reconstructed into the raw graph data. In the server, we generate consensus prototypes from multiple condensed structure-oriented signals through Gaussian estimation, which are subsequently transferred to each client to promote the great encoding capacity of the local model for better clustering. Extensive experiments across multiple non-IID graph datasets have demonstrated the effectiveness and superiority of FedGCN against its competitors.

Subgraphs of a complete graph are usually distributed across multiple devices and can only be accessed locally because the raw data cannot be directly shared. However, existing node-level federated graph learning suffers from at least one of the following issues: 1) heavily relying on labeled graph samples that are difficult to obtain in real-world applications, and 2) partitioning a complete graph into several subgraphs inevitably causes missing links, leading to sub-optimal sample representations. To solve these issues, we propose a novel $\underline{\text{Fed}}$erated $\underline{\text{N}}$ode-level $\underline{\text{C}}$lustering $\underline{\text{N}}$etwork (FedNCN), which mends the destroyed cross-subgraph links using clustering prior knowledge. Specifically, within each client, we first design an MLP-based projector to implicitly preserve key clustering properties of a subgraph in a denoising learning-like manner, and then upload the resultant clustering signals that are hard to reconstruct for subsequent cross-subgraph links restoration. In the server, we maximize the potential affinity between subgraphs stemming from clustering signals by graph similarity estimation and minimize redundant links via the N-Cut criterion. Moreover, we employ a GNN-based generator to learn consensus prototypes from this mended graph, enabling the MLP-GNN joint-optimized learner to enhance data privacy during data transmission and further promote the local model for better clustering. Extensive experiments demonstrate the superiority of FedNCN.

Graph-level clustering remains a pivotal yet formidable challenge in graph learning. Recently, the integration of deep learning with representation learning has demonstrated notable advancements, yielding performance enhancements to a certain degree. However, existing methods suffer from at least one of the following issues: 1) the original graph structure has noise, and 2) during feature propagation and pooling processes, noise is gradually aggregated into the graph-level embeddings through information propagation. Consequently, these two limitations mask clustering-friendly information, leading to suboptimal graph-level clustering performance. To this end, we propose a novel Dual Boost-Driven Graph-Level Clustering Network (DBGCN) to alternately promote graph-level clustering and filtering out interference information in a unified framework. Specifically, in the pooling step, we evaluate the contribution of features at the global and optimize them using a learnable transformation matrix to obtain high-quality graph-level representation, such that the model’s reasoning capability can be improved. Moreover, to enable reliable graph-level clustering, we first identify and suppress information detrimental to clustering by evaluating similarities between graph-level representations, providing more accurate guidance for multi-view fusion. Extensive experiments demonstrated that DBGCN outperforms the state-of-the-art graph-level clustering methods on six benchmark datasets.

Federated Graph Learning (FGL) effectively facilitates cross-domain graph model training by enabling decentralized learning across multiple domains, while ensuring data privacy through local data storage and communication of model updates instead of raw data. Existing approaches usually assume shared generic knowledge (e.g., prototypes, spectral features) via aggregating local structures statistically to alleviate structural heterogeneity. However, imposing overly strict assumptions about the presumed correlation between structural features and the global objective often fails in generalizing to local tasks, leading to suboptimal performance. To tackle this issue, we propose a **Fed**erated **I**nvariant **G**raph **L**earning (**FedIGL**) framework based on invariant learning, which effectively disrupts spurious correlations and further mines the invariant factors across different distributions. Specifically, a server-side global model is trained to capture client-agnostic subgraph patterns shared across clients, whereas client-side models specialize in client-specific subgraph patterns. Subsequently, without compromising privacy, we propose a novel Bi-Gradient Regularization strategy that introduces gradient constraints to guide the model in identifying client-agnostic and client-specific subgraph patterns for better graph representations. Extensive experiments on graph-level clustering and classification tasks demonstrate the superiority of FedIGL against its competitors.

Mobile crowd sensing (MCS), as an innovative data acquisition model in the Internet of Things (IoT), employs an incentive mechanism based on users’ reputation evaluation, which is a mainstream reward allocation method. However, in the existing incentive mechanisms based on reputation evaluation, unidirectional incentive strategies and nonadaptive reputation models result in unequal reward allocation. To tackle this issue, we propose an effective interactive incentive mechanism based on adaptive reputation evaluation. Specifically, we generate user status thresholds to classify, rate, and weight user behaviors, based on the average quality thresholds of tasks released or data submitted by different users in each interaction round. Meanwhile, we achieve multiparty consensus by incorporating the obtained user reputation values and combining them with the cumulative reputation values from multiple rounds to obtain adaptive reputation evaluation results. Moreover, we design an interactive incentive strategy that measures users’ incentive values based on their reputation evaluation results in each round, mutually punishing malicious behaviors from both the publisher’s and the worker’s perspectives. Extensive experiments have demonstrated that our method consistently outperforms existing advanced incentive mechanisms.

Deep graph clustering, as a fundamental task in data mining, has attracted widespread attention. Recently, excellent performance has been achieved by integrating graph structure and node attributes to generate consensus latent embeddings. However, existing clustering methods are limited by redundant information and unreliable clustering distribution, which hinders the discriminative power of the latent embeddings. To address this issue, we propose a novel deep graph clustering framework called Multi-dimensional Topological Association Strengthening Clustering Network (MTASCN). Specifically, we design a Multi-dimensional Feature Association Mechanism (MFAM), which extracts the competitive or cooperative relationship between features to alleviate the interference of redundant features and enhance the dominant features. In addition, we develop a Structure-oriented Multi-order Loss Module (SMLM) that reinforces the generation of clustering distribution under reliable structure information guidance by calculating the multi-order similarity between the latent embeddings and the original graph structure. Extensive experiments on five benchmark datasets have demonstrated that MTASCN consistently outperforms other clustering methods.

Graph representation is an important part of graph clustering. Recently, contrastive learning, which maximizes the mutual information between augmented graph views that share the same semantics, has become a popular and powerful paradigm for graph representation. However, in the process of patch contrasting, existing literature tends to learn all features into similar variables, i.e., representation collapse, leading to less discriminative graph representations. To tackle this problem, we propose a novel self-supervised learning method called dual contrastive learning network (DCLN), which aims to reduce the redundant information of learned latent variables in a dual manner. Specifically, the dual curriculum contrastive module (DCCM) is proposed, which approximates the node similarity matrix and feature similarity matrix to a high-order adjacency matrix and an identity matrix, respectively. By doing this, the informative information in high-order neighbors could be well collected and preserved while the irrelevant redundant features among representations could be eliminated, hence improving the discriminative capacity of the graph representation. Moreover, to alleviate the problem of sample imbalance during the contrastive process, we design a curriculum learning strategy, which enables the network to simultaneously learn reliable information from two levels. Extensive experiments on six benchmark datasets have demonstrated the effectiveness and superiority of the proposed algorithm compared with state-of-the-art methods.