Incomplete attribute-oriented causal perception federal map clustering method and device

Abstract

The embodiment of the invention provides an incomplete attribute-oriented causal perception federal map clustering method and device, electronic equipment and a storage medium, each client can update a local GNN model, a local MLP model and a local causal structure according to a global causal structure, a global clustering center and a consensus model parameter, so that the clustering efficiency is improved. And collaborative clustering-oriented attribute completion is executed, so that the clustering performance of local nodes is improved.

Description

Technical Field

[0001] This application relates to the field of graphics processing technology, and more particularly to a method, apparatus, electronic device, and storage medium for causal-aware federated graph clustering oriented towards incomplete attributes. Background Technology

[0002] Subgraphs of a complete graph are typically distributed across multiple devices and can only be accessed locally due to privacy restrictions. However, node-level federated graph learning is a privacy-preserving technique for training graph neural networks (GNNs) on distributed graph data. Its core objective is to achieve collaborative modeling across devices / institutions without sharing the original node data.

[0003] Most existing federated graph learning frameworks face difficulties in extracting useful features for clustering on graphs with missing attributes. Improving the clustering performance of various local clients has become an urgent technical problem to be solved. Summary of the Invention

[0004] This application provides a method, apparatus, electronic device, and storage medium for causal-aware federated graph clustering for incomplete attributes, which can improve the clustering performance of local nodes.

[0005] In a first aspect, embodiments of this application provide a method for causal-aware federated graph clustering oriented towards incomplete attributes, including: Each client performs preliminary completion of missing node attributes in its local subgraph to obtain an attribute completion matrix; Each client completes the matrix based on the aforementioned attributes to obtain the local cluster centers and the directed acyclic local causal graph; Each client sends its local cluster center, local causal structure matrix, and model parameters to the server; The server aggregates local cluster centers and local causal structure matrices from multiple clients to generate global cluster centers and global causal structures, respectively. The server optimizes the global causal structure to obtain an optimized global causal structure; The server distributes the optimized global causal structure, global cluster center, and consensus model parameters to each client. Each client updates its local GNN model, MLP model, and local causal structure based on the optimized global causal structure, global cluster center, and consensus model parameters, and performs collaborative clustering-oriented attribute completion to improve the clustering performance of local nodes.

[0006] Optionally, each client obtains local cluster centers and a directed acyclic local causal graph based on the attribute completion matrix, including: Based on the attribute completion matrix, a node embedding vector is generated using a graph neural network (GNN) model. Perform a clustering operation on the node embedding vectors to obtain local cluster centers; Another set of node embedding vectors is extracted from the attribute completion matrix using a multilayer perceptron (MLP), and the weight vectors of the input layer of the MLP are concatenated to generate a local causal structure matrix. Based on the local causal structure matrix, a corresponding directed acyclic local causal graph is generated.

[0007] Optionally, generating a corresponding directed acyclic local causal graph based on the local causal structure matrix includes: applying acyclic constraints to the local causal structure matrix to eliminate loops, thereby obtaining a directed acyclic local causal graph.

[0008] Optionally, the server optimizes the global causal structure to obtain an optimized global causal structure, including: Pseudo-labels are generated based on the global cluster centers, and the mutual information between each feature in the global causal structure and the pseudo-labels is calculated. Clustering key features with mutual information higher than a threshold are selected. The non-root nodes corresponding to the key clustering features are masked, and the global causal structure is optimized based on the masked global causal structure and the global missing information matrix to obtain the optimized global causal structure.

[0009] Optionally, each client performs preliminary completion of missing node attributes in its local subgraph, including: Each client uses the feature propagation method to initially complete the missing node attributes in the local subgraph.

[0010] Secondly, embodiments of this application provide an apparatus for causal-aware federated graph clustering for incomplete attributes, comprising: a first acquisition module, set in each client, for performing preliminary completion of missing node attributes in the local subgraph to obtain an attribute completion matrix; The second acquisition module, set in each client, is used to complete the matrix based on the attributes and obtain the local cluster center and the directed acyclic local causal graph. The sending module, located in each client, is used to send the local cluster centers, local causal structure matrix, and model parameters to the server. The generation module, located on the server, is used to aggregate local cluster centers and local causal structure matrices from multiple clients to generate global cluster centers and global causal structures, respectively. The third acquisition module, located in the server, is used to optimize the global causal structure to obtain an optimized global causal structure. The distribution module, located on the server, is used to distribute the optimized global causal structure, global cluster center, and consensus model parameters to each client. The execution module, located on the server, is used to update the local GNN model, MLP model, and local causal structure based on the optimized global causal structure, global cluster center, and consensus model parameters, and to perform collaborative clustering-oriented attribute completion to improve the clustering performance of local nodes.

[0011] Optionally, the second acquisition module includes: A generation unit is used to generate node embedding vectors based on the attribute completion matrix and using a graph neural network (GNN) model. The acquisition unit is used to perform clustering operations on the node embedding vectors to obtain local cluster centers; The first generation unit is used to extract another set of node embedding vectors from the attribute completion matrix through a multilayer perceptron (MLP) and to concatenate the weight vectors of the input layer of the MLP to generate a local causal structure matrix. The second generation unit is used to generate a corresponding directed acyclic local causal graph based on the local causal structure matrix.

[0012] Optionally, the second generation unit is specifically used to apply acyclic constraints to the local causal structure matrix to eliminate loops and obtain a directed acyclic local causal graph.

[0013] Optionally, the third acquisition module is specifically used for: Pseudo-labels are generated based on the global cluster centers, and the mutual information between each feature in the global causal structure and the pseudo-labels is calculated. Clustering key features with mutual information higher than a threshold are selected. The non-root nodes corresponding to the key clustering features are masked, and the global causal structure is optimized based on the masked global causal structure and the global missing information matrix to obtain the optimized global causal structure.

[0014] Optionally, the first acquisition module is specifically used for: each client to use a feature propagation method to initially complete the missing node attributes in the local subgraph.

[0015] Thirdly, embodiments of this application provide an electronic device, including: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the electronic device implements the method described in the first aspect or various possible implementations of the first aspect.

[0016] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer instructions, which, when executed by a processor, are used to implement the method described in the first aspect or various possible implementations of the first aspect.

[0017] Fifthly, embodiments of this application provide a computer program product comprising a computing program, wherein when the computer program is executed by a processor, it implements the method described in the first aspect or various possible implementations of the first aspect.

[0018] This application provides a method, apparatus, electronic device, and storage medium for causal-aware federated graph clustering for incomplete attributes. Each client can update its local GNN model, MLP model, and local causal structure based on the global causal structure, global cluster center, and consensus model parameters, and perform collaborative clustering-oriented attribute completion to improve the clustering performance of local nodes. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the structure of IFedGC provided in an embodiment of this application; Figure 2 These are experimental results comparing the performance of different federated node-level clustering methods on five benchmark datasets; Figure 3 These are the node-level FGC performance results of different FL aggregation strategies provided in the embodiments of this application on the attribute-missing graph; Figure 4 These are the ablation study results of the CFM strategy provided in the embodiments of this application; Figure 5 This is the convergence result of the algorithm provided in the embodiments of this application; Figure 6 This is a schematic diagram of a device for causal-aware federated graph clustering oriented towards incomplete attributes provided in an embodiment of this application; Figure 7 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0021] In this article, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The symbol " / " in this article indicates that the related objects are in an "or" relationship; for example, A / B means A or B.

[0022] The terms "first" and "second," etc., used in the specification and claims herein are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0023] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0024] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processors means two or more processors, multiple elements means two or more elements, etc.

[0025] Node-level federated graph clustering allows multiple unlabeled subgraph holders to collaboratively train on node-level tasks without sharing private information. Existing methods typically assume complete node attributes and have made good progress in this area. However, in the context of federated graph learning (FGL), this assumption is too stringent because data collection equipment failures can lead to missing data. Therefore, most existing FGL frameworks struggle to extract useful features for clustering on graphs with missing attributes, a problem that has not been adequately investigated.

[0026] To fill this gap, this application proposes a causal-aware attribute completion method (IFedGC) for incomplete federated graph clustering with missing links across subgraphs. This method constructs a reliable global causal structure, incorporating clustering-friendly information to guide attribute completion for each subgraph. Specifically, in the attribute completion step, we first construct a causal structure to extract causal relationships between initialization features and then upload it to the server. Subsequently, we integrate multiple uploaded causal structures into a global causal structure to achieve cross-client attribute completion. Furthermore, to support reliable clustering, we first utilize a graph neural network (GNN) model to collect high-confidence cluster centers from each subgraph and then aggregate these cluster centers on the server. These two steps are seamlessly integrated into a unified FGL framework to obtain a cluster-oriented causal structure, which is returned to the client, promoting high-quality attribute completion and improving clustering results. Extensive experimental results on five benchmark datasets demonstrate that IFedGC has significant performance and advantages over other methods, which will be discussed in detail later.

[0027] The following provides background information relevant to this application.

[0028] Node-level federated graph learning (FGL) is a widely used technique that effectively leverages graph structures to achieve efficient collaboration at the node level without directly exchanging raw data (Cai et al. 2024b). In recent years, FGL has attracted significant research attention due to its successful applications in many real-world scenarios, such as disease prediction (Fu et al. 2022), social network analysis (Lei et al. 2023), and fraud detection (Mao et al. 2025). Despite these significant achievements, these studies heavily rely on large amounts of labeled data samples, which are difficult to obtain in real-world scenarios. Once reliable supervision signals are unavailable, existing methods struggle to learn high-quality embedding representations, which affects the effective negotiation of multi-source information on the server side.

[0029] Recently, an advanced node-level federated graph clustering (FGC) algorithm, FedNCN, was proposed, representing the first attempt to recover lost links between clients due to graph partitioning in an unsupervised setting (Liu et al. 2025b). Its core idea is to upload the clustering signal from each client to the server to repair missing links across subgraphs, thereby learning a consensus prototype to improve clustering performance. A fundamental premise for FedNCN's success is the assumption that graph data is complete (i.e., without any missing attributes). However, this assumption does not always hold in real-world scenarios, as privacy constraints and data collection failures inevitably lead to missing attributes, further limiting the clustering performance of each local model. For example, in biomedical settings, the relationship between patients and diseases is often represented as an unlabeled graph (Peng et al. 2023). However, due to non-standard data storage and privacy restrictions, node attributes across subgraphs are often missing and cannot be shared in a federated learning (FL) environment. This weakens unsupervised inference of medical data in a distributed framework and may pose risks to patient care. It is worth noting that the existing FGL framework lacks a customized attribute completion method for clustering of distributed subgraphs with missing attributes.

[0030] An intuitive approach is to aggregate high-confidence clustering cues from clients on the server to reach a consensus on attribute completion, and then use this consensus to optimize the local model to improve clustering performance. However, graphs with missing attributes are divided into multiple subgraphs, inevitably leading to missing links. This phenomenon weakens the reliability of information propagation between nodes, thus affecting the completion effect. Inspired by recent research (Um et al. 2023), which revealed implicit dependencies between initialization feature channels, our goal is to obtain global relationships between features to facilitate higher-quality attribute completion and thus improve the clustering performance of the local model. To achieve this goal, two key challenges need to be addressed: 1) how to construct channel-level relationships from local data under privacy constraints and collect representative samples to preserve clustering assignment signals; 2) how to utilize these uploaded pseudo-supervision signals to optimize channel-level relationships, thereby achieving better clustering performance on each client. For the first challenge, we are inspired by MIRACLE (Kyono et al. 2021), which revealed causal relationships between initialization features in graphs with missing attributes. This observation inspired us to extract causal relationships from subgraphs where each attribute is missing, and to collect representative samples without exposing the private information of each client. For the second challenge, we were inspired by the shared semantic information among subgraphs from the same graph (He et al. 2021). This inspiration led us to integrate multiple local causal relationships into a single global causal relationship, which we optimized by leveraging uploaded pseudo-supervision signals.

[0031] Based on these observations, we propose a novel causal-aware attribute completion method (IFedGC) for incomplete federated graph clustering with missing links across subgraphs. This method captures reliable causal relationships between feature channels and uses learned clustering-friendly information to complete nodes with missing attributes. To this end, we design a novel clustering-oriented completion-re-optimization federated graph learning (FGL) scheme, which is the core idea of ​​our approach. To achieve cross-client attribute completion, we employ a two-path approach. First, for each client, we build a local causal structure revealing the relationships between initial feature channels and upload it to the server. Then, we integrate multiple local causal structures into a global causal structure. Second, to enhance multi-client clustering performance, we use a graph neural network (GNN) model to capture privacy-preserving cluster centers from each subgraph and upload them to obtain global cluster centers. Based on these two steps, we propose a clustering-based masking strategy to optimize the global causal structure using the uploaded cluster centers. Finally, the updated causal structure is encouraged to become more reliable and is then returned to each client to optimize attribute completion, thereby achieving better clustering results. Our main contributions are summarized as follows: A novel research task: To the best of our knowledge, we are the first to explore federated node-level clustering on attribute-missing graphs, which is more practical and challenging than its counterpart on complete graph data (i.e., without any missing attributes).

[0032] A novel FGL framework: A novel unsupervised federated graph learning (FGL) framework—causal-aware attribute completion—is proposed for causal-aware attribute completion (IFedGC) of incomplete federated graph clustering with missing cross-subgraph links. This method not only effectively constructs a channel-aware causal structure to achieve high-quality attribute completion, but also helps to integrate clustering information into the updated causal structure, thereby improving clustering results.

[0033] Superior clustering performance: Extensive experimental evidence validates the effectiveness and superiority of the proposed IFedGC over baseline methods on five benchmark graph datasets.

[0034] Federated Learning (FL) is a widely used distributed machine learning framework that trains a global model through a central server and multiple clients in collaboration, while ensuring privacy protection (Wang et al., 2021a;b; 2023a; 2024b;c;e; Meng et al., 2024; Wang et al., 2023b; 2024a;d; Chen et al., 2024b; Huang et al., 2024a; Yang et al., 2024b). Federated Learning has seen rapid development in recent years, particularly in graph data analysis, due to its ability to effectively leverage various technologies to expand its applications. For example, FedSage+ (Zhang et al., 2021) designed a missing neighbor generator using node labels to address the problem of missing links in distributed subgraph systems. Furthermore, FedPUB (Baek et al., 2023) uploads randomly labeled nodes to a server, which then generates a random graph to mitigate heterogeneity issues. Similarly, FedTAD (Zhu et al., 2024) evaluates the reliability of node category knowledge through topology awareness, then uploads it to the server to guide pseudograph generation for better classification. Previous research has shown that the FGL framework can be combined with some advanced technologies and achieve good performance with the help of data labels. In contrast, to adapt to unlabeled scenarios, we designed a clustering projector to generate corresponding samples that are difficult to reconstruct, in order to maintain the clustering characteristics of each cluster on the client side for better clustering.

[0035] Attribute Graph Clustering. Thanks to the powerful generalization ability of Graph Neural Networks (GNNs) in processing graph data, significant progress has been made in node-level clustering tasks in recent years (Wang et al., 2021d; Tu et al., 2021; Li et al., 2022; Tang et al., 2022; Gong et al., 2022a;b; Pan & Kang, 2023). CCGC (Yang et al., 2023) constructs two views of the complete graph and uses a Siamese encoder to guide the generation of positive and negative sample pairs, thereby improving clustering performance. Similarly, MAGC (Lin et al., 2024) uses weight factors to mine complementary information from multi-view data, learning consistency and discriminative relationships. Furthermore, AMGC (Tu et al., 2024) designs a unified framework that alternately optimizes clustering and attribute complementation performance under the complete graph condition, promoting mutual reinforcement between the two. Typically, these methods assume that the graph data is centralized. However, this assumption is too stringent in real-world scenarios because subgraphs of a complete graph are typically distributed across multiple devices and are only accessible locally due to privacy constraints, inevitably leading to the loss of links between subgraphs. To address the link loss problem caused by graph partitioning, we construct potential affinity relationships across subgraphs based on prior clustering knowledge to recover the structural information damaged by uploaded clustering signals.

[0036] The contents of this application are described in detail below.

[0037] like Figure 1 As shown, the IFedGC proposed in this application consists of two main parts: causal structure construction and optimization. The former includes two branches, blue and red, for collecting shared signals. The blue branch captures cluster centers to preserve clustering properties, while the red branch constructs causal structures to reveal causal relationships between features. The latter utilizes the uploaded cluster centers to optimize the integrated causal structure, which is used for high-quality completion and enhanced cluster-friendly embeddings, respectively. The two parts are seamlessly integrated into a unified FGL framework.

[0038] Symbol definition. Let... Represents a node with missing node attributes and An undirected graph with clusters, where and These are the node set and the edge set, respectively. We assume the graph... Classified as Each subgraph Assigned to a single client. For simplicity, we choose a subgraph. The explanation is the same for other subgraphs. Assume... Include There are clusters, and the node attributes are: The original adjacency matrix is ,in It is the number of nodes. It is the completed attribute dimension.

[0039] Problem Definition. In a federated learning (FL) scenario, the causal discovery problem can be defined as follows. Given observation data... Each of them This represents the local data held by each client, and the consistent feature set is... The goal is to learn a consensus directed acyclic graph (DAG) C that captures causal relationships between raw features without exposing the raw data from each client. While recent research has shown that a consensus DAG C can be learned across decentralized clients in a federated learning setting (Yang et al. 2024), this problem becomes more challenging in clustering tasks, especially when data has missing attributes. On the one hand, missing features obscure the true causal relationships between features; on the other hand, the lack of supervision exacerbates the difficulty of learning a reliable DAG C on a server. To address this, our aim is to extract a globally consensus causal structure (i.e., C can typically be represented as an adjacency matrix) that not only improves the quality of data completion but also facilitates more accurate clustering.

[0040] The architecture of IFedGC. Figure 1 illustrates the architecture of the proposed IFedGC framework, designed to address the issue of missing attributes in node-level FGC tasks. Its core idea is to integrate multiple local causal structures from each client into a global causal structure, and then optimize it using uploaded cluster centers to achieve high-quality attribute completion and better clustering results. The framework consists of three stages: causal structure construction, causal structure optimization, and collaborative clustering-guided completion.

[0041] The following details the causal structure construction phase.

[0042] Inspired by MIRACLE (Kyono et al. 2021) and prototype learning (Liu et al. 2025a), we attempt to extract local causal structures and cluster centers from the initially completed subgraph in order to perform subsequent global causal structure optimization.

[0043] First, on each client, a feature propagation method can be used to identify missing node attributes in the local subgraph. Perform preliminary completion to obtain the attribute completion matrix. .

[0044] Secondly, in order to extract cluster centers We first developed a GNN model to capture attribute-complete subgraphs. Node embedding in .

[0045] (1) in, Represents the identity matrix. Indicates the first The node embedding of the layer encoder, and , It is the first The learnable weight matrix of the layer encoder, d is the activation function, and d′ is the dimension of the latent space. The subgraph embedding of the final encoder layer of the GNN is... To ensure that what is learned... To make it more reliable, we introduce GNN reconstruction loss. Clustering loss Referring to FedNCN (Liu et al. 2025b), we then used the K-means algorithm to... Divide into different groups and collect .

[0046] Third, in order to extract The local causal structure matrix (i.e., the attribute completion matrix). We first designed an MLP to extract embeddings from the encoder. Its form is: (2) in, Indicates the first The node embedding of the layer encoder, and , and These are the learnable weight matrix and bias matrix, respectively. The subgraph embedding of the final encoder layer of the MLP is... It is worth noting that we will use the input layer's weight vector The data is then concatenated to generate a causal relationship matrix. Its form is: (3) in, This represents the weight matrix of the input layer. express -norm. Then, in order to avoid Since there are loops, we introduce a constraint using the extended Lagrangian method (Kyono et al. 2021), which has the following form: (4) (5) in, This represents the regularization constraint operation used to detect the existence of loops. Here, Represents the trace of a matrix. This represents an exponential function. If... , then it means There is a loop within it. During training, a secondary penalty term... and linear penalty term Used to constrain Its form is: (6) Meanwhile, we utilize MLP reconstruction loss (Liu et al. 2025b) to optimize .final, pass Generate. Next, after good training... , and model parameters It is uploaded to the server for subsequent global causal structure optimization.

[0047] In summary, the proposed local causal structure construction strategy has two main advantages: 1) it collects and uploads rich signals in clustering and completion without exposing privacy information; 2) it preserves the key attributes of each cluster and reliable channel-level relationships between features to promote subsequent global causal structure optimization, thereby achieving better clustering and completion.

[0048] The following details the causal structure optimization phase.

[0049] After the server receives multiple uploaded signals, our goal is to leverage these signals to optimize causality in order to achieve high-quality attribute completion and cluster-friendly embedding.

[0050] In the first step, in order to obtain the global cluster center on the server and global causal structure We will upload multiple and The integration will take the following form: (7) in, The loops in the process are removed, in a manner similar to that of each client.

[0051] In the second step, in order to mask the features that are crucial for clustering, we first use the K-means algorithm to... Derivation of pseudo-monitoring signals Then, we calculate... Each feature and Mutual information between features is used to measure the impact of each feature on the clustering results. The contribution takes the form of: (8) in, Represents the key mutual information function for clustering. yes The first in 1 eigenvector Indicates the first Pseudo-labels for each sample yes and The joint probability distribution, and They are and The marginal probability distribution.

[0052] In the third step, after selecting the key clustering features, our goal is to optimize... To reach a consensus. Specifically, to meet the requirements of causality, we select high mutual information (MI) features from non-root nodes for masking, thereby obtaining... Then, we initialize the masked... To obtain and by using It is updated in the following form: (9) in, This represents the global missing indicator matrix, used for marking... Missing attributes in. , and These represent the corresponding elements. Finally, the loss function is minimized. To optimize The format is: (10) in, ,and Indicates the loss due to acyclic connectivity. These are the hyperparameters analyzed in the "Hyperparameter Influence" section.

[0053] In the final step, to obtain the consensus model parameters, we use an average aggregation strategy to combine multiple data points from each client. Aggregate as: (11) in, It includes two model parameters (i.e., consensus model parameters). and ),and This represents the relative sample size for each client, ensuring that each client's impact on the global model is proportional to its data volume.

[0054] The advantages of the proposed causal structure optimization scheme can be summarized as follows: 1) It effectively utilizes rich prior knowledge from clustering and completion to optimize the global causal structure, so as to achieve high-quality completion and better clustering; 2) It is a clustering-oriented optimization method that refines the causal structure by selecting key clustering features for masking, thereby integrating beneficial clustering information into nodes with missing attributes.

[0055] The following section details the collaborative clustering-guided completion phase.

[0056] After information sharing, trustworthy and consensus model parameters Transmitted from the server to each client. Then, using... , and Update the local causal structure separately. Local GNN model parameters and local MLP model parameters In this way, the correct guide The optimization is performed in the following form: (12) in, This represents the local missing indicator matrix, used for marking Missing attributes in , and These represent the corresponding elements. Based on the above steps, the subgraph with missing attributes is updated to facilitate cluster-oriented attribute completion in each client. This prompts each node with missing attributes to collect causally consistent and semantically relevant features within its cluster.

[0057] The technical effects of this application will be explained in detail below through experimental results.

[0058] Benchmark Datasets. To evaluate the superiority and effectiveness of the proposed IFedGC, we used five benchmark graph datasets: CiteSeer (Liu et al. 2023a), PubMed (Jiang et al. 2024), Computer, Photo (Lin et al. 2021), and Cora (Lei et al. 2023). Furthermore, to simulate a distributed subgraph scenario, following the experimental setup of FedNCN (Liu et al. 2025b), we divided each dataset into 5, 10, and 20 clients, respectively, with each client holding a subgraph derived from the original graph.

[0059] Benchmark Methods. We compare IFedGC with three sets of benchmark methods. The first set includes FedNCN, the only clustering method targeting node-level FGL and using attribute-complete graphs. The second set consists of four supervised attribute-complete FGL methods: FedPUB (Baek et al. 2023), FedTAD (Zhu et al. 2024), FedGTA (Li et al. 2024), and FedIIH (Yu et al. 2025). The third set comprises three classic FL aggregation strategies: FedAVG (McMahan et al. 2017), FedPer (Arivazhagan et al. 2019), and FedProx (Li et al. 2020). Details of these methods are provided in Appendix C.2.

[0060] Implementation Details. To ensure a fair comparison, IFedGC and all comparison methods were implemented in PyTorch 2.4.0 and evaluated on an NVIDIA GeForce RTX 4090 GPU. In the attribute missing setting, 30% of the attributes in the node feature matrix were randomly masked as missing, while ensuring no features were completely missing. For the proposed IFedGC, within each client, we learned node embeddings using a GNN and extracted local causal structure from the attribute-completed subgraph using an MLP. Both models were trained using the Adam optimizer with learning rates of 1e-3 and 1e-2, respectively. On the server side, we masked 30% of the clustering key features and global causal structure and optimized using the Adam optimizer with a learning rate of 1e-2. Communication between the client and server took 10 rounds, with each client performing 10 local training iterations per round. To mitigate the negative impact of randomness, each experiment was repeated 5 times, and the mean and standard deviation were reported. For the comparison methods, we used their published code and reported the reproducible results.

[0061] Clustering metrics. To comprehensively evaluate the clustering performance of all methods, we adopted four commonly used evaluation metrics: accuracy (ACC) (Liu et al. 2022b; Wang et al. 2022b,a; Wang, Liu, and Zhu 2022; Cai et al. 2022a), normalized mutual information (NMI) (Liu et al. 2021, 2022a; Wang et al. 2021; Liang et al. 2023; Cai et al. 2022b), adjusted RAND index (ARI) (Yang et al. 2023), and F1 score (F1) (Liu et al. 2023b; Cai et al. 2024a).

[0062] Performance Comparison To validate the effectiveness of IFedGC, the first federated node-level clustering framework for attribute-missing graphs, we employed four representative federated node-level classification methods and a unique federated node-level clustering method, extending them to unsupervised versions for attribute-missing graphs to ensure fair comparison. To mitigate the negative impact of randomness, each experiment was performed five times. Figure 2The report presents the mean and standard deviation of four clustering metrics. Several important observations can be drawn from the experimental results: 1) Under different client assignment settings, IFedGC consistently outperforms FedPUB, FedTAD, FedGTA, and FedIIH on all five datasets. This result demonstrates that IFedGC can effectively perform cluster-guided attribute completion in scenarios with missing attributes; 2) Taking the CiteSeer dataset as an example, IFedGC surpasses FedNCN by 8.9%, 4.5%, and 8.6% in NMI for 5, 10, and 20 clients, respectively. This significant improvement stems from IFedGC integrating the uploaded causal structure and cluster centers into a unified optimization framework and optimizing it through a cluster-based masking strategy. In turn, the optimized causal structure is sent back to the client to guide attribute completion, promoting good cluster separation. To further validate the effectiveness of IFedGC, we compare it with four representative supervised FGL methods (trained using 5% labeled data).

[0063] Figure 2 Performance comparisons of different federated node-level clustering methods are shown on five benchmark datasets. Notably, all comparison methods were evaluated in an unsupervised setting using graphs with missing attributes to ensure a fair comparison. ∗ indicates that these supervised FGL methods have been adapted for unsupervised scenarios with graphs lacking attributes. † indicates that the unsupervised FGL framework has been manually converted to a version suitable for graphs with missing attributes.

[0064] ablation experiment Impact of FL Aggregation Strategies. We evaluated the effectiveness of the aggregation strategies used in IFedGC by comparing them with three classic FL aggregation strategies. In our setup, clustering hints are extracted using a local model and then shared with the server via FL aggregation strategies (i.e., FedAvg, FedProx, and FedPer). Figure 3 The average performance of four clustering metrics and the average improvement relative to the local model are presented. Experimental results show that IFedGC outperforms classic strategies in clustering performance. For example, compared to the local model, IFedGC achieves an average improvement of up to 28.0% on the Cora dataset (5 clients). These findings demonstrate that integrating our aggregation strategy significantly improves the model's generalization ability across different datasets.

[0065] CBM Strategy Analysis. We evaluated the effectiveness of the proposed clustering-based masking (CBM) strategy on the CiteSeer, PubMed, and Cora datasets. In our setup, "IFedGC_V1" represents the IFedGC variant with CBM removed, while "IFedGC_V2" represents the IFedGC variant using random masking. Figure 4 As shown, we can observe that IFedGC consistently outperforms "IFedGC_V1" and "IFedGC_V2" in all four clustering metrics. These findings can be attributed to the following points. First, IFedGC_V1 only integrates multiple local causal structures into a single global structure, which may introduce noise. Second, unlike IFedGC_V2, our CBM strategy selectively masks key clustering features and then completes them using a global causal structure. In this process, the global causal structure is optimized to improve the quality of attribute completion, thereby promoting better clustering.

[0066] Convergence Analysis. To evaluate the stability of IFedGC, we investigated its convergence on the Computer and Photo datasets. The results are as follows: Figure 5 As shown, we recorded the clustering-related metrics of the method and plotted its performance curves during the iteration process. From the results, we can draw the following conclusions: 1) The clustering-related metrics of IFedGC initially showed a significant upward trend, then gradually stabilized with small fluctuations under different client settings; 2) IFedGC converged within 10 local-global interaction iterations on both datasets. These results further confirm the strong convergence and training stability of IFedGC.

[0067] Analysis of hyperparameter k. In formula (10), a hyperparameter λ is introduced to balance the two losses. We studied the sensitivity of λ to IFedGC by analyzing the effect of λ on five datasets, and adjusted the value of λ from 0.01 to 100 in a step of 10. We can observe that: 1) λ plays a key role in IFedGC, indicating that choosing a reasonable range of λ can improve clustering performance; 2) when the value of λ changes from 0.01 to 100, the clustering performance of IFedGC remains relatively stable, proving the robustness of our method; 3) when λ is set to 1, IFedGC generally achieves better clustering performance on all datasets.

[0068] Secondly, such as Figure 6As shown in the illustration, this application provides an apparatus for causal-aware federated graph clustering based on incomplete attributes, comprising: a first acquisition module, configured in each client, for initially completing missing node attributes in the local subgraph to obtain an attribute completion matrix; a second acquisition module, configured in each client, for obtaining local cluster centers and a directed acyclic local causal graph based on the attribute completion matrix; a sending module, configured in each client, for sending the local cluster centers, the local causal structure matrix, and model parameters to a server; and a generation module, configured in the server, for aggregating local cluster centers and local causal structures from multiple clients. The system comprises a structure matrix, which generates global cluster centers and a global causal structure, respectively; a third acquisition module, located on the server, optimizes the global causal structure to obtain an optimized global causal structure; a distribution module, also located on the server, distributes the optimized global causal structure, global cluster centers, and consensus model parameters to each client; and an execution module, also located on the server, updates the local GNN model, multilayer perceptron (MLP) model, and local causal structure based on the optimized global causal structure, global cluster centers, and consensus model parameters, and performs collaborative clustering-oriented attribute completion to improve the clustering performance of local nodes.

[0069] Optionally, the second acquisition module includes: a generation unit, used to generate node embedding vectors based on the attribute completion matrix using a graph neural network (GNN) model; an acquisition unit, used to perform clustering operations on the node embedding vectors to obtain local cluster centers; a first generation unit, used to extract another set of node embedding vectors from the attribute completion matrix using a multilayer perceptron (MLP), and to concatenate the weight vectors of the input layer of the MLP to generate a local causal structure matrix; and a second generation unit, used to generate a corresponding directed acyclic local causal graph based on the local causal structure matrix.

[0070] Optionally, the second generation unit is specifically used to apply acyclic constraints to the local causal structure matrix to eliminate loops and obtain a directed acyclic local causal graph.

[0071] Optionally, the third acquisition module is specifically used to: generate pseudo-labels based on the global clustering center, calculate the mutual information between each feature in the global causal structure and the pseudo-labels, select clustering key features with mutual information higher than a threshold; mask the non-root nodes corresponding to the clustering key features, and optimize the global causal structure based on the masked global causal structure and the global missing indicator matrix to obtain the optimized global causal structure.

[0072] Optionally, the first acquisition module is specifically used for: each client using a feature propagation method to initially complete the missing node attributes in the local subgraph. The apparatus for causal-aware federated graph clustering for incomplete attributes provided in this application embodiment can execute the relevant technical content in the above embodiments, and its implementation principle and technical effect are similar, so they will not be repeated here.

[0073] like Figure 7 As shown in the embodiments of this application, an electronic device is also provided. The electronic device includes a memory and a processor. The memory is used to store a computer program. When the computer program is executed by the processor, it can implement the causal-aware federated graph clustering method for incomplete attributes as described above. For details, please refer to the description of the foregoing embodiments.

[0074] Specifically, at the hardware level, the electronic device may include a processor, an internal bus, and memory. The memory may include main memory and non-volatile memory. The processor reads the corresponding computer program from the non-volatile memory into main memory and then executes it. Those skilled in the art will understand that... Figure 7 The structure shown is for illustrative purposes only and does not limit the structure of the electronic device described above. For example, the electronic device may also include components that are larger than... Figure 7 The components shown may include more or fewer components, such as other processing hardware like a GPU (Graphics Processing Unit) or external communication ports. Of course, this application does not exclude other implementation methods besides software implementations, such as logic devices or a combination of hardware and software.

[0075] In this embodiment, the processor may include a central processing unit (CPU) or a graphics processing unit (GPU), and may also include other microcontrollers, logic gates, integrated circuits, or appropriate combinations thereof with logic processing capabilities. The memory described in this embodiment can be a storage device for storing information. In digital systems, a device capable of storing binary data can be a memory; in integrated circuits, a circuit without physical form but with storage function can also be a memory, such as RAM or FIFO; in a system, a storage device with physical form can also be called a memory. In implementation, this memory can also be implemented using a cloud storage method; the specific implementation method is not limited in this specification.

[0076] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, can implement the causal-aware federated graph clustering method for incomplete attributes as described above.

[0077] This application also provides a computer program product comprising a computer program that, when executed by a processor, implements the method for causal-aware federated graph clustering oriented towards incomplete attributes as described above.

[0078] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments. The above descriptions are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for causal-aware federated graph clustering oriented towards incomplete attributes, characterized in that, include: Each client performs preliminary completion of missing node attributes in its local subgraph to obtain an attribute completion matrix; Each client completes the matrix based on the aforementioned attributes to obtain the local cluster centers and the directed acyclic local causal graph; Each client sends its local cluster center, local causal structure matrix, and model parameters to the server; The server aggregates local cluster centers and local causal structure matrices from multiple clients to generate global cluster centers and global causal structures, respectively. The server optimizes the global causal structure to obtain an optimized global causal structure; The server distributes the optimized global causal structure, global cluster center, and consensus model parameters to each client. Each client updates its local GNN model, MLP model, and local causal structure based on the optimized global causal structure, global cluster center, and consensus model parameters, and performs collaborative clustering-oriented attribute completion to improve the clustering performance of local nodes.

2. The method for causal-aware federated graph clustering oriented towards incomplete attributes according to claim 1, characterized in that, Each client obtains local cluster centers and a directed acyclic local causal graph based on the attribute completion matrix, including: Based on the attribute completion matrix, a node embedding vector is generated using a graph neural network (GNN) model. Perform a clustering operation on the node embedding vectors to obtain local cluster centers; Another set of node embedding vectors is extracted from the attribute completion matrix using a multilayer perceptron (MLP), and the weight vectors of the input layer of the MLP are concatenated to generate a local causal structure matrix. Based on the local causal structure matrix, a corresponding directed acyclic local causal graph is generated.

3. The method for causal-aware federated graph clustering oriented towards incomplete attributes according to claim 2, characterized in that, Based on the local causal structure matrix, a corresponding directed acyclic local causal graph is generated, including: applying acyclic constraints to the local causal structure matrix to eliminate loops, thereby obtaining a directed acyclic local causal graph.

4. The method for causal-aware federated graph clustering oriented towards incomplete attributes according to claim 1, characterized in that, The server optimizes the global causal structure to obtain an optimized global causal structure, including: Pseudo-labels are generated based on the global cluster centers, and the mutual information between each feature in the global causal structure and the pseudo-labels is calculated. Clustering key features with mutual information higher than a threshold are selected. The non-root nodes corresponding to the key clustering features are masked, and the global causal structure is optimized based on the masked global causal structure and the global missing information matrix to obtain the optimized global causal structure.

5. The method for causal-aware federated graph clustering oriented towards incomplete attributes according to claim 1, characterized in that, Each client performs preliminary completion of missing node attributes in its local subgraph, including: Each client uses the feature propagation method to initially complete the missing node attributes in the local subgraph.

6. A device for causal-aware federated graph clustering oriented towards incomplete attributes, characterized in that, include: The first acquisition module, set in each client, is used to initially complete the missing node attributes in the local subgraph to obtain the attribute completion matrix; The second acquisition module, set in each client, is used to complete the matrix based on the attributes and obtain the local cluster center and the directed acyclic local causal graph. The sending module, located in each client, is used to send the local cluster centers, local causal structure matrix, and model parameters to the server. The generation module, located on the server, is used to aggregate local cluster centers and local causal structure matrices from multiple clients to generate global cluster centers and global causal structures, respectively. The third acquisition module, located in the server, is used to optimize the global causal structure to obtain an optimized global causal structure. The distribution module, located on the server, is used to distribute the optimized global causal structure, global cluster center, and consensus model parameters to each client. The execution module, located on the server, is used to update the local GNN model, MLP model, and local causal structure based on the optimized global causal structure, global cluster center, and consensus model parameters, and to perform collaborative clustering-oriented attribute completion to improve the clustering performance of local nodes.

7. The apparatus for causal-aware federated graph clustering oriented towards incomplete attributes according to claim 6, characterized in that, The second acquisition module includes: A generation unit is used to generate node embedding vectors based on the attribute completion matrix and using a graph neural network (GNN) model. The acquisition unit is used to perform clustering operations on the node embedding vectors to obtain local cluster centers; The first generation unit is used to extract another set of node embedding vectors from the attribute completion matrix through a multilayer perceptron (MLP) and to concatenate the weight vectors of the input layer of the MLP to generate a local causal structure matrix. The second generation unit is used to generate a corresponding directed acyclic local causal graph based on the local causal structure matrix.

8. The apparatus for causal-aware federated graph clustering oriented towards incomplete attributes according to claim 7, characterized in that, The second generation unit is specifically used to apply acyclic constraints to the local causal structure matrix to eliminate loops and obtain a directed acyclic local causal graph.

9. The apparatus for causal-aware federated graph clustering oriented towards incomplete attributes according to claim 6, characterized in that, The third acquisition module is specifically used for: Pseudo-labels are generated based on the global cluster centers, and the mutual information between each feature in the global causal structure and the pseudo-labels is calculated. Clustering key features with mutual information higher than a threshold are selected. The non-root nodes corresponding to the key clustering features are masked, and the global causal structure is optimized based on the masked global causal structure and the global missing information matrix to obtain the optimized global causal structure.

10. The apparatus for causal-aware federated graph clustering oriented towards incomplete attributes according to claim 6, characterized in that, The first acquisition module is specifically used for: Each client uses the feature propagation method to initially complete the missing node attributes in the local subgraph.

11. An electronic device comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it causes the electronic device to implement the method as described in any one of claims 1 to 5.

12. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 5.

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