Variational Graph Generator for Multi-View Graph Clustering

TL;DR

This work addresses multi-view graph clustering by learning a discrete variational consensus graph that captures both shared topological structure and view-specific information. It introduces a parameter-free, transformer-style inference of the consensus graph and a simple yet effective graph encoder to fuse consensus and view graphs into per-view embeddings, followed by a self-supervised belief-based multi-view fusion for clustering. The approach is theoretically grounded in an information-bottleneck perspective and a variational IB framework, delivering a tractable ELBO-based objective and a lower bound on mutual information to optimize embeddings. Empirically, VGMGC achieves competitive to state-of-the-art results across eight diverse datasets, with ablation studies confirming the importance of the consensus graph, reconstruction terms, and belief-based fusion. The method offers a scalable, robust framework for leveraging cross-view information in graph-structured data, with potential extensions to other graph-related tasks.

Abstract

Multi-view graph clustering (MGC) methods are increasingly being studied due to the explosion of multi-view data with graph structural information. The critical point of MGC is to better utilize view-specific and view-common information in features and graphs of multiple views. However, existing works have an inherent limitation that they are unable to concurrently utilize the consensus graph information across multiple graphs and the view-specific feature information. To address this issue, we propose Variational Graph Generator for Multi-View Graph Clustering (VGMGC). Specifically, a novel variational graph generator is proposed to extract common information among multiple graphs. This generator infers a reliable variational consensus graph based on a priori assumption over multiple graphs. Then a simple yet effective graph encoder in conjunction with the multi-view clustering objective is presented to learn the desired graph embeddings for clustering, which embeds the inferred view-common graph and view-specific graphs together with features. Finally, theoretical results illustrate the rationality of the VGMGC by analyzing the uncertainty of the inferred consensus graph with the information bottleneck principle.Extensive experiments demonstrate the superior performance of our VGMGC over SOTAs. The source code is publicly available at https://github.com/cjpcool/VGMGC.

Figures (7)

• Figure 1: Two types of multi-view graph clustering. $\oplus$ denotes any combination operation (e.g., concatenation). One type tries to capture consensus topological information, but view-specific information in features is ignored (left); another type embeds view-specific graphs at first, then learns a global embedding cooperatively, but global topological information is lost (right).
• Figure 2: Overview of the VGMGC framework. The symbols $\overline{\mathbf{X}}$, $\hat{\mathbf{S}}$, $\mathbf{A}^v$ and $\mathbf{Z}^v$ represent the global representation derived from all views $\{\textbf{X}^v\}^V_{v=1}$, the learned consensus graph, the adjacency matrix, and final output representations of $v$-th view, respectively. $q(\cdot)$ and $p(\cdot)$ denote the posterior and prior probabilities, respectively. Symbol $\oplus$ denotes the concatenation operation. $\psi(\cdot)$ is the proposed message passing scheme in Eq. \ref{['eqMessagePassing']} and $f(\cdot)$ is the MLP for low-dimensional representation learning. VGMGC first infers a cross-view consensus graph $\mathbf{\hat{S}}$ by the variational graph generator (a). Then this variational consensus graph, combined with each attributed view-specific graph, is processed by the global and specific graph encoder (b). This encoder generates the latent features $\mathbf{Z}^v$ for each view. Finally, the latent features from all views are weighted and concatenated for training and clustering (c).
• Figure 3: The Bayesian net of our variational graph generator about variables: $\mathbf{A}^v$, $\mathbf{\hat{S}}$, $\mathbf{\overline{X}}$ and $\mathbf{X}^v$.
• Figure 4: The learned $b^v$ on six multi-view datasets, which shows the task relevance of each view. The parameter $\rho$ is fixed to $1$ in this figure. 'AMZ' means Amazon and 'CS' denotes Computers.
• Figure 5: The performance of VGMGC with different orders (left), and the training process on ACM (right).

Theorems & Definitions (10)

• Theorem 1: Consensus among graphs
• proof : Proof
• Theorem 2: Task relevance of each graph
• proof : Proof
• Corollary 1
• Definition 1: Supervised IB
• Definition 2: Variational graph IB
• Theorem 3
• proof : Proof
• Definition 3