Dual-Optimized Adaptive Graph Reconstruction for Multi-View Graph Clustering

Multi-view clustering is an important machine learning task for multi-media data, encompassing various domains such as images, videos, and texts. Moreover, with the growing abundance of graph data, the significance of multi-view graph clustering (MVGC) has become evident. Most existing methods focus on graph neural networks (GNNs) to extract information from both graph structure and feature data to learn distinguishable node representations. However, traditional GNNs are designed with the assumption of homophilous graphs, making them unsuitable for widely prevalent heterophilous graphs. Several techniques have been introduced to enhance GNNs for heterophilous graphs. While these methods partially mitigate the heterophilous graph issue, they often neglect the advantages of traditional GNNs, such as their simplicity, interpretability, and efficiency. In this paper, we propose a novel multi-view graph clustering method based on dual-optimized adaptive graph reconstruction, named DOAGC. It mainly aims to reconstruct the graph structure adapted to traditional GNNs to deal with heterophilous graph issues while maintaining the advantages of traditional GNNs. Specifically, we first develop an adaptive graph reconstruction mechanism that accounts for node correlation and original structural information. To further optimize the reconstruction graph, we design a dual optimization strategy and demonstrate the feasibility of our optimization strategy through mutual information theory. Numerous experiments demonstrate that DOAGC effectively mitigates the heterophilous graph problem.

SiMilarity-Enhanced Homophily for Multi-View Heterophilous Graph Clustering

With the increasing prevalence of graph-structured data, multi-view graph clustering has been widely used in various downstream applications. Existing approaches primarily rely on a unified message passing mechanism, which significantly enhances clustering performance. Nevertheless, this mechanism limits its applicability to heterophilous situations, as it is fundamentally predicated on the assumption of homophily, i.e., the connected nodes often belong to the same class. In reality, this assumption does not always hold; a moderately or even mildly homophilous graph is more common than a fully homophilous one due to inevitable heterophilous information in the graph. To address this issue, in this paper, we propose a novel SiMilarity-enhanced Homophily for Multi-view Heterophilous Graph Clustering (SMHGC) approach. By analyzing the relationship between similarity and graph homophily, we propose to enhance the homophily by introducing three similarity terms, i.e., neighbor pattern similarity, node feature similarity, and multi-view global similarity, in a label-free manner. Then, a consensus-based inter- and intra-view fusion paradigm is proposed to fuse the improved homophilous graph from different views and utilize them for clustering. The state-of-the-art experimental results on both multi-view heterophilous and homophilous datasets collectively demonstrate the strong capacity of similarity for unsupervised multi-view heterophilous graph learning. Additionally, the consistent performance across semi-synthetic datasets with varying levels of homophily serves as further evidence of SMHGC's resilience to heterophily.

Homophily-Related: Adaptive Hybrid Graph Filter for Multi-View Graph Clustering

Recently there is a growing focus on graph data, and multi-view graph clustering has become a popular area of research interest. Most of the existing methods are only applicable to homophilous graphs, yet the extensive real-world graph data can hardly fulfill the homophily assumption, where the connected nodes tend to belong to the same class. Several studies have pointed out that the poor performance on heterophilous graphs is actually due to the fact that conventional graph neural networks (GNNs), which are essentially low-pass filters, discard information other than the low-frequency information on the graph. Nevertheless, on certain graphs, particularly heterophilous ones, neglecting high-frequency information and focusing solely on low-frequency information impedes the learning of node representations. To break this limitation, our motivation is to perform graph filtering that is closely related to the homophily degree of the given graph, with the aim of fully leveraging both low-frequency and high-frequency signals to learn distinguishable node embedding. In this work, we propose Adaptive Hybrid Graph Filter for Multi-View Graph Clustering (AHGFC). Specifically, a graph joint process and graph joint aggregation matrix are first designed by using the intrinsic node features and adjacency relationship, which makes the low and high-frequency signals on the graph more distinguishable. Then we design an adaptive hybrid graph filter that is related to the homophily degree, which learns the node embedding based on the graph joint aggregation matrix. After that, the node embedding of each view is weighted and fused into a consensus embedding for the downstream task. Experimental results show that our proposed model performs well on six datasets containing homophilous and heterophilous graphs.

Variational Graph Generator for Multi-View Graph Clustering

Multi-view graph clustering (MGC) methods are increasingly being studied due to the rising of multi-view data with graph structural information. The critical point of MGC is to better utilize the 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 infer 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 consensus and view-specific graphs together with features. Finally, theoretical results illustrate the rationality of VGMGC by analyzing the uncertainty of the inferred consensus graph with information bottleneck principle. Extensive experiments demonstrate the superior performance of our VGMGC over SOTAs.