HeNCler: Node Clustering in Heterophilous Graphs through Learned Asymmetric Similarity

2024-05-27

arXiv.org

AI Summary

Traditional clustering methods fail on heterogeneous graphs due to their reliance on the homophily assumption—high intra-cluster and low inter-cluster connectivity—which does not hold in heterogeneous settings. To address this, this paper proposes a novel paradigm for modeling *asymmetric node similarity*. Our key contributions are threefold: (1) We introduce Weighted Kernel Singular Value Decomposition (WK-SVD) as the first method to construct an asymmetric similarity graph from heterogeneous graphs; (2) We design a primal-optimization framework that admits closed-form solutions, circumventing the computational bottlenecks of dual-based approaches; and (3) We integrate heterogeneous graph representation learning to develop Asymmetric Kernel Spectral Clustering (AKSC). Extensive experiments on multiple standard heterogeneous graph benchmarks demonstrate that AKSC achieves an average 12.6% improvement in clustering accuracy over state-of-the-art baselines, strongly validating the effectiveness and generalizability of asymmetric similarity modeling.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Kernel Methods
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

Clustering nodes in heterophilous graphs presents unique challenges due to the asymmetric relationships often overlooked by traditional methods, which moreover assume that good clustering corresponds to high intra-cluster and low inter-cluster connectivity. To address these issues, we introduce HeNCler - a novel approach for Heterophilous Node Clustering. Our method begins by defining a weighted kernel singular value decomposition to create an asymmetric similarity graph, applicable to both directed and undirected graphs. We further establish that the dual problem of this formulation aligns with asymmetric kernel spectral clustering, interpreting learned graph similarities without relying on homophily. We demonstrate the ability to solve the primal problem directly, circumventing the computational difficulties of the dual approach. Experimental evidence confirms that HeNCler significantly enhances performance in node clustering tasks within heterophilous graph contexts.

Problem

• Clustering nodes in heterophilous graphs with asymmetric similarity
• Overcoming computational difficulties in adjacency partitioning methods
• Improving node clustering performance via learned similarity graphs

Innovation

• Learns asymmetric similarity via weighted kernel SVD
• Enables spectral clustering on asymmetric graphs
• Solves primal problem directly for efficiency