Clustering with Multi-Layer Graphs: A Spectral Perspective

TL;DR

This paper introduces two spectral methods for multi-layer graph clustering, effectively combining information from different graph layers to improve clustering accuracy over existing techniques.

Contribution

It proposes novel joint spectrum methods based on matrix factorization and graph regularization for multi-layer graph clustering, demonstrating superior performance.

Findings

Outperforms state-of-the-art clustering methods

Effective in social network data analysis

Shows robustness across multiple datasets

Abstract

Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this paper, we address the problem of combining different layers of the multi-layer graph for improved clustering of the vertices compared to using layers independently. We propose two novel methods, which are based on joint matrix factorization and graph regularization framework respectively, to efficiently combine the spectrum of the multiple graph layers, namely the eigenvectors of the graph Laplacian matrices. In each case, the resulting combination, which we call a "joint spectrum" of multiple graphs, is used for clustering the vertices. We evaluate our approaches by simulations with several real world social network datasets. Results demonstrate the superior or competitive performance of the proposed methods over state-of-the-art technique and common baseline methods, such as co-regularization and summation of information from individual graphs.