Spectral Graph Partitioning Based on a Random Walk Diffusion Similarity Measure

Abstract

Spectral graph partitioning is a powerful tool for unsupervised data learning. Most existing algorithms for spectral graph partitioning directly utilize the pairwise similarity matrix of the data to perform graph partitioning. Consequently, they are incapable of fully capturing the intrinsic structural information of graphs. To address this problem, we propose a novel random walk diffusion similarity measure (RWDSM) for capturing the intrinsic structural information of graphs. The RWDSM is composed of three key components—emission, absorbing, and transmission. It is proven that graph partitioning on the RWDSM matrix performs better than on the pairwise similarity matrix of the data. Moreover, a spectral graph partitioning objective function (referred to as DGPC) is used for capturing the discriminant information of graphs. The DGPC is designed to effectively characterize the intra-class compactness and the inter-class separability. Based on the RWDSM and DGPC, we further develop a novel spectral graph partitioning algorithm (referred to as DGPCA). Theoretic analysis and experimental evaluations demonstrate the promise and effectiveness of the developed DGPCA.