Spectral feature vectors for graph clustering

Abstract

This paper investigates whether vectors of graph-spectral features can be used for the purposes of graph-clustering. We commence from the eigenvalues and eigenvectors of the adjacency matrix. Each of the leading eigenmodes represents a cluster of nodes and is mapped to a component of a feature vector. The spectral features used as components of the vectors are the eigenvalues, the cluster volume, the cluster perimeter, the cluster Cheeger constant, the inter-cluster edge distance, and the shared perimeter length. We explore whether these vectors can be used for the purposes of graph-clustering. Here we investigate the use of both central and pairwise clustering methods. On a data-base of view-graphs, the vectors of eigenvalues and shared perimeter lengths provide the best clusters.