Graph representations using adjacency matrix transforms for clustering

Abstract

This paper is meant as a proof of concept regarding the application of standard 2D signal representation and feature extraction tools that have wide use in their respective fields to graph related pattern recognition tasks such as, in this case, clustering. By viewing the adjacency matrix of a graph as a 2-dimensional signal, we can apply 2D Discrete Cosine Transform (DCT) to it and use the relation between the adjacency matrix and the values of the DCT bases in order to cluster nodes into strongly connected components. By viewing the adjacency matrices of multiple graphs as feature vectors, we can apply Principal Components Analysis (PCA) to decorrelate them and achieve better clustering performance. Experimental results on synthetic data indicate that there is potential in the use of such techniques to graph analysis.