A FastMap-Based Algorithm for Block Modeling

Ang Li, Peter J. Stuckey, Sven Koenig, T. K. Satish Kumar

Abstract: Block modeling algorithms are used to discover important latent structures in graphs. They are the graph equivalent of clustering algorithms. However, existing block modeling algorithms work directly on the given graphs, making them computationally expensive and less effective on large complex graphs. In this paper, we propose a FastMap-based algorithm for block modeling on single-view undirected graphs. FastMap embeds a given undirected graph into a Euclidean space in near-linear time such that the pairwise Euclidean distances between vertices approximate a desired graph-based distance function between them. In the first phase, our FastMap-based block modeling (FMBM) algorithm uses FastMap with a probabilistically-amplified shortest-path distance function between vertices. In the second phase, it uses Gaussian Mixture Models (GMMs) for identifying clusters (blocks) in the resulting Euclidean space. FMBM outperforms other state-of-the-art methods on many benchmark and synthetic instances, both in efficiency and solution quality. It also enables a perspicuous visualization of clusters (blocks) in the graphs, not provided by other methods.