A spectral approach to learning structural variations in graphs

Abstract

This paper investigates the use of graph-spectral methods for learning the modes of structural variation in sets of graphs. Our approach is as follows. First, we vectorise the adjacency matrices of the graphs. Using a graph-matching method we establish correspondences between the components of the vectors. Using the correspondences we cluster the graphs using a Gaussian mixture model. For each cluster we compute the mean and covariance matrix for the vectorised adjacency matrices. We allow the graphs to undergo structural deformation by linearly perturbing the mean adjacency matrix in the direction of the modes of the covariance matrix. We demonstrate the method on sets of corner Delaunay graphs for 3D objects viewed from varying directions. © Springer-Verlag Berlin Heidelberg 2003.