Learning modes of structural variation in graphs

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.