Spectral method for learning structural variations in graphs

The 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.