Title: A statistical interpretation of spectral embedding: The generalised random dot product graph
Authors: Patrick Rubin-delanchy - University of Bristol (United Kingdom)
Joshua Cape - University of Pittsburgh (United States) [presenting]
Minh Tang - North Carolina State University (United States)
Carey Priebe - Johns Hopkins University (United States)
Abstract: The purpose is to introduce the generalised random dot product graph model, a latent space network model that provides a unified setting in which to study spectral clustering methods, factorizations of matrices, and the geometry of point cloud configurations. We establish that, for both the normalised Laplacian and adjacency matrix, the vector representations of nodes obtained by spectral embedding provide strongly consistent latent position estimates with asymptotically Gaussian error. Direct methodological consequences follow from the observation that mixed membership and standard stochastic block models are special cases where the latent positions live respectively inside or on the vertices of a simplex. Hence, estimation via spectral embedding can be achieved by estimating the simplicial support or by fitting a Gaussian mixture model, respectively. We highlight applications of our results to the analysis of cybersecurity data and connectomics.