Matrix Means for Signed and Multilayer Graph Clustering


In this talk we present an extension of spectral clustering for the case when different kinds of interactions are present. We study suitable matrix functions to merge information that comes from different kinds of interactions encoded in multilayer graphs, and their effect in cluster identification. We consider a one-parameter family of matrix functions, known as matrix power means, and show that different means identify clusters under different settings of the stochastic block model in expectation. For instance, we show that a limit case identifies clusters if at least one layer is informative and the remaining layers are potentially just noise.