Learning anisotropic filters on product graphs

The extension of convolutional neural networks to irregular domains has pavedthe way to promising graph data analysis methods. It has however come at theexpense of a reduced representation power, as most of these new network archi-tectures can only learn isotropic filters and therefore often underfit the trainingdata. In this work, we propose a method for building anisotropic filters whenlearning representations of signals on a cartesian product graph. Instead of learn-ing directly on the product graph, we factorize it and learn different filters foreach factor, which is beneficial both in terms of computational cost and expressiv-ity of the filters. We show experimentally that anisotropic Laplacian polynomialsindeed outperform their isotropic counterpart on image classification and matrixcompletion tasks.