Learning graph Laplacian from intrinsic patterns via Gaussian process

In this paper, we present a novel scheme to learn a graph topology named Laplacian constrained Gaussian process (LCGP). Previous graph learning methods directly use raw observed signals, which often degrades estimation accuracy due to the noise effects and the sample imbalances. LCGP tackles this problem by introducing a small number of intrinsic patterns, that is, LCGP assumes representative signals on a graph. These signals are derived as Bayesian latent variables, and we estimate the graph topology with objective after marginalizing them. Furthermore, the number of the intrinsic patterns is automatically determined by a Bayesian inference procedure. In the experiment, we compared LCGP with baseline and state-of-the-art methods in graph learning and confirmed the effectiveness of LCGP.