Graph Learning with Low-rank and Diagonal Structures: A Riemannian Geometric Approach

Abstract

We study the problem of learning graphs in Gaussian graphic models by assuming that the underlying precision matrix has a "low-rank and diagonal" (LRaD) structure. This assumption enjoys a latent factor representation interpretation and can reduce the dimensionality of the problem, thus leading to superior performance with fewer samples. To address the optimization challenges caused by the LRaD constraint, we design a Riemannian quotient manifold to transform the proposed model into an unconstrained problem on the manifold. Then, we devise a Riemannian conjugate gradient algorithm to solve the proposed model. Experimental results on synthetic and real data illustrate the effectiveness of the proposed method.