Fast Gradient Methods for Symmetric Nonnegative Matrix Factorization.

TITLE: Fast Gradient Methods for Symmetric Nonnegative Matrix Factorization.

AUTHORS: Radu-Alexandru Dragomir, Jérôme Bolte, Alexandre d'Aspremont.

ABSTRACT: We study a generalized nonconvex Burer-Monteiro formulation for low-rank minimization problems. We use recent results on non-Euclidean first order methods to provide efficient and scalable algorithms. Our approach uses geometries induced by quartic kernels on matrix spaces; for unconstrained cases we introduce a novel family of Gram kernels that considerably improves numerical performances. Numerical experiments for Euclidean distance matrix completion and symmetric nonnegative matrix factorization show that our algorithms scale well and reach state of the art performance when compared to specialized methods.

STATUS: Submitted

ArXiv PREPRINT: ArXiv:1901.10791

PAPER: Fast Gradient Methods for Symmetric Nonnegative Matrix Factorization in pdf