Fast Hybrid Algorithm for Big Matrix Recovery

Tengfei Zhou, Hui Qian, Zebang Shen, Congfu Xu
2016 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Large-scale Nuclear Norm penalized Least Square problem (NNLS) is frequently encountered in estimation of low rank structures. In this paper we accelerate the solution procedure by combining non-smooth convex optimization with smooth Riemannian method. Our methods comprise of two phases. In the first phase, we use Alternating Direction Method of Multipliers (ADMM) both to identify the fix rank manifold where an optimum resides and to provide an initializer for the subsequent refinement. In the
more » ... econd phase, two superlinearly convergent Riemannian methods: Riemannian NewTon (NT) and Riemannian Conjugate Gradient descent (CG) are adopted to improve the approximation over a fix rank manifold. We prove that our Hybrid method of ADMM and NT (HADMNT) converges to an optimum of NNLS at least quadratically. The experiments on large-scale collaborative filtering datasets demonstrate very competitive performance of these fast hybrid methods compared to the state-of-the-arts.
doi:10.1609/aaai.v30i1.10161 fatcat:g6rzzemefjdgdfu5ziff4yaoqi