PSDBoost: Matrix-generation linear programming for positive semidefinite matrices learning

Abstract

In this work, we consider the problem of learning a positive semidefinite matrix. The critical issue is how to preserve positive semidefiniteness during the course of learning. Our algorithm is mainly inspired by LPBoost [1] and the general greedy convex optimization framework of Zhang [2]. We demonstrate the essence of the algorithm, termed PSDBoost (positive semidefinite Boosting), by focus-ing on a few different applications in machine learning. The proposed PSDBoost algorithm extends traditional Boosting algorithms in that its parameter is a posi-tive semidefinite matrix with trace being one instead of a classifier. PSDBoost is based on the observation that any trace-one positive semidefinite matrix can be de-composed into linear convex combinations of trace-one rank-one matrices, which serve as base learners of PSDBoost. Numerical experiments are presented. 1