A Convex Programming Approach to the Trace Quotient Problem

Abstract. The trace quotient problem arises in many applications in pattern classification and computer vision, e.g., manifold learning, low-dimension embedding, etc. The task is to solve a optimization problem involving maximizing the ratio of two traces, i.e., maxW Tr(f(W ))/Tr(h(W )). This optimization problem itself is non-convex in general, hence it is hard to solve it directly. Conventionally, the trace quotient objective function is replaced by a much simpler quotient trace formula, i.e., maxW Tr   h(W )−1 f(W ) ¡ , which accommodates a much simpler solution. However, the result is no longer optimal for the original problem setting, and some desirable properties of the original problem are lost. In this paper we proposed a new formulation for solving the trace quotient problem directly. We reformulate the original non-convex problem such that it can be solved by efficiently solving a sequence of semidefinite feasibility problems. The solution is therefore globally optimal...

• Type: Conference
• Year: 2007
• Where: ACCV
• Authors: Chunhua Shen, Hongdong Li, Michael J. Brooks
• Keywords: ACCV 2007, Computer Vision, Optimization Problem, Quotient Problem Arises, Trace Quotient Problem