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ACCV
2007
Springer

A Convex Programming Approach to the Trace Quotient Problem

9 years 1 months ago
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...
Chunhua Shen, Hongdong Li, Michael J. Brooks
Added 18 Oct 2010
Updated 18 Oct 2010
Type Conference
Year 2007
Where ACCV
Authors Chunhua Shen, Hongdong Li, Michael J. Brooks
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