Trace Ratio vs. Ratio Trace for Dimensionality Reduction

A large family of algorithms for dimensionality reduction end with solving a Trace Ratio problem in the form of arg maxW Tr(WT SpW)/Tr(WT SlW)1 , which is generally transformed into the corresponding Ratio Trace form arg maxW Tr[ (WT SlW)-1 (WT SpW) ] for obtaining a closed-form but inexact solution. In this work, an efficient iterative procedure is presented to directly solve the Trace Ratio problem. In each step, a Trace Difference problem arg maxW Tr[WT (Sp -Sl)W] is solved with being the trace ratio value computed from the previous step. Convergence of the projection matrix W, as well as the global optimum of the trace ratio value , are proven based on point-to-set map theories. In addition, this procedure is further extended for solving trace ratio problems with more general constraint WT CW=I and providing exact solutions for kernel-based subspace learning problems. Extensive experiments on faces and UCI data demonstrate the high convergence speed of the proposed solution, as w...

• Type: Conference
• Year: 2007
• Where: CVPR
• Authors: Huan Wang, Shuicheng Yan, Dong Xu, Xiaoou Tang, Thomas S. Huang
• Keywords: Computer Vision, Corresponding Ratio Trace, CVPR 2007, Ratio Trace Problem, Trace Ratio Problem, Trace Ratio Problems, Trace Ratio Value