Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:C1L-C
Session:
Number:C1L-C1
A Derivation of the Trace Difference ??Optimization Algorithm for the Trace Ratio Optimization Problem
Kohei Inoue, Kenji Hara, Kiichi Urahama,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
It is well known that a large number of problems for dimensionality reduction result in the trace ratio optimization problem (TROP). Recently, Wang et al. have proposed an iterative procedure for solving TROP. They transform TROP into a trace difference optimization problem (TDOP) which is effciently solved with the eigenvalue decomposition method. However, the mechanism of the transformation of TROP into TDOP is not clear in their papers. In this paper, we derive the TDO algorithm for TROP on the basis of the Lagrange multipliers. Moreover, we show that multilinear principal component analysis proposed by Lu et al. recently is a special case of tensor sub-space learning which is also formulated as a TROP.