Supervised dimensionality reduction via sequential semidefinite programming

Date

2008

Authors

Shen, Chunhua
Li, Hongdong
Brooks, Michael

Journal Title

Journal ISSN

Volume Title

Publisher

Pergamon-Elsevier Ltd

Abstract

Many dimensionality reduction problems end up with a trace quotient formulation. Since it is difficult to directly solve the trace quotient problem, traditionally the trace quotient cost function is replaced by an approximation such that the generalized eigenvalue decomposition can be applied. In contrast, we directly optimize the trace quotient in this work. It is reformulated as a quasi-linear semidefinite optimization problem, which can be solved globally and efficiently using standard off-the-shelf semidefinite programming solvers. Also this optimization strategy allows one to enforce additional constraints (for example, sparseness constraints) on the projection matrix. We apply this optimization framework to a novel dimensionality reduction algorithm. The performance of the proposed algorithm is demonstrated in experiments by several UCI machine learning benchmark examples, USPS handwritten digits as well as ORL and Yale face data.

Description

Keywords

Keywords: Artificial intelligence; Demodulation; Learning algorithms; Learning systems; Nonlinear programming; Standards; Dimensionality reduction; Dimensionality reduction algorithms; Face data; Generalized eigenvalue decomposition; Handwritten digits; Linear disc Dimensionality reduction; Linear discriminant analysis; Semidefinite programming

Citation

Source

Pattern Recognition

Type

Journal article

Book Title

Entity type

Access Statement

License Rights

Restricted until

2037-12-31