Supervised dimensionality reduction via sequential semidefinite programming

Chunhua Shen*, Hongdong Li, Michael J. Brooks

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    25 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)3644-3652
    Number of pages9
    JournalPattern Recognition
    Issue number12
    Publication statusPublished - Dec 2008


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