A new optimization criterion for generalized discriminant analysis on undersampled problems

Jieping Ye, Ravi Janardan, Cheong Hee Park, Haesun Park

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

A new optimization criterion for discriminant analysis is presented. The new criterion extends the optimization criteria of the classical linear discriminant analysis (LDA) by introducing the pseudo-inverse when the scatter matrices are singular. It is applicable regardless of the relative sizes of the data dimension and sample size, overcoming a limitation of the classical LDA. Recently, a new algorithm called LDA/GSVD for structure-preserving dimension reduction has been introduced, which extends the classical LDA to very high-dimensional undersampled problems by using the generalized singular value decomposition (GSVD). The solution from the LDA/GSVD algorithm is a special case of the solution for our generalized criterion in this paper, which is also based on GSVD. We also present an approximate solution for our GSVDbased solution, which reduces computational complexity by finding sub-clusters of each cluster, and using their centroids to capture the structure of each cluster. This reduced problem yields much smaller matrices of which the GSVD can be applied efficiently. Experiments on text data, with up to 7000 dimensions, show that the approximation algorithm produces results that are close to those produced by the exact algorithm.

Original languageEnglish (US)
Title of host publicationProceedings - 3rd IEEE International Conference on Data Mining, ICDM 2003
Pages419-426
Number of pages8
StatePublished - Dec 1 2003
Event3rd IEEE International Conference on Data Mining, ICDM '03 - Melbourne, FL, United States
Duration: Nov 19 2003Nov 22 2003

Publication series

NameProceedings - IEEE International Conference on Data Mining, ICDM
ISSN (Print)1550-4786

Other

Other3rd IEEE International Conference on Data Mining, ICDM '03
CountryUnited States
CityMelbourne, FL
Period11/19/0311/22/03

ASJC Scopus subject areas

  • Engineering(all)

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  • Cite this

    Ye, J., Janardan, R., Park, C. H., & Park, H. (2003). A new optimization criterion for generalized discriminant analysis on undersampled problems. In Proceedings - 3rd IEEE International Conference on Data Mining, ICDM 2003 (pp. 419-426). (Proceedings - IEEE International Conference on Data Mining, ICDM).