NDLI: A new optimization criterion for generalized discriminant analysis on undersampled problems

Content Provider	IEEE Xplore Digital Library
Author	Ye, J. Janardan, Ravi Park, C.H. Park, H.
Copyright Year	2003
Description	Author affiliation: Dept. of Comput. Sci. & Eng., Minnesota Univ., Minneapolis, MN, USA (Ye, J.; Ravi Janardan; Park, C.H.; Park, H.)
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, which is also based on GSVD. We also present an approximate solution for our GSVD-based solution, which reduces computational complexity by finding subclusters 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.
Sponsorship	IEEE Comput. Soc. Tech. Committee on Computational Intelligence IEEE Comput. Soc. Tech. Committee on Pattern Analysis and Machine Intelligence
Starting Page	419
Ending Page	426
File Size	483270
Page Count	8
File Format	PDF
ISBN	0769519784
DOI	10.1109/ICDM.2003.1250948
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2003-11-22
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Linear discriminant analysis Clustering algorithms Matrix decomposition Singular value decomposition Approximation algorithms Data mining Scattering Computational complexity Computer science High performance computing
Content Type	Text
Resource Type	Article

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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