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Generalizing discriminant analysis using the generalized singular value decomposition.

Peg Howland1, Haesun Park

  • 1Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN 55455, USA. howland@cs.umn.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|January 12, 2005
PubMed
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This study generalizes discriminant analysis using generalized singular value decomposition. This overcomes limitations with matrix nonsingularity, enabling feature extraction for datasets with fewer samples than dimensions.

Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Discriminant analysis is a feature extraction technique that uses covariance matrices.
  • Its application is limited by the nonsingularity requirement of these matrices.
  • This nonsingularity constraint restricts use with datasets where sample size is less than data dimension.

Purpose of the Study:

  • To generalize discriminant analysis by overcoming the nonsingularity requirement.
  • To extend the applicability of discriminant analysis to datasets with limited sample sizes.
  • To explore alternative optimization criteria for feature extraction.

Main Methods:

  • Utilized generalized singular value decomposition (GSVD) to circumvent matrix nonsingularity.
  • Examined various optimization criteria for discriminant analysis.

Related Experiment Videos

  • Applied GSVD to the scatter matrices within and between clusters.

    • Main Results:

    • Developed a generalized discriminant analysis applicable to datasets with sample size smaller than data dimension.
    • The generalized method effectively extracts features preserving class separability.
    • Classification results demonstrate the approach's effectiveness compared to alternatives.

    Conclusions:

    • The generalized discriminant analysis offers a robust solution for feature extraction.
    • GSVD effectively removes the nonsingularity limitation of traditional methods.
    • This approach enhances the utility of discriminant analysis across diverse datasets.