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An optimization criterion for generalized discriminant analysis on undersampled problems.

Jieping Ye1, Ravi Janardan, Cheong Hee Park

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

IEEE Transactions on Pattern Analysis and Machine Intelligence
|January 12, 2005
PubMed
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This study introduces a new optimization criterion for discriminant analysis, extending Linear Discriminant Analysis (LDA) using the pseudoinverse for singular matrices. This method works for any data dimension and sample size, offering a more robust approach to classification problems.

Area of Science:

  • Machine Learning
  • Data Science
  • Pattern Recognition

Background:

  • Classical Linear Discriminant Analysis (LDA) faces limitations with singular scatter matrices and when data dimensions exceed sample size.
  • Existing methods for undersampled problems often lack theoretical justification.

Purpose of the Study:

  • To present a novel optimization criterion for discriminant analysis that overcomes limitations of classical LDA.
  • To provide a theoretical foundation for using the pseudoinverse in undersampled discriminant analysis.
  • To develop an efficient approximation algorithm for the proposed method.

Main Methods:

  • The proposed criterion extends classical LDA by employing the pseudoinverse for singular scatter matrices.
  • The optimization problem is solved analytically using Generalized Singular Value Decomposition (GSVD).

Related Experiment Videos

  • An approximation algorithm is introduced that reduces computational complexity by using cluster centroids.

    • Main Results:

    • The new criterion is applicable irrespective of the relative data dimension and sample size.
    • The GSVD technique provides an analytical solution to the optimization problem.
    • The approximation algorithm yields results comparable to the exact GSVD method on high-dimensional text data.

    Conclusions:

    • The presented optimization criterion offers a theoretically sound and broadly applicable extension to LDA.
    • The GSVD-based approach and its approximation algorithm enhance discriminant analysis for complex datasets.
    • The findings are particularly relevant for high-dimensional pattern recognition tasks, such as text analysis.