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Class-incremental generalized discriminant analysis.

Wenming Zheng1

  • 1Research Center for Learning Science, Southeast University, Nanjing, Jiangsu 210096, China. wenming_zheng@seu.edu.cn

Neural Computation
|February 24, 2006
PubMed
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This study introduces a new QR decomposition algorithm for Generalized Discriminant Analysis (GDA), improving incremental updates and numerical stability over traditional SVD methods for small sample problems.

Area of Science:

  • Machine Learning
  • Pattern Recognition
  • Dimensionality Reduction

Background:

  • Generalized Discriminant Analysis (GDA) extends Linear Discriminant Analysis (LDA) using kernel methods.
  • Existing GDA algorithms often rely on Singular Value Decomposition (SVD), posing challenges for incremental learning and large matrix computations.

Purpose of the Study:

  • To propose a novel algorithm for GDA that overcomes the limitations of SVD-based methods, particularly for small sample size problems.
  • To develop an incremental solution for GDA that allows for updating discriminant vectors as new classes are added.

Main Methods:

  • The study proposes a GDA algorithm utilizing QR decomposition instead of SVD.
  • A modified kernel Gram-Schmidt (MKGS) orthogonalization algorithm is introduced for numerically stable QR decomposition in feature space.

Related Experiment Videos

Main Results:

  • The proposed QR decomposition-based GDA algorithm facilitates incremental updates of discriminant vectors.
  • The MKGS algorithm demonstrates superior numerical stability compared to the standard Kernel Gram-Schmidt (KGS) algorithm.
  • Experimental results on simulated and real data validate the enhanced performance of the proposed methods.

Conclusions:

  • The novel QR decomposition approach offers a more stable and incrementally adaptable solution for GDA.
  • This method addresses key limitations of SVD in GDA, especially for scenarios with evolving datasets or small sample sizes.