GA-Fisher: A new LDA-based face recognition algorithm with selection of principal components

Wei Shi Zheng*, Jian Huang Lai, Pong Chi YUEN

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

86 Citations (Scopus)


This paper addresses the dimension reduction problem in Fisherface for face recognition. When the number of training samples is less than the image dimension (total number of pixels), the within-class scatter matrix (Sw) in Linear Discriminant Analysis (LDA) is singular, and Principal Component Analysis (PCA) is suggested to employ in Fisherface for dimension reduction of Sw so that it becomes nonsingular. The popular method is to select the largest nonzero eigenvalues and the corresponding eigenvectors for LDA. To attenuate the illumination effect, some researchers suggested removing the three eigenvectors with the largest eigenvalues and the performance is improved. However, as far as we know, there is no systematic way to determine which eigenvalues should be used. Along this line, this paper proposes a theorem to interpret why PCA can be used in LDA and an automatic and systematic method to select the eigenvectors to be used in LDA using a Genetic Algorithm (GA). A GA-PCA is then developed. It is found that some small eigenvectors should also be used as part of the basis for dimension reduction. Using the GA-PCA to reduce the dimension, a GA-Fisher method is designed and developed. Comparing with the traditional Fisherface method, the proposed GA-Fisher offers two additional advantages. First, optimal bases for dimensionality reduction are derived from GA-PCA. Second, the computational efficiency of LDA is improved by adding a whitening procedure after dimension reduction. The Face Recognition Technology (FERET) and Carnegie Mellon University Pose, Illumination, and Expression (CMU PIE) databases are used for evaluation. Experimental results show that almost 5% improvement compared with Fisherface can be obtained, and the results are encouraging.

Original languageEnglish
Pages (from-to)1065-1078
Number of pages14
JournalIEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Issue number5
Publication statusPublished - Oct 2005

Scopus Subject Areas

  • Control and Systems Engineering
  • Software
  • Information Systems
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering

User-Defined Keywords

  • Dimension reduction
  • Face recognition
  • GA-PCA
  • Genetic algorithms
  • LDA
  • PCA


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