Eigenface and Fisher FaceComparing Eigen-face and Fisher FaceFisher Linear Discriminating SolutionTechnical ChallengesEigenface and Fisher FaceComparing Eigen-face and Fisher Face•PCA (Eigenface) approach maps features to principle subspaces that contains most energy.•Fisher linear discriminating (FLD, Fisherface) approach maps the feature to subspaces that most separate the two classes.Belhumeur, et al. IEEE Trans PAMI, July 1997, pp 771-720Fisher Linear Discriminating SolutionEquivalent, wopt can be found by maximizing wTSBw subject to wTSWw = 1. This gives a LaGrange Multiplier:arg maxTBoptTwWw S www S w=( )arg max ( )( ) 1Set ( ) 0 0 is a generalized eigenvectoroptwT TB Ww B Ww L wL w w S w w S wL w S w S wwll== - -� = � - =�Technical Challenges•Within cluster scattering matrix SW is often singular in face recognition problem since the # of training faces is often smaller than the # of pixels in a face
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