What's wrong with Fisher criterion?

“…Optimal γ j can be found by maximizing (5) under suitable constraints (Yang et al 2002). The most common one is the constraint of the classical linear discriminant analysis (CDA):…”

Section: Notation and Fisher Criterionmentioning

confidence: 99%

Linear dimension reduction in classification: adaptive procedure for optimum results

Luebke

Weihs

2011

Adv Data Anal Classif

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“…The problems caused by the singularity of the scatter matrices on undersampled problems are circumvented by two-stage decompositions of the scatter matrices [14,15,16], and the criterion itself of LDA is criticized in [17]. Howland et al [18,19] applied the generalized singular value decomposition (GSVD) due to Paige and Saunders [20] which is applicable for undersampled problems.…”

Section: Linear Discriminant Analysismentioning

confidence: 99%

A Relationship between Linear Discriminant Analysis and the Generalized Minimum Squared Error Solution

Park¹,

Park²

2005

SIAM J. Matrix Anal. & Appl.

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Abstract. In this paper, a relationship between linear discriminant analysis (LDA) and the generalized minimum squared error (MSE) solution is presented. The generalized MSE solution is shown to be equivalent to applying a certain classification rule in the space defined by LDA. The relationship between the MSE solution and Fisher discriminant analysis is extended to multiclass problems and also to undersampled problems for which the classical LDA is not applicable due to singularity of the scatter matrices. In addition, an efficient algorithm for LDA is proposed exploiting its relationship with the MSE procedure. Extensive experiments verify the theoretical results.

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“…Note that here, in order to eliminate the statistical correlation between the LDA-transformed features, the projection axes are required to satisfy the S t -orthogonal constraints rather than the usual orthogonal constraints [7,17,19]. Yang et al [17] have proved that the optimal projection axes w 1 ; …; w d (d # c 2 1; where c is the number of classes) can be selected as the S t -orthogonal generalized eigenvectors corresponding to d largest eigenvalues of the generalized eigen-equation S b X ¼ lS w X: The following algorithm can be used to determine the optimal projection axes w 1 ; …; w d :…”

Section: Complex Fisher Linear Discriminant Analysismentioning

confidence: 99%