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Full rank principal component analysis (FR-PCA) is a special form of principal component analysis (PCA) which retains all nonzero components of PCA. Generally speaking, it is hard to estimate how the accuracy of a classifier will change after data are compressed by PCA. However, this paper reveals an interesting fact that the transformation by FR-PCA does not change the accuracy of many well-known classification algorithms. It predicates that people can safely use FR-PCA as a preprocessing tool to compress high-dimensional data without deteriorating the accuracies of these classifiers. The main contribution of the paper is that it theoretically proves that the transformation by FR-PCA does not change accuracies of the k nearest neighbor, the minimum distance, support vector machine, large margin linear projection, and maximum scatter difference classifiers. In addition, through extensive experimental studies conducted on several benchmark face image databases, this paper demonstrates that FR-PCA can greatly promote the efficiencies of above-mentioned five classification algorithms in appearance-based face recognition. [ABSTRACT FROM AUTHOR]

Abstract: When locality preserving projection (LPP) is applied to face recognition, it usually suffers from the small sample size (SSS) problem, which means that the eigen-equation of LPP cannot be solved directly. In order to address this issue, we propose a novel LPP scheme. This scheme transforms the objective function of LPP into a new function, which allows the resultant eigen-equation to be directly solved no matter whether the SSS problem occurs or not. Moreover, the fact that the proposed scheme has an adjustable parameter enables us to be able to obtain the best classification accuracy by adjusting the parameter. Our analysis comprehensively reveals the theoretical properties of the proposed scheme and its relationship with other LPP methods. Our analysis also shows that the conventional LPP can be regarded as a special form of the proposed scheme, which also implies that the classification accuracy of the conventional LPP will be lower than the best classification accuracy of the proposed scheme. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a novel dimensionality-reduction method—Fisher discriminant with Schur decomposition (FDS). Similar to Foley–Sammon discriminant analysis (FSD), FDS is an improvement of Fisher discriminant analysis (FDA) in that it eliminates linear dependences among discriminant vectors. In comparison with FSD, FDS is very simple in theory and realization. Experimental results conducted on two benchmark face-image databases, i.e. ORL and AR, demonstrate that FDS is highly effective and efficient in reducing dimensionalities of facial image spaces. Especially when the size of a database is large, FDS can even outperform the state-of-the-art facial feature extraction methods such as the null space method. [Copyright &y& Elsevier]

The Foley–Sammon discriminant (FSD) exhibits higher performance in face recognition than the Fisher linear discriminant due to its elimination of dependences among discriminant vectors. But its theory is complex and the calculation is time expensive. The orthogonalized Fisher discriminant (OFD), which also derives a set of orthogonal discriminant vectors, is very simple and easy to implement. Experiments show that OFD is more effective and efficient than FSD in pattern recognition. [Copyright &y& Elsevier]

Unlike linear discriminant analysis, the large margin linear projection (LMLP) classifier presented in this paper, which also roots in linear Fisher discriminant, takes full advantage of the singularity of within-class scatter matrix, and classifies projected points in one-dimensional space by itself. Theoretical analysis and experimental results both reveal that LMLP is well suited for high-dimensional small-sample pattern recognition problems such as face recognition. [Copyright &y& Elsevier]