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PubMed2005

Kernel machine-based one-parameter regularized fisher discriminant method for face recognition.

This paper addresses two problems in linear discriminant analysis (LDA) of face recognition. The first one is the problem of recognition of human faces under pose and illumination variations. It is well known that the distribution of face images with different pose, illumination, and face expression is complex and nonlinear. The traditional linear methods, such as LDA, will not give a satisfactory performance. The second problem is the small sample size (S3) problem. This problem occurs when the number of training samples is smaller than the dimensionality of feature vector. In turn, the within-class scatter matrix will become singular. To overcome these limitations, this paper proposes a new kernel machine-based one-parameter regularized Fisher discriminant (K1PRFD) technique. K1PRFD is developed based on our previously developed one-parameter regularized discriminant analysis method and the well-known kernel approach. Therefore, K1PRFD consists of two parameters, namely the regularization parameter and kernel parameter. This paper further proposes a new method to determine the optimal kernel parameter in RBF kernel and regularized parameter in within-class scatter matrix simultaneously based on the conjugate gradient method. Three databases, namely FERET, Yale Group B, and CMU PIE, are selected for evaluation. The results are encouraging. Comparing with the existing LDA-based methods, the proposed method gives superior results.

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PubMed2005

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

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.

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