Efficient linear and nonlinear feature extraction and its application to fingerprint classification

Extracting optimal features and reducing the dimension of data space is an important preprocessing step for efficient and effective processing in data mining and pattern recognition. Linear Discriminant Analysis (LDA) is one of' the most commonly used linear dimension reduction methods. However, for undersampled problems where the number of data items is smaller than the data dimension, the classical LDA is difficult to apply due to the singularity of scatter matrices. A comparative analysis of generalized LDA algorithms for undersampled problems is presented. Utilizing the relationships among them, efficient algorithms for the generalized LDA are also proposed.; While linear dimension reduction is conceptually simple and easy to compute, it is difficult to capture a nonlinear relationship in the data with a linear mapping. In order to overcome such a limitation, nonlinear feature extraction based on kernel methods is pro posed. A generalized eigenvalue problem is formulated in the feature space transformed through kernel methods. It is shown that under this formulation any generalized LDA algorithms can be applied in the feature space, resulting in nonlinear discriminant analysis. Comparisons of generalized LDA algorithms both in the original data space and in the feature space show interesting results. An efficient nonlinear feature extraction method based on centroids and kernel methods is also presented. It applies the centroid-based orthogonal transformation to the data transformed by kernel-based nonlinear mapping. Computational efficiency is obtained by utilizing the cholesky decomposition to much smaller matrix instead of solving eigenvalue problems.; As an application of nonlinear feature extraction methods, a new approach for fingerprint classification is proposed which is based on Discrete Fourier Transform (DFT) and nonlinear discriminant analysis. Utilizing DFT and directional filters, a reliable and efficient directional image is constructed from each fingerprint image, and then nonlinear discriminant analysis is applied to the constructed directional images. The proposed method explores the capability of DFT and directional filtering in dealing with low quality images and the effectiveness of a nonlinear feature extraction method in fingerprint classification.