Comparison of statistical pattern-recognition algorithms for hybrid processing II Eigenvector-based algorithm

Abstract

The pattern-recognition algorithms based on eigenvector analysis (group 2) are theoretically and experimentally compared. Group 2 consists of Foley–Sammon (F-S) transform, Hotelling trace criterion (HTC), Fukunaga–Koontz (F-K) transform, linear discriminant function (LDF), and generalized matched filter (GMF) algorithms. It is shown that all eigenvector-based algorithms can be represented in a generalized eigenvector form. However, the calculations of the discriminant vectors are different for different algorithms. Summaries of methods of calculating the discriminant functions for the F-S, HTC, and F-K transforms are provided. Especially for the more practical, underdetermined case, where the number of training images is less than the number of pixels in each image, the calculations usually require the inversion of a large, singular pixel correlation (or covariance) matrix. We suggest solving this problem by finding its pseudoinverse, which requires inverting only the smaller, nonsingular image-correction (or covariance) matrix plus multiplying several nonsingular matrices. We also compare theoretically the classification performance with discriminant functions of the F-S, HTC, and F-K with the LDF and GMF algorithms and the linear-mapping-based algorithms with the eigenvector-based algorithms. Experimentally, we compare the eigenvector-based algorithms, using two sets of image data bases with each image consisting of 64 × 64 pixels.