Comparison of statistical pattern-recognition algorithms for hybrid processing. I. Linear-mapping algorithms

Two groups of pattern-recognition algorithms for hybrid optical-digital computer processing are theoretically and experimentally compared. The first group is based on linear mapping, while the second group is based on feature extraction and eigenvector analysis. We study the relations among various linear-mapping-based algorithms by formulating a more general unified pseudoinverse algorithm. We show that the least-squares linear-mapping technique, the simplified least-squares linear-mapping technique, the synthetic discriminant function, the equalcorrelation-peak method, and the Caulfield-Maloney filter are in fact all special cases of the unified pseudoinverse algorithm. When the total number of the training images (KM, where K is the number of classes and M is the number of training images in each class) is larger than the dimension of the images (N), the overdetermined case of the unified pseudoinverse algorithm is the same as the least-squares linear-mapping technique, because both algorithms are based on optimization processes of minimization of the mean-square error. When KM < N, the underdetermined case of the unified pseudoinverse algorithm is the same as the least-squares linear-mapping technique and the synthetic discriminant function. Furthermore, when KM < N, the synthetic discriminant function method can be considered a degenerate case of the least-squares linear-mapping technique. Among the algorithms studied, the simplified least-squares linear-mapping technique requires the least computation time for filter synthesis. Experimental results on classification with linear-mapping-based algorithms are provided and show good agreement with the theoretical analysis.