Some properties of the multisurface method for pattern classification

摘要

Fisher(2) (R. A. Fisher, The use of multiple measurements in taxonomic problems, Ann. Eugenics 7, Part II, 179–188, 1936) introduced a criterion function for classification of two categories of patterns by a hyperplane σai,xi + h = 0. He then found the normal vector {ai}, that maximizes this criterion function.In the present paper we generalize Fisher's criterion function, making it suitable for a piecewise linear classifier. We build the optimal piecewise linear classifier that maximizes the generalized Fisher's criterion function.The basis of the method is presented in reference (1) (S. Spivak, A multisurface method for pattern classification, Pattern Recognition 22, 587–591, 1989). Here, we explore further the properties of the method, which include extracting irrelevant planes from the desired classifier and removing ineffective features from each plane. It is shown that the method can be easily generalized for separation of more than two categories of patterns.