Polychotomous kernel Fisher discriminant via top–down induction of binary tree

In spite of the popularity of Fisher discriminant analysis in the realm of feature extraction and pattern classification, it is beyond the capability of Fisher discriminant analysis to extract nonlinear structures from the data. That is where the kernel Fisher discriminant algorithm sets in the scenario of supervised learning. In this article, a new trail is blazed in developing innovative and effective algorithm for polychotomous kernel Fisher discriminant with the capability in estimating the posterior probabilities, which is exceedingly necessary and significant in solving complex nonlinear pattern recognition problems arising from the real world. Different from the conventional ‘divide-and-combine’ approaches to polychotomous classification problems, such as pairwise and one-versus-others, the method proposed herein synthesizes the multi-category classifier via the induction of top-to-down binary tree by means of kernelized group clustering algorithm. The deficiencies inherited in the conventional multi-category kernel Fisher discriminant are surmounted and the simulation on a benchmark image dataset demonstrates the superiority of the proposed approach.