Journal of Pattern Recognition Research

Kernel Discriminant Analysis (KDA) is the usual extension of Fisher Linear Discriminant Analysis (FLDA) in a high dimensional feature space via kernel mapping. KDA recently has become a popular classification technique in machine learning and in data mining. The performance of KDA depends very heavily on the choice of the best kernel function for a given data set and the optimal choice of the kernelparameters. In this paper, we develop a novel data adaptive simultaneous parameter and kernel selection approach in KDA using information complexity (ICOMP) type criteria. We achieve this by reducing the multivariate input data into one dimension in order to find a range of the possible values to tune the parameters of the kernel mapping directly from the data rather than using trial-and-error. We tune the parameters of the kernel functions by utilizing the Mahalanobis distance of eachpoint from the multivariate mean (centroid), Jackknife Mahalanobis distance Data Depth (JMDD), and the Smoothed Complexity Mahalanobis distanc (SCMD). Such an approach provides the researcher a new and novel method to simultaneously choose optimal tuning parameters of the kernel functions; how to choose the optimal kernel function; and their effect on the KDA classifier using ICOMP. We show numerical examples on real benchmark data sets to illustrate the efficiency and the performance of our new approach in terms of reducing the misclassification error rate.