On adaptive smoothing in kernel discriminant analysis

One popular application of kernel density estimation is in kernel discriminant analysis, where kernel estimates of population densities are plugged in the Bayes rule to develop a nonparametric classifier. Performance of these kernel density estimates and that of the corresponding classifier depend on the values of associated smoothing parameters commonly known as the bandwidths. Bandwidths that minimize mean integrated square errors of kernel density estimates often lead to poor misclassification rates in classification problems. In discriminant analysis, usually a cross validated estimate of misclassification probability is minimized to find the optimal bandwidth, and that bandwidth is used for classifying all observations. However, in addition to depending on the training data set, a good choice of bandwidth should also depend on the specific observation to be classified. Therefore, instead of fixing the value of the bandwidth parameter, in practice it may be more useful to choose it adaptively. This article presents one such adaptive classification technique, where the bandwidth is chosen based on the training sample and also on the data point to be classified. Performance of the proposed method has been illustrated using some benchmark data sets.