  The decision boundaries of Bayes classifier are optimal because they lead to
maximum probability of correct decision. It means if we knew the prior
probabilities and the class-conditional densities, we could design a classifier
which gives the lowest probability of error. However, in classification based
on nonparametric density estimation methods such as Parzen windows, the
decision regions depend on the choice of parameters such as window width.
Moreover, these methods suffer from curse of dimensionality of the feature
space and small sample size problem which severely restricts their practical
applications. In this paper, we address these problems by introducing a novel
dimension reduction and classification method based on local component
analysis. In this method, by adopting an iterative cross-validation algorithm,
we simultaneously estimate the optimal transformation matrices (for dimension
reduction) and classifier parameters based on local information. The proposed
method can classify the data with complicated boundary and also alleviate the
course of dimensionality dilemma. Experiments on real data show the superiority
of the proposed algorithm in term of classification accuracies for pattern
classification applications like age, facial expression and character
recognition. Keywords: Bayes classifier, curse of dimensionality dilemma,
Parzen window, pattern classification, subspace learning.
