Toward Bayes-optimal linear dimension reduction

Dimension reduction is the process of transforming multidimensional vectors into a low-dimensional space. In pattern recognition, it is often desired that this task be performed without significant loss of classification information. The Bayes error is an ideal criterion for this purpose; however, it is known to be notoriously difficult for mathematical treatment. Consequently, suboptimal criteria have been used in practice. We propose an alternative criterion, based on the estimate of the Bayes error, that is hopefully closer to the optimal criterion than the criteria currently in use. An algorithm for linear dimension reduction, based on this criterion, is conceived and implemented. Experiments demonstrate its superior performance in comparison with conventional algorithms.