On the Optimum Choice of Categories for the Classification of Biomedical Data Patterns

Abstract

The optimum choice of categories for pattern recognition problems is on the one hand determined by the requirement of a low rate of misclassification. On the other hand, the classification of a pattern should result in an information gain as high as possible. A criterion for an optimum choice of categories which is the best compromise between the demands mentioned above is worked out. The Bayes rule is used as a decision function. The alteration of the Bayes risk as indicator for the rate of malrecognition is examined for different choice of categories concerning the very same classification problem. As the calculation of the Bayes risk is commonly difficult, an estimation using the Bhattacharyya coefficient is given. The information content of a choice of categories is defined using Shannon’s information measure. The alteration of the information contents is analyzed by putting together certain categories, i.e. a coarser choice of categories. With the aid of the relative information loss and the relative reduction of the Bayes risk coefficient, a criterion on the goodness of a choice of categories can be given. The criterion also serves as an optimum choice of classes. The extension of the latter criterion to a generalized decision rule is possible.