Analysis of a multi-category classifier

The use of boxes for pattern classification has been widespread and is a fairly natural way in which to partition data into different classes or categories. In this paper we consider multi-category classifiers which are based on unions of boxes. The classification method studied may be described as follows: find boxes such that all points in the region enclosed by each box are assumed to belong to the same category, and then classify remaining points by considering their distances to these boxes, assigning to a point the category of the nearest box. This extends the simple method of classifying by unions of boxes by incorporating a natural way (based on proximity) of classifying points outside the boxes. We analyze the generalization accuracy of such classifiers and we obtain generalization error bounds that depend on a measure of how definitive is the classification of training points.