Supervised box clustering

In this work we address a technique for effectively clustering points in specific convex sets, called homogeneous boxes, having sides aligned with the coordinate axes (isothetic condition). The proposed clustering approach is based on homogeneity conditions, not according to some distance measure, and, even if it was originally developed in the context of the logical analysis of data, it is now placed inside the framework of Supervised clustering. First, we introduce the basic concepts in box geometry; then, we consider a generalized clustering algorithm based on a class of graphs, called incompatibility graphs. For supervised classification problems, we consider classifiers based on box sets, and compare the overall performances to the accuracy levels of competing methods for a wide range of real data sets. The results show that the proposed method performs comparably with other supervised learning methods in terms of accuracy.