Supervised Classification Using Graph-based Space Partitioning for Multiclass Problems

We introduce and investigate in multiclass setting an efficient classifier which partitions the training data by means of multidimensional parallelepipeds called boxes. We show that multiclass classification problem at hand can be solved by combining the heuristic minimum clique cover approach and the $k$-nearest neighbor rule. Our algorithm is motivated by an algorithm for partitioning a graph into a minimal number of cliques. The main advantage of a new classifier called Box classifier is that it optimally utilizes the geometrical structure of the training set by reducing the 1-class classification problem to a single nearest neighbor problem. We discuss computational complexity of the proposed Box classifier. The extensive experiments performed on the simulated and real data from UCI Machine Learning Repository for binary and multiclass problems show that in almost all cases the Box classifier performs significantly better than k-NN, SVM and decision trees.