A new geometrical approach for solving the supervised pattern recognition problem

This paper explores the supervised pattern recognition problem based on feature partitioning. This formulation leads to a new problem in computational geometry. The supervised pattern recognition problem is formulated as an heuristic good clique cover problem satisfying the k-nearest neighbors rule. First it is applied a heuristic algorithm for partitioning a graph into a minimal number of cliques. Next cliques are merged using the k-nearest neighbors rule. An important advantage of this approach is the decomposition of a problem involving l classes into l optimization problems involving a single class. The computational complexity of the method, computational procedures, and classification rules are discussed. A geometrical interpretation of the solution is also given. Using the proposed approach, the geometrical structure of the training set is utilized in the best possible way.