Training digital circuits with Hamming Clustering

A new algorithm, called Hamming Clustering (HC), for the solution of classification problems with binary inputs is proposed. It builds a logical network containing only and, or and not ports, which, besides satisfying all the input-output pairs included in a given finite consistent training set, is able to reconstruct the underlying Boolean function. The basic kernel of the method is the generation of clusters of input patterns that belong to the same class and are close to each other according to the Hamming distance. A pruning phase precedes the construction of the digital circuit so as to reduce its complexity or to improve its robustness. A theoretical evaluation of the execution time required by HC shows that the behavior of the computational cost is polynomial. This result is confirmed by extensive simulations on artificial and real-world benchmarks, which point out also the generalization ability of the logical networks trained by HC.