Minimization of the empirical risk in piecewise-linear classifiers

Optimal pieeewise-linear classifiers are obtained by using partially integer linear programming. A procedure of designing pieeewise-linear classifiers with simultaneous choice of the “structure” and learning for two classes of patterns is described. An optimal classifier in a family of pieeewise-linear ones for the case of more than two classes of patterns is determined. A procedure of designing pieeewise-linear classifiers for this case is deyeloped.