Adaptive Linear Classifier by Linear Programming

A linear classifier based on linear programming which is adaptive to a change in the set of input vectors is discussed. Different from other linear classifiers, this one maintains the maximum reliability of its operation, provided that the set of pattern vectors is linearly separable. A procedure of deriving an optimum structure of the linear classifier for a change in the set of input vectors is a modification of the ordinary simplex method and yields an optimum structure in much fewer iterations than the straightforward application of the ordinary simplex method does. The adaptive procedure is then extended to the case in which a linear classifier maintains the minimum number of erroneously classified input vectors even if the set of input pattern vectors is not linearly separable. This is based on Gomory´s algorithm for integer linear programming. The feasibility and efficiency of these linear classifiers are computationally proved by some examples.