Discriminant function implementation of a minimum risk classifier

The paper discusses the possibility of implementing a minimum risk classifier using the learning machine approach. Necessary conditions on the choice of pairwise classification costs are imposed so that the minimum risk classifier can be implemented using pairwise class separating functions. Parameters of these functions are obtained using a two stage algorithm which minimizes a modified least squares criterion of class separation. In comparison to normal least squares objective function, this criterion increases the sensitivity of the learning scheme near the class separating surface and, consequently, allows for an improvement in the performance of the discriminant function decision making processor. Simplicity of the design procedure is achieved by partitioning the multimodal classes into unimodal subsets, since discriminant functions of unimodal classes can usually be implemented simply and with sufficient accuracy as low order polynomials. The proposed design approach is tested experimentally on an artificial pattern recognition problem.