Neural modeling of piecewise linear classifiers

We show that every piecewise linear classifier can be constructed as a three-layer network of linear decision functions. We define neural modeling as the replacement and subsequent training of each of these linear decision functions by a formal neuron with a differentiable activation function. We show that neural modeling of a piecewise linear classifier provides a means of combining the economy of design of piecewise linear classifiers with the good generalizing ability and low error rates of well designed neural classifiers. We show that globally optimized neural classifiers can be obtained from neural modeling of genetically designed piecewise linear classifiers. We describe applications of these techniques to an artificial data set and to a detector of lines and edges in a noisy aerial image