Classification Capabilities of Exact Two-Layered Perceptrons

摘要

The problem of finding a two layered perceptron that exactly classifies a givensubset is studied. Such a two layered perceptron is called exact with respect to a given subset. A necessary and a sufficient condition for a given subset to be classifiable by an exact two layered perceptron is derived. The necessary condition can be viewed as a generalization of the linear separability condition of the one layered perceptron and confirms the conjecture that the capabilities of exact two layered perceptrons are more limited than those of exact three layered perceptrons. The sufficient condition shows that the capabilities of exact two layered perceptron extend beyond the exact classification of convex subsets. A systematic verification method for the given sufficient condition is presented.