Exact Classification with Two-Layered Perceptrons

Aarts, E.H.L., Zwietering, P.J., & Wessels, J. (1992). Exact Classification with Two-Layered Perceptrons. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-92-049

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Abstract

We study the capabilities of two-layered perceptrons for classifying exactly a given subset. Both necessary and sufficient conditions are derived for subsets to be exactly classifiable with two-layered perceptrons that use the hard-limiting response function. The necessary conditions can be viewed as generalizations of the linear-separability condition of one-layered perceptrons and confirm the conjecture that the capabilities of two-layered perceptrons are more limited than those of three-layered perceptrons. The sufficient conditions show that the capabilities of two-layered perceptrons extend beyond the exact classification of convex subsets. Furthermore, we present an algorithmic approach to the problem of verifying the sufficiency condition for a given subset.

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