Learning separations by Boolean combinations of half-spaces

Given two subsets S/sub 1/ and S/sub 2/ (not necessarily finite) of /spl Rfr//sup d/ separable by a Boolean combination of learning half-spaces, the authors consider the problem of (in the sense of Valiant) the separation function from a finite set of examples, i.e., they produce with a high probability a function close to the actual separating function. The authors' solution consists of a system of N perceptrons and a single consolidator which combines the outputs of the individual perceptrons; it is shown that an off-line version of this problem, where the examples are given in a batch, can be solved in time polynomial in the number of examples. The authors also provide an on-line learning algorithm that incrementally solves the problem by suitably training a system of N perceptrons much in the spirit of the classical perceptron learning algorithm.<
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