Communications of the ACM
A new polynomial-time algorithm for linear programming
Combinatorica
Computational geometry: an introduction
Computational geometry: an introduction
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Fractals everywhere
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
On learning a union of half spaces
Journal of Complexity
Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
On Piecewise-Linear Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Learning Sets and Functions
Machine Learning
Divide-and-conquer in multidimensional space
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
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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.