J. Phys. I France
Volume 3, Numéro 2, February 1993
Page(s) 277 - 290
DOI: 10.1051/jp1:1993129
J. Phys. I France 3 (1993) 277-290

A fast method for calculating the perceptron with maximal stability

Pál Ruján

Fachbereich 8 Physik, Carl-von-Ossietzky Universität, D-2900 Oldenburg, Germany

(Received 12 May 1992, accepted 5 June 1992)

For the class of linearly separable two class (boolean) functions the Perceptron with maximal stability defines in the space of all possible input configurations the direction along which the gap between the two classes is maximal. This solution has several advantages: it is unique, it is robust, and has the best generalization probability among all known linear discriminants. present here an active set approach to the dual problem, finding the minimal connector between two disjoint convex hulls. If N is the number of the input units and M is the number of examples, this algorithm runs in average $O \,(M N^2)$ steps and requires the storage of a symmetric $(N + 3) \times (N + 3)$ matrix.

87.10E - 02.50F - 05.20Y

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