Journal de Physique I

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DOI: 10.1051/jp1:1992131
J. Phys. I France 2 (1992) 167-180

Learning multi-class classification problems

Timothy L. H. Watkin¹, Albrecht Rau¹, Desiré Bollé¹ and Jort van Mourik²

¹ Theoretical Physics, Oxford University, 1 Keble Road, GB-Oxford OX1 3NP, G.B.
² Inst. voor Theor. Fysica, K. U. Leuven, B-3001 Leuven, Belgium

(Received 26 August 1991, accepted in final form 20 October 1991)

Abstract
A multi-class perceptron can learn from examples to solve problems whose answer may take several different values. Starting from a general formalism, we consider the learning of rules by a Hebbian algorithm and by a Monte-Carlo algorithm at high temperature. In the benchmark "prototype-problem" we show that a simple rule may be more than an order of magnitude more efficient than the well-known solution, and in the conventional limit is in fact optimal. A multi-class perceptron is significantly more efficient than a more complicated architecture of binary perceptrons.