J. Phys. I France 2 (1992) 167-180
Learning multi-class classification problemsTimothy 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)
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.
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