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Invariant Set of Weight of Perceptron Trained by Perceptron Training Algorithm

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3 Author(s)
Charlotte Yuk-Fan Ho ; School of Mathematical Sciences, Queen Mary, University of London, London, U.K. ; Bingo Wing-Kuen Ling ; Herbert Ho-Ching Iu

In this paper, an invariant set of the weight of the perceptron trained by the perceptron training algorithm is defined and characterized. The dynamic range of the steady-state values of the weight of the perceptron can be evaluated by finding the dynamic range of the weight of the perceptron inside the largest invariant set. In addition, the necessary and sufficient condition for the forward dynamics of the weight of the perceptron to be injective, as well as the condition for the invariant set of the weight of the perceptron to be attractive, is derived.

Published in:

IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)  (Volume:40 ,  Issue: 6 )