Invariant set of weight of perceptron trained by perceptron training algorithm

Authors:
Charlotte Yuk-Fan Ho;Bingo Wing-Kuen Ling;Herbert Ho-Ching Iu
Affiliations:
School of Mathematical Sciences, Queen Mary, University of London, London, UK;Department of Electronic Engineering, Division of Engineering, King's College London, London, UK;School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Perth, WA, Australia
Venue:
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Year:
2010

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Abstract

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.