ON THE CONVERGENCE OF THE L(P)-NORM ALGORITHM FOR POLYNOMIAL PERCEPTRON HAVING DIFFERENT ERROR SIGNAL DISTRIBUTIONS

Abstract

The convergence property of the l(p)-norm algorithm for polynomial-perceptron having different error signal distributions will be analyzed in this paper. To see the effect of error signal on the convergence rate, two types of activation functions are considered in the analysis: one is of a linear type and the other is of a sigmoidal type. Different activation functions yield different ranges of output signal and, in turn, yield different error signal distributions. Linear activation function causes the error signal to be distributed in an uncertain way, while sigmoidal activation function causes it to be distributed in a tightly bounded region. Based on this difference the convergence property of the l(p)-norm algorithm, 1 less than or equal to p less than or equal to 2, is investigated in this paper. Expressions of average learning gains are obtained in terms of the power metric p, the error probability, and the upper bound bf the error signal distribution. Analytic results indicate that it is of particular value in using the l(p)-norm algorithm for the perceptron using sigmoidal activation functions. Computer simulation of an adaptive equalizer using this algorithm confirms the theoretical analysis.