Experiments with learning rules for a single neuron

In this paper we investigate a variation of perceptron-like learning rules for single neural unit. The existing learning rules lack one important element: if the patterns are not linearly separable, the rule either does not converge or converges to an approximate solution. So, the deficiency is that one can not draw any conclusion as to the nature of the problem (linear or nonlinear). We propose to design a class of dual purpose rules such that (1) if the patterns are linearly separable, the performance of a rule will be equivalent to that of the perceptron rule and (2) if the patterns are not linearly separable then the rule will indicate to that effect and therefore, appropriate nonlinear methods (e.g., multilayer neural network, nonlinear transformation on input-space etc.) can be used to address this problem. We present experimental results with linearly-separable as well as linearly nonseparable data using the proposed rule and compare its performance with that of the perceptron rule