Performance analysis of a converged single-layer perceptron for nonseparable data models with bias terms

Rosenblatt´s (1985) algorithm is a recursive method used to adjust the weights of a single-layer perceptron. It is capable of partitioning the input signal space into two regions that are separated by a hyperplane boundary. Thus, when the values of the input signal are linearly separable, the algorithm will converge to a stable stationary point that yields zero mean-square error. The authors examine the stationary points of Rosenblatt´s algorithm when the data is not linearly separable. A system identification model is used to generate the data. The model incorporates the effects of bias terms so that the hyperplane boundaries do not necessarily pass through the origin of the signal space. An expression is also derived for the probability of an incorrect classification of the output signal when the weights are converged at a stationary point