Linear classifiers by window training

Window training, based on an extended form of stochastic approximation, offers a means of producing linear classifiers that minimize the probability of misclassification of statistically generated data. Associated with window training is a window criterion function. We show that minimizing the window criterion function yields a linear classifier that minimizes the probability of misclassification (i.e., the "error rate"). However window training may produce a local minimum that exceeds the global minimum error rate. We show that this defect does not occur in the error-correcting perceptron. The criterion minimized by that training procedure is "convex"; i.e., the perceptron criterion has only one local minimum. Consequently we recommend that window training be preceded by perceptron training, the perceptron training producing a decision surface which the window training process will move to a position that is likely to be globally optimum.<
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