TRAINING A THRESHOLD LOGIC UNIT WITH IMPERFECTLY CLASSIFIED PATTERNS
Richard O. Duda, R. C. Singleton · 1944
Abstract : A threshold logic unit (TLU) having adjustable weights is a particularly simple machine that can be trained to dichotomize patterns. It is trained on a representative set of patterns, each pattern having been labeled with a desired category number. If the patterns so labeled are linearly separable, then any of several training procedures can be used to adjust the weights so that eventually the TLU classifies all of the patterns as desired. There are many circumstances in which the patterns used for training are, in effect, occasionally mislabeled. This paper is concerned with training a TLU under such conditions. The patterns used for training are assumed to be selected from a linearly separable set. However these patterns are presented to the TLU after having been randomly mislabeled with probability less than one-half. In addition to forming the usual (instantaneous) weight vector, a second (average) weight vector is formed by averaging the instantaneous weight vector. It is shown that for orthogonal pattern vectors the average weight vector converges to a solution vector for the correctly labeled pattern set. (Author)