The Sum-Line Extrapolative Algorithm and Its Application to Statistical Classification Problems

Abstract

The sum-line algorithm (SLA) for use with an adaptive linear threshold element is shown experimentally to have excellent extrapolative properties when applied to two-class multivariate Gaussian pattern-classification problems, even when the number of sample patterns is severely limited. The algorithm iteratively adapts the desired analog-output sum of the threshold element while simultaneously adapting the weights of the element. The algorithm converges toward a solution weight vector. It is shown experimentally that this vector tends toward the solution provided by the least-mean-square (LMS) algorithm or that provided by the matched-filter (MF) algorithm, whichever is best able to extrapolate from a given set of sample patterns to patterns that are derived from the same statistical populations but are not included in the sample set.