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.

A linear reinforcement learning technique is proposed to provide a memory and thus accelerate the convergence of successive approximation algorithms. The learning scheme is used to update weighting coefficients applied to the components of the correction terms of the algorithm. A direction of the search approaching the direction of a ridge will result in a gradient peak-seeking method which accelerates considerably the convergence to a neighborhood of the extremum. In a stochastic approximation algorithm the learning scheme provides the required memory to establish a consistent direction or search insensitive to perturbations introduced by the random variables involved. The accelerated algorithms and the respective proofs of convergence are presented. Illustrative examples demonstrate the validity of the proposed algorithms.