Fast-converging adaptive algorithms for well-balanced separating linear classifier

摘要

The perception-adaline-type adaptive linear decision function converges, in a seperable case, to a separating hyperplane, but its location depends on the initial trial function, the order of presentation of paradigms (class samples) and the parameters involved and is often ill-balanced with reference to the distribution of the paradigms of the two classes. The Widrow-Hoff-type least-mean-error algorithm does not necessarily give a separating hyperplane even in a separable case, and is often too sensitive to the shapes of the clusters of paradigms. The adaptive approximation to this least-mean-error hyperplane converges extremely slowly. We propose various adaptive algorithms which converge rapidly to a separating hyperplane whose location is well-balanced with regard (1) to the distances of the centroids of the clusters from the plane and (2) to the direction of the plane relative to the line connecting the two centroids. This method shows also an exellent separation in the linearly-non-separable, quadratically-separable case.