The Bootstrap Widrow-Hoff Rule as a Cluster-Formation Algorithm

An algorithm that is widely used for adaptive equalization in current modems is the “bootstrap” or “decision-directed” version of the Widrow-Hoff rule. We show that this algorithm can be viewed as an unsupervised clustering algorithm in which the data points are transformed so that they form two clusters that are as tight as possible. The standard algorithm performs gradient ascent in a crude model of the log likelihood of generating the transformed data points from two gaussian distributions with fixed centers. Better convergence is achieved by using the exact gradient of the log likelihood.