An Analysis of the Cluster-Detecting Property of the BCM Neuron

Abstract

The BCM learning rule, named for Elie Bienenstock, Leon Cooper, and Paul Munro, was first proposed to measure the selectivity of neurons in the primary visual cortex and its dependency on neuronal inputs. We show that an artificial BCM neuron has the ability to detect clusters in a dataset. By exploring the qualitative behaviors of an underlying system of differential equations, we present a rigorous mathematical analysis of this cluster-detecting property. While the focus of this work is not to develop a robust state-of-the-art clustering method, we also analyze and discuss the performance of a resulting preliminary clustering algorithm.