Time-Domain Solutions of Oja's Equations

Abstract

Oja's equations describe a well-studied system for unsupervised Hebbian learning of principal components. This paper derives the explicit time-domain solution of Oja's equations for the single-neuron case. It also shows that, under a linear change of coordinates, these equations are a gradient system in the general multi-neuron case. This latter result leads to a new Lyapunov-like function for Oja's equations.