Convergence of a Hebbian-type learning algorithm

A Hebbian-type learning algorithm was proposed by Gao et al. (1994) for extracting the minor components of the input signals. In this paper, we demonstrate that some solutions of the averaging differential equation of this algorithm can become unbounded in a finite time. We derive five sufficient conditions to ensure that the solutions of its averaging differential equation are bounded and can be extended to the time interval [0, ∞]. Any one of these conditions can guarantee that this algorithm can be used to find the minor components of the input signals