Convergence of a hebbian-type learning algorithm

A Hebbian-type learning algorithm was proposed in [1] 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 lind the minor components of the input signals.