A Fast Algorithm for ICA Deduced from a Closed-Form Solution of Kurtosis Maximization

An independent component analysis (ICA) algorithm based on the kurtosis is presented. As well known, one of the original signals can be extracted from observations by maximizing the absolute value of kurtosis. The conventional algorithms, however, often show oscillation or slow convergence because these methods seek a true solution in an iterative manner. We prove in this paper that in the two-signal case the optimum solution of the kurtosis-based cost function can be obtained in closed form. By exploiting this closed-form solution, we establish a new fast algorithm for ICA. In addition, experimental results show that when there are more than three signals, the method can find optimum solution faster than the conventional algorithms. It is also observed that the oscillation does not occur within the proposed method.