Analysis of the Kurtosis-Sum Objective Function for ICA

The majority of existing Independent Component Analysis (ICA) algorithms are based on maximizing or minimizing a certain objective function with the help of gradient learning methods. However, it is rather difficult to prove whether there is no spurious solution in ICA under any objective function as well as the gradient learning algorithm to optimize it. In this paper, we present an analysis on the kurtosis-sum objective function, i.e., the sum of the absolute kurtosis values of all the estimated components, with a kurtosis switching algorithm to maximize it. In two-source case, it is proved that any local maximum of this kurtosis-sum objective function corresponds to a feasible solution of the ICA problem in the asymptotic sense. The simulation results further show that the kurtosis switching algorithm always leads to a feasible solution of the ICA problem for various types of sources.

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