Asymptotic performance of the fastica algorithm for independent component analysis and its iprovements

The fixed point algorithm, known as FastICA, is one of the most successful algorithms for independent component analysis in terms of accuracy and low computational complexity. This paper derives analytic closed form expressions that characterize separating ability of both one-unit and symmetric version of the algorithm in a local sense. Based on the analysis it is possible to combine advantages of the two versions. Although the analysis assumes a "good" initialization of the algorithms and long data records, our computer simulations demonstrate validity of the theoretical expressions in the case of arbitrary initialization and moderate data lengths