Independent Component Analysis without Predetermined Learning Parameters

This paper presents a power iteration (PI) algorithm for independent component analysis (ICA), such that it is termed as "PowerICA". In each iteration the updating of ICA matrix is fully-multiplicative, rather than the partly multiplicative and partly additive as in the conventional learning algorithms. Therefore, this algorithm presents a new algorithm class to ICA. The criterion for the independence between outputs is based on diagonality of a nonlinearized covariance matrix that is define both by ICA outputs and non-linear mapped ICA outputs. The activation function, which features the probability distribution of sources, is chosen as such a non-linear map. One of desired features is that the algorithm does not include any predetermined parameter such as the learning step size as in the gradient-based algorithm, which is especially promising for ICA applications to such cases with unknown types of sources. Numerical results show the effectiveness of PowerICA.