Exploring Independent Component Analysis Based on Ball Covariance

For estimating the original signals only through observing the mixed data, independent component analysis (ICA) is a useful dimension reduction method, since it contains more statistical concepts: independence and non-Gaussianity. In other words, it does not end up in solving (generalized) eigenvalue problems, which are mostly restricted in considering up to the second moment as many other dimension reduction methods are. In this paper, we reviewed and explored various methods of ICA, such as Fast-ICA, Infomax-ICA, joint approximate diagonalization of eigenmatrices ICA (JADE ICA), product density estimation ICA (ProDenICA), and distance covariance ICA (dCovICA). We also proposed a method based on ball covariance, called B-dCovICA. Compared to other methods, B-dCovICA showed relatively high performance, supported by the higher accuracy of results when applied to simulated/real data. B-dCovICA is better than dCovICA, in that a non-parametric way is used to measure dependence, yet showed higher accuracy than dCovICA.