Underdetermined independent component analysis by data generation

In independent component analysis (ICA), linear transformation that minimizes the dependence among the components is estimated. Conventional ICA algorithms are applicable when the numbers of sources and observations are equal; however, they are inapplicable to the underdetermined case where the number of sources is larger than that of observations. Most underdetermined ICA algorithms have been developed with an assumption that all sources have sparse distributions. In this paper, a novel method for converting the underdetermined ICA problem to the conventional ICA problem is proposed; by generating hidden observation data, the number of the observations can be made to equal that of the sources. The hidden observation data are generated so that the probability of the estimated sources is maximized. The proposed method can be applied to separate the underdetermined mixtures of sources without the assumption that the sources have sparse distribution. Simulation results show that the proposed method separates the underdetermined mixtures of sources with both sub- and super-Gaussian distributions.