Exploring latent structure of mixture ICA models by the minimum β-divergence method

Independent component analysis (ICA) attempts to extract original independent signals (source components) that are linearly mixed in a basic framework. This letter discusses a learning algorithm for the separation of different source classes in which the observed data follow a mixture of several ICA models, where each model is described by a linear combination of independent and nongaussian sources. The proposed method is based on a sequential application of the minimum β-divergence method to separate all source classes sequentially. The proposed method searches the recovering matrix of each class on the basis of a rule of sequential change of the shifting parameter. If the initial choice of the shifting parameter vector is close to the mean of a data class, then all of the hidden sources belonging to that class are recovered properly with independent and nongaussian structure considering the data in other classes as out-liers. The value of the tuning parameter β is a key in the performance of the proposed method. A cross-validation technique is proposed as an adaptive selection procedure for the tuning parameter β for this algorithm, together with applications for both real and synthetic data analysis.