Mixture of ICAs model for natural images solved by manifold optimization method

A finite mixture model composed of several components that are each described by a linear mixture of independent sources is proposed in this paper. Randomly selected patches from a dataset of natural images constitute our main dataset. Independent sources and mixing matrix for each mixture component are estimated that help us derive a qualitative inspection about the performance of the algorithm where no ground truth data is available. This method extends the mixture of Gaussians model in a way that components are not restricted to be Gaussian anymore. Each source signal is represented as a mixture of Gaussians which increases its flexibility to model both super- and sub-Gaussian sources. The proposed mixture model is formulated as a manifold optimization problem that gives a desirable convergence behavior. We believe that the non-Gaussian character of informative natural signals, makes them suitable to be modeled by this method. Finally, The learned features in each mixture component can provide us with useful insights into how early sensory pathways process information in an efficient way.