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We extend the mixtures of Gaussians (MOG) model to the projected mixture ofGaussians (PMOG) model. In the PMOG model, we assume that q dimensional inputdata points z_i are projected by a q dimensional vector w into 1-D variablesu_i. The projected variables u_i are assumed to follow a 1-D MOG model. In thePMOG model, we maximize the likelihood of observing u_i to find both the modelparameters for the 1-D MOG as well as the projection vector w. First, we derivean EM algorithm for estimating the PMOG model. Next, we show how the PMOG modelcan be applied to the problem of blind source separation (BSS). In contrast toconventional BSS where an objective function based on an approximation todifferential entropy is minimized, PMOG based BSS simply minimizes thedifferential entropy of projected sources by fitting a flexible MOG model inthe projected 1-D space while simultaneously optimizing the projection vectorw. The advantage of PMOG over conventional BSS algorithms is the more flexiblefitting of non-Gaussian source densities without assuming near-Gaussianity (asin conventional BSS) and still retaining computational feasibility.

PMOG: The projected mixture of Gaussians model with application to blind source separation