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