A "nonnegative PCA" algorithm for independent component analysis

Abstract

We consider the task of independent component analysis when the independent sources are known to be nonnegative and well-grounded, so that they have a nonzero probability density function (pdf) in the region of zero. We propose the use of a "nonnegative principal component analysis (nonnegative PCA)" algorithm, which is a special case of the nonlinear PCA algorithm, but with a rectification nonlinearity, and we conjecture that this algorithm will find such nonnegative well-grounded independent sources, under reasonable initial conditions. While the algorithm has proved difficult to analyze in the general case, we give some analytical results that are consistent with this conjecture and some numerical simulations that illustrate its operation.