BLIND SEPARATION OF POSITIVE SOURCES USING NON-NEGATIVE PC A
Erkki Oja, Mark D. Plumbley, E London · 2003
The instantaneous noise-free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full rank mixing matrix. However, with some prior information on the sources, like positivity, new analysis and perhaps simplified solution methods may yet become possible. In this paper, we consider the task of independent component analysis when the independent sources are known to be non-negative and well-grounded, which means that they have a non-zero pdf in the region of zero. We propose the use of a `Non-Negative PCA' algorithm which is a special case of the nonlinear PCA algorithm, but with a rectification nonlinearity, and we show that this algorithm will find such non-negative well-grounded independent sources. Although the algorithm has proved difficult to analyze in the general case, we give an analytical convergence result here, complemented by a numerical simulation which illustrates its operation.