Source Separation and Density Estimation by Faithful Equivariant SOM

Jack D. Cowan Department of Math University of Chicago Chicago, IL 60637 [email protected] We couple the tasks of source separation and density estimation by extracting the local geometrical structure of distributions obtained from mixtures of statistically independent sources. Our modifications of the self-organizing map (SOM) algorithm results in purely digital learning rules which perform non-parametric histogram density estimation. The non-parametric nature of the separation allows for source separation of non-linear mixtures. An anisotropic coupling is introduced into our SOM with the role of aligning the network locally with the independent component contours. This approach provides an exact verification condition for source separation with no prior on the source distributions.