  Extraction of latent sources of complex stimuli is critical for making sense
of the world. While the brain solves this blind source separation (BSS) problem
continuously, its algorithms remain unknown. Previous work on
biologically-plausible BSS algorithms assumed that observed signals are linear
mixtures of statistically independent or uncorrelated sources, limiting the
domain of applicability of these algorithms. To overcome this limitation, we
propose novel biologically-plausible neural networks for the blind separation
of potentially dependent/correlated sources. Differing from previous work, we
assume some general geometric, not statistical, conditions on the source
vectors allowing separation of potentially dependent/correlated sources.
Concretely, we assume that the source vectors are sufficiently scattered in
their domains which can be described by certain polytopes. Then, we consider
recovery of these sources by the Det-Max criterion, which maximizes the
determinant of the output correlation matrix to enforce a similar spread for
the source estimates. Starting from this normative principle, and using a
weighted similarity matching approach that enables arbitrary linear
transformations adaptable by local learning rules, we derive two-layer
biologically-plausible neural network algorithms that can separate mixtures
into sources coming from a variety of source domains. We demonstrate that our
algorithms outperform other biologically-plausible BSS algorithms on correlated
source separation problems.
