  An important problem in neuroscience is to understand how brains extract
relevant signals from mixtures of unknown sources, i.e., perform blind source
separation. To model how the brain performs this task, we seek a biologically
plausible single-layer neural network implementation of a blind source
separation algorithm. For biological plausibility, we require the network to
satisfy the following three basic properties of neuronal circuits: (i) the
network operates in the online setting; (ii) synaptic learning rules are local;
(iii) neuronal outputs are nonnegative. Closest is the work by Pehlevan et al.
[Neural Computation, 29, 2925--2954 (2017)], which considers Nonnegative
Independent Component Analysis (NICA), a special case of blind source
separation that assumes the mixture is a linear combination of uncorrelated,
nonnegative sources. They derive an algorithm with a biologically plausible
2-layer network implementation. In this work, we improve upon their result by
deriving 2 algorithms for NICA, each with a biologically plausible single-layer
network implementation. The first algorithm maps onto a network with indirect
lateral connections mediated by interneurons. The second algorithm maps onto a
network with direct lateral connections and multi-compartmental output neurons.
