Blind Nonnegative Source Separation Using Biological Neural Networks

Abstract

Blind source separation, i.e. extraction of independent sources from a mixture, is an important problem for both artificial and natural signal processing. Here, we address a special case of this problem when sources (but not the mixing matrix) are known to be nonnegative, for example, due to the physical nature of the sources. We search for the solution to this problem that can be implemented using biologically plausible neural networks. Specifically, we consider the online setting where the dataset is streamed to a neural network. The novelty of our approach is that we formulate blind nonnegative source separation as a similarity matching problem and derive neural networks from the similarity matching objective. Importantly, synaptic weights in our networks are updated according to biologically plausible local learning rules.

Manifold-tiling Localized Receptive Fields are Optimal in Similarity-preserving Neural Networks

“…These results add to the versatility of NSM networks previously shown to cluster data, learn sparse dictionaries and blindly separate sources [11,18,16], depending on the nature of input data. This illustrates how a universal neural circuit in the brain can implement various learning tasks [11].…”

“…In the absence of sign constraints, such objectives are provably optimized by projecting inputs onto the principal subspace [13,14,15], which can be done online by networks of linear neurons [8,9,10]. Constraining the sign of the output leads to networks of rectifying neurons [11] which have been simulated numerically in the context of clustering and feature learning [11,12,16,17], and analyzed in the context of blind source extraction [18]. In the context of manifold learning, optimal solutions of Nonnegative Similarity-preserving Mapping objectives have been missing because optimization of existing NSM objectives is challenging.…”

The Neuronal Basis of an Illusory Motion Percept Is Explained by Decorrelation of Parallel Motion Pathways

“…Interestingly, since each cell type computes its phi and reverse-phi responses from distinct points in space, reverse-phi responses cannot merely be ‘illusory’ byproducts of motion detection circuitry for phi signals. Furthermore, this organization of responses allows T4 and T5 to represent motion signals with non-negative neuronal responses, and non-negativity constraints might generally help relate the algorithms of neural computation to their implementations [56,59]. Notably, since T4 and T5 are non-spiking neurons, non-negativity was not a priori required for biological plausibility.…”

In vitro neural networks minimise variational free energy

“…These form observations speak to the biological plausibility of the variational message passing scheme used to simulate neural responses in this paper. Although several biologically plausible BSS methods in the continuous state space have been developed [44][45][46][47][48], to our knowledge, this is the first attempt to explain neuronal BSS using a biologically plausible learning algorithm in the discrete (binary) state space.…”