  Despite our extensive knowledge of biophysical properties of neurons, there
is no commonly accepted algorithmic theory of neuronal function. Here we
explore the hypothesis that single-layer neuronal networks perform online
symmetric nonnegative matrix factorization (SNMF) of the similarity matrix of
the streamed data. By starting with the SNMF cost function we derive an online
algorithm, which can be implemented by a biologically plausible network with
local learning rules. We demonstrate that such network performs soft clustering
of the data as well as sparse feature discovery. The derived algorithm
replicates many known aspects of sensory anatomy and biophysical properties of
neurons including unipolar nature of neuronal activity and synaptic weights,
local synaptic plasticity rules and the dependence of learning rate on
cumulative neuronal activity. Thus, we make a step towards an algorithmic
theory of neuronal function, which should facilitate large-scale neural circuit
simulations and biologically inspired artificial intelligence.
