  Cortical pyramidal neurons receive inputs from multiple distinct neural
populations and integrate these inputs in separate dendritic compartments. We
explore the possibility that cortical microcircuits implement Canonical
Correlation Analysis (CCA), an unsupervised learning method that projects the
inputs onto a common subspace so as to maximize the correlations between the
projections. To this end, we seek a multi-channel CCA algorithm that can be
implemented in a biologically plausible neural network. For biological
plausibility, we require that the network operates in the online setting and
its synaptic update rules are local. Starting from a novel CCA objective
function, we derive an online optimization algorithm whose optimization steps
can be implemented in a single-layer neural network with multi-compartmental
neurons and local non-Hebbian learning rules. We also derive an extension of
our online CCA algorithm with adaptive output rank and output whitening.
Interestingly, the extension maps onto a neural network whose neural
architecture and synaptic updates resemble neural circuitry and synaptic
plasticity observed experimentally in cortical pyramidal neurons.
