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Cortical pyramidal neurons receive inputs from multiple distinct neuralpopulations and integrate these inputs in separate dendritic compartments. Weexplore the possibility that cortical microcircuits implement CanonicalCorrelation Analysis (CCA), an unsupervised learning method that projects theinputs onto a common subspace so as to maximize the correlations between theprojections. To this end, we seek a multi-channel CCA algorithm that can beimplemented in a biologically plausible neural network. For biologicalplausibility, we require that the network operates in the online setting andits synaptic update rules are local. Starting from a novel CCA objectivefunction, we derive an online optimization algorithm whose optimization stepscan be implemented in a single-layer neural network with multi-compartmentalneurons and local non-Hebbian learning rules. We also derive an extension ofour online CCA algorithm with adaptive output rank and output whitening.Interestingly, the extension maps onto a neural network whose neuralarchitecture and synaptic updates resemble neural circuitry and synapticplasticity observed experimentally in cortical pyramidal neurons.

A biologically plausible neural network for multi-channel Canonical Correlation Analysis