Clustering and Principal Component Analysis as Distinct Computational Regimes of a Biologically Motivated Neural Circuit

Background: Characteristic circuitry in superficial layers of neocortex has been repeatedly shown to carry out lateral inhibition: excitatory–inhibitory interactions within a specific anatomical design. Methods: We provide simulation and formal analyses of the emergent operations of this circuitry. Results: Derived directly from anatomical circuit layout and physiological activation patterns, we show that this circuit carries out two distinct effective procedures on its inputs: categorization, and component analysis; moreover, we show that each procedure’s emergence is dependent on a single biological parameter: the relative strength of local feedback inhibitory cells. We characterize the detailed nature of both the biological activity and the emergent statistical operations and evaluate them in the context of extensive related literature in statistics, machine learning, and computational neuroscience. Conclusions: Very notably, the two emergent operations (clustering and component analysis) have not previously been shown to contain deep mathematical connections to each other, let alone to each be derivable from a single overarching algorithmic precursor that has clustering and component analysis as two special cases. The identification of that deep formal mathematical connection, and its arrival directly from a detailed biological circuit, represents a rare instance of novel mathematical relations arising from biological analyses.