Abstract
A key step in insect olfaction is the transformation of a dense representation of odors in a small population of neurons - projection neurons (PNs) of the antennal lobe - into a sparse representation in a much larger population of neurons -Kenyon cells (KCs) of the mushroom body. What computational purpose does this transformation serve? We propose that the PN-KC network implements an online clustering algorithm which we derive from the k-means cost function. The vector of PN-KC synaptic weights converging onto a given KC represents the corresponding cluster centroid. KC activities represent attribution indices, i.e. the degree to which a given odor presentation is attributed to each cluster. Remarkably, such clustering view of the PN-KC circuit naturally accounts for several of its salient features. First, attribution indices are nonnegative thus rationalizing rectification in KCs. Second, the constraint on the total sum of attribution indices for each presentation is enforced by a Lagrange multiplier identified with the activity of a single inhibitory interneuron reciprocally connected with KCs. Third, the soft-clustering version of our algorithm reproduces observed sparsity and overcompleteness of the KC representation which may optimize supervised classification downstream.
