Identifying neuronal assemblies with local and global connectivity with scale space spectral clustering

A nonparametric approach is proposed to identify clusters of functionally interdependent neurons, independent of the time scale at which they are maximally correlated. The neural point processes are represented in a N-dimensional scale space using the Haar wavelet transform. A similarity measure between any given pair of neurons is defined in the scale space. Clusters of “similar” neurons are identified by first reducing the N-dimensional scale space representation using principal components to obtain a Q-dimensional space. The weighted principal components are subsequently used to connect each neuron to the others in a graph representation. A probabilistic spectral clustering algorithm is used to perform graph partitioning by maximizing cluster compactness. Performance is compared to that of the k-means and the expectation–maximization algorithms for 120 neurons with time-varying intensity functions consisting of spontaneous background activity and phased response elicited at distinct time scales.