A Directional-Linear Bayesian Network and Its Application for Clustering and Simulation of Neural Somas

Neural somas perform most of the metabolic activities in the neuron and support the chemical process that generates the basic elements of the synapses, and consequently the brain activity. The morphology of the somas is one of the fundamental features for classifying neurons and their functionality. In this paper, we characterize the morphology of the 39 three-dimensional reconstructed human pyramidal somas in terms of their multiresolutional Reeb graph representation, from which we extract a set of directional and linear variables to perform model-based clustering. To deal with this dataset, we introduce the novel Extended Mardia-Sutton mixture model whose mixture components are distributed according to a newly proposed multivariate probability density function that is able to capture the directional-linear correlations. We exploit the capabilities of Bayesian networks in combination with the Structural Expectation-Maximization algorithm to learn the finite mixture model that clusters the neural somas by their morphology and the conditional independence constraints between variables. We also derive the Kullback-Leibler divergence of the Extended Mardia-Sutton distribution to be used as a measure of similarity between soma clusters. The proposed finite mixture model discovered three subtypes of human pyramidal somas. We performed Weltch t-tests and Watson-Williams tests, as well as rule-based identification of clusters to characterize each group by its most prominent features. Furthermore, the resulting model allows us to simulate the 3D virtual representations of somas from each cluster, which can be a useful tool for neuroscientists to reason and suggest new hypotheses.