STATISTICAL TREATMENT OF GRAVITATIONAL CLUSTERING ALGORITHM by

STATISTICAL TREATMENT OF GRAVITATIONAL CLUSTERING ALGORITHM Yao Zhang, PhD University of Pittsburgh, 2010 In neuroscience, simultaneously recorded spike trains from multiple neurons are increasingly common; however, the computational neuroscience problem of how to quantitatively analyze such data remains a challenge. Gerstein, et al. [5] proposed a gravitational clustering algorithm (GCA) for multiple spike trains to qualitatively study interactions, in particular excitation, among multiple neurons. This thesis is mainly focused on a probabilistic treatment of GCA and a statistical treatment of Gerstein’s interaction mode. For a formal probabilistic treatment, we adopt homogeneous Poisson processes to generate the spike trains; define an interaction mode based on Gerstein’s formulation; analyze the asymptotic properties of its cluster index – GCA distances (GCAD). Under this framework, we show how the expectation of GCAD is related to a particular interaction mode, i.e., we prove that a time-adjusted-GCAD is a reasonable cluster index for large samples. We also indicate possible stronger results, such as central limit theorems and convergence to a Gaussian process. In our statistical work, we construct a generalized mixture model to estimate Gerstein’s interaction mode. We notice two key features of Gerstein’s proposal: (1) each spike from each spike train was assumed to be triggered by either one previous spike from one other spike train or environment; (2) each spike train was transformed into a continuous longitudinal curve. Inspired by their work, we develop a Bayesian model to quantitatively estimate excitation effects in the network structure. Our approach generalizes the mixture model to