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Statistical Treatment of Gravitational Clustering Algorithm

Zhang, Yao (2010) Statistical Treatment of Gravitational Clustering Algorithm. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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. 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 accommodate the network structure through a matrix Dirichlet distribution. The network structure in our model could either approximate the directed acyclic graph of a Bayesian network or be the directed graph in a dynamic Bayesian network. This model can be generally applied on high-dimensional longitudinal data to model its dynamics. Finally, we assess the sampling properties of this model and its application to multiple spike trains by simulation.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairIyengar, Satishssi@pitt.eduSSI
Committee MemberBlock, Henry Whwb@pitt.eduHWB
Committee MemberCheng, Yuyucheng@pitt.eduYUCHENG
Committee MemberDruzdzel, Marek Jmarek@sis.pitt.eduDRUZDZEL
Date: 1 October 2010
Date Type: Completion
Defense Date: 19 December 2009
Approval Date: 1 October 2010
Submission Date: 22 April 2010
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Statistics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Bayes network; generalized mixture model; high-dimensional longitudinal data; matrix Dirichlet distribution; multiple spike trains; Poisson process
Other ID:, etd-04222010-053115
Date Deposited: 10 Nov 2011 19:41
Last Modified: 15 Nov 2016 13:41


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