title: Point-process principal components analysis via geometric optimization.
abstract: There has been a fast-growing demand for analysis tools for multivariate point-process data driven by work in neural coding and, more recently, high-frequency finance. Here we develop a true or exact (as opposed to one based on time binning) principal components analysis for preliminary processing of multivariate point processes. We provide a maximum likelihood estimator, an algorithm for maximization involving steepest ascent on two Stiefel manifolds, and novel constrained asymptotic analysis. The method is illustrated with a simulation and compared with a binning approach.
authors.affiliation: School of Electrical Engineering and Telecommunications, UNSW Sydney, NSW 2052, Australia v.solo@unsw.edu.au
authors.forename: Victor
authors.initials: V
authors.lastname: Solo
authors.forename: Syed Ahmed
authors.initials: SA
authors.lastname: Pasha
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D016013:Likelihood Functions; D015999:Multivariate Analysis; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D025341:Principal Component Analysis