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Statistics Seminar - "Nonparametric Density Estimation on Riemannian Manifolds: A Methodology for Developing Spatio-Temporal Features," Dr. Justin Jacobs - Sandia National Lab

Event Type
Bo Li
106B1 Engineering Hall
Oct 26, 2017   3:30 - 4:30 pm  
Dr. Justin Jacobs -- Sandia National Lab

When data points are observed on a particular Riemannian manifold, traditional statistical applications may not be appropriate for the manifold of interest or they may obfuscate meaningful information captured by the sampling methodology on the manifold. In certain scenarios, modeling techniques such as Frechet means (Bhattacharya, Patrangenaru), circular and spherical statistics (von Mises, Mardia, Jupp), and advanced manifold learning methods (Shrivastava, Klassen) have proven feasible and faithful to the geometric structures of interest. However, in these methods, development of spatio-temporal quantities is left to be understood. In this vein, we identify a method of density estimation that not only remains faithful to the manifold of interest, but also yields features that can be used to create a waterfall scheme, usable by temporal methods. In this talk, we describe the density estimation aspect of estimating a probability distribution through the Laplace-Beltrami operator acting on the space of square-integrable functions. From this estimation procedure, we identify an associated signature of the distribution of observations on the manifold and in-turn identify how we might proceed in using this structure in a temporal setting.

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