February 20, 2018: Rudrasis Chakraborty

A Geometric framework for statistical analysis of trajectories of distinct temporal spans
Rudrasis Chakraborty
PostDoctoral associate,
McGovern Institute for Brain Research,
MIT, USA
Email: rudrasischa@gmail.com

Date  : February 20, 2018
Time  : 12:00 HRS
Venue: ECSU Seminar Room, 9th Floor, S N Bose Bhavan (Library Building)

 
Abstract

Analyzing data representing multifarious trajectories is central to the many fields in Science and Engineering; for example, trajectories representing a tennis serve, a gymnast's parallel bar routine, progression/remission of disease and so on. We present a novel geometric algorithm for performing statistical analysis of trajectories with distinct number of samples representing longitudinal (or temporal) data. A key feature of our proposal is that unlike existing schemes, our model is deployable in regimes where each participant provides a different number of acquisitions (trajectories have different number of sample points). To achieve this, we develop a novel method involving the parallel transport of the tangent vectors along each given trajectory to the starting point of the respective trajectories and then use the span of the matrix whose columns consist of these vectors, to construct a linear subspace in R^m. We then map these linear subspaces of R^m on to a single high dimensional hypersphere. This enables computing group statistics over trajectories by instead performing statistics on the hypersphere (equipped with a simpler geometry). Given a point on the hypersphere representing a trajectory, we also provide a "reverse mapping" algorithm to uniquely (under certain assumptions) reconstruct the subspace that corresponds to this point. Finally, by using existing algorithms for recursive Frechet mean and exact principal geodesic analysis on the hypersphere, we present several experiments on synthetic and real (vision and medical) data sets showing how group testing on such diversely sampled longitudinal data is possible by analyzing the reconstructed data in the subspace spanned by the first few PGs.

All are cordially invited.
 
Dipti Prasad Mukherjee
Head, Electronics and Communication Sciences Unit