A0628
Title: How are random objects distributed in a metric space?
Authors: Paromita Dubey - University of Southern California (United States)
Yaqing Chen - Rutgers University (United States) [presenting]
Hans-Georg Mueller - University of California Davis (United States)
Abstract: New tools are proposed for the geometric exploration of data objects taking values in a general separable metric space. For a random object, the concept of distance profiles is first introduced. Specifically, the distance profile of a point in a metric space is the distribution of distances between the point and the random object. Distance profiles can be harnessed to define transport ranks based on optimal transport, which captures the centrality and outlyingness of each element in the metric space with respect to the probability measure induced by the random object. The properties of transport ranks are studied, and it is shown that they provide an effective device for detecting and visualizing patterns in samples of random objects. In particular, the theoretical guarantees are established for the estimation of the distance profiles and the transport ranks for a wide class of metric spaces, followed by practical illustrations.
