ARO Statistical Foundations for Analyzing Large Collections of Network-Data Objects
Abstract
This proposal seeks to investigate new ways to use concepts from geometry, probability and statistics on manifolds in order to analyze and categorize classes of data objects. This project will progress along the following three thrusts. 1. It will attempt to associate classes of data objects with sub manifolds of Euclidean spaces through their (combinatorial) Laplacians. Techniques of differential geometry will enable mathematical characterization of these novel spaces and of appropriate notions of averaging of objects in these spaces. 2. Concepts from probability and statistics on manifolds will be extended to adapt to the high-dimensional and geometrically complex nature of these data spaces. An appropriate probabilistic framework will be developed for describing the statistical behavior of such averages. 3. From this probabilistic foundation, a variety of statistical methodologies will be constructed and tested for analyzing large collections of data objects.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 19, 2019
- Source ID
- W911NF1510440
Entities
People
- Eric D. Kolaczyk
Organizations
- Army Contracting Command
- Boston University
- United States Army