SATA II - Stochastic Algebraic Topology and Applications
Abstract
Objective: The Stochastic Algebraic Topology and Applications (SATA) project aims to exploit recent advances in the complementary areas of topology and stochastic processes to tackle a wide range of data analytic problems of importance to the USAF. Approach: The project will build on the recent successes of previous DoD programs, notably the Sensor Topology for Minimal Planning (SToMP) and Topological Data Analysis (TDA) programs by allowing for stochastic scenarios that were, to a large extent, not studied there. Treating data topologically is crucial in scenarios in which it is important to detect, localize, and perhaps perform an initial classification of objects without attempting to completely characterize them. Adding a stochastic element allows for the almost pervasive situation in which the data itself is imperfectly observed, due to the presence of background noise. It also covers the sampling situation, in which a small number of (random) observations are taken as representatives of a full data population. As current probabilistic and statistical methodology is ill-suited to detect such qualitative structures, the project aims to develop generic stochastic models whose topological structures are amenable to mathematical analysis, as a first step towards implementation of a broader, more quantitative program. Core topics will include random functions on manifolds, random manifolds created by random embeddings, and random manifolds arising in machine learning, and their theoretical and practical interplay. The fundamental mathematical, computational, and statistical tools developed in this program will have broad impact across several avenues of defense application as the data sets amenable to the proposed analysis reside throughout the military. Examples include sensor, intelligence, biological, logistical, and other DoD-critical applications.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 24, 2016
- Source ID
- FA95501510032
Entities
People
- Robert Adler
Organizations
- Air Force Office of Scientific Research
- Technion – Israel Institute of Technology
- United States Air Force