Zigzag persistent Homology and Network Methods for Topological Signal Processing
Abstract
Automatic detection of qualitative changes in the influx of data is central to the USAF mission. When the underlying system is modeled using dynamical systems, changes are called bifurcations and signal important, often critical, changes in the operating conditions. Examples include switching from normal flying patterns to stall, a decline in pilots vitals or awareness, or adversarial cyberspace activities. However, modern Air Force systems are a complicated mix of sophisticated engineering and a network of entangled logistics. Therefore, it is important to investigate methods that can autonomously monitor large amounts of complicated data for possible changes in the underlying system. Time series analysis (TSA) is a mature, extensive field of research providing methods for understanding, classifying, quantifying, and interpreting signals. However, many available tools are plagued by issues including noise sensitivity and computational complexity. Recently, a new viewpoint has emerged for analyzing time series by leveraging tools quantifying the shape of data from Topological Data Analysis (TDA); taken together, these new methods are known as Topological Signal Processing (TSP). This proposal outlines a new direction for TSP methods that leverages and advances the fundamental mathematics at the interface of dynamical systems, algebraic topology, and graph theory. Specifically, the PIs will research the underlying mathematics connecting bifurcation analysis with zigzag persistent homology of network-based structures, along with computational advancements for the realistic treatment of applications. The PIs are leaders in this field, as the first to combine network TSA methods with TDA, and the first to utilize zigzag persistence in this context. This research area will lead to novel, noise-robust bifurcation detection tools that can be widely used to analyze complex systems.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 07, 2023
- Source ID
- FA95502210007
Entities
People
- Firas A Khasawneh
Organizations
- Air Force Office of Scientific Research
- Michigan State University
- United States Air Force