Topological Data Analysis: An Overview

reportActive / Technical Report | Accesssion Number: AD1136048 | DOI: http://dx.doi.org/10.21079/11681/40943 | Open PDF

Abstract:

A growing area of mathematics topological data analysis (TDA) uses fundamental concepts of topology to analyze complex, high-dimensional data. A topological network represents the data, and the TDA uses the network to analyze the shape of the data and identify features in the network that correspond to patterns in the data. These patterns extract knowledge from the data. TDA provides a framework to advance machine learnings ability to understand and analyze large, complex data. This paper provides background information about TDA, TDA applications for large data sets, and details related to the investigation and implementation of existing tools and environments.

Author(s):
Bednar, Amy E.
Author Organization(s):
ENGINEER RESEARCH AND DEVELOPMENT CENTER VICKSBURG MS
Funding Organization(s):
Office of the Secretary of Defense, Washington DC , DC
Document Type:
Technical Report/Final Report
Publication Date:
2021 Jun 01
Pagination:
16

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution Code:
A - Approved For Public Release
Distribution Statement: Public Release

RECORD

Collection: TRECMS
Identifying Numbers
Program Element Number(s):
PE0603833D8Z
Project Number(s):
403
Subject Terms
Modernization Areas:
Autonomy
Communities of Interest:
Engineered Resilient Systems
Descriptor(s):
data analysis, data sets, graphical user interface, internet of things, machine learning, topology, engineers, algorithms, engineering, mathematics, geometry, information science, intrusion detection, learning, visualizations, abstracts, environment
Keyword(s):
Electronic data processing, tda (topological data analysis), tda applications, tda technology, Mapper algorithm
Subject Categories:
Mathematical and Computer Sciences; Behavioral and Social Sciences
Creation Date:
2021 Jun 25
Update Date:
2021 Sep 02