Topological Methods for the Analysis of Applications

DOI

10.2991/assehr.k.200306.069How to use a DOI?

Keywords

TDA, Persistent Homology, Hausdorff Distance, text classification, face detection

Abstract

Topological Data Analysis(TDA) is a rapidly developing data analysis field in recent years. It provides topological and geometric methods to obtain the relevant features of high-dimensional data. This paper introduces the related mathematical principles of Persistent Homology, Mapper, Hausdorff Distance in topology and enumerates two applications of TDA. One is about text classification of natural language. It uses persistent homology to analyze poetry data and mapper algorithm to analyze and visualize data sets. The other application is based on the principle of Robust Hausdorff Distance, and proposes a fast and accurate shape comparison method for face detection. The result shows that the TDA method is not only accurate, but also can realize data visualization.

Copyright

© 2020, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Yumiao Lei
PY  - 2020
DA  - 2020/03/12
TI  - Topological Methods for the Analysis of Applications
BT  - Proceedings of the International Conference on Modern Educational Technology and Innovation and Entrepreneurship (ICMETIE 2020)
PB  - Atlantis Press
SP  - 6
EP  - 9
SN  - 2352-5398
UR  - https://doi.org/10.2991/assehr.k.200306.069
DO  - 10.2991/assehr.k.200306.069
ID  - Lei2020
ER  -