Year: 2020
Type: preprint
Abstract: Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that tracks changes in topological information. These changes can be recorded in multi-sets known as {\it persistence diagrams}. Converting information stored in persistence diagrams into a form compatible with modern machine learning algorithms is a major vein of research in TDA. {\it Persistence curves}, a recently developed framework, provides a canonical and flexible way to encode the information presented in persistence diagrams into vectors. In this work, we propose a new set of metrics based on persistence curves. We prove the stability of the proposed metrics. Finally, we apply these metrics to the UCR Time Series Classification Archive. These empirical results show that our metrics perform better than the relevant benchmark in most cases and warrant further study.
Source: arXiv (Cornell University)
Authors: Chung, Yu-Min, Cruse, William, Lawson, Austin
Institution: University of North Carolina at Greensboro
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3011993352