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An introduction to persistent homology for time series
Author(s) -
Ravishanker Nalini,
Chen Renjie
Publication year - 2021
Publication title -
wiley interdisciplinary reviews: computational statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.693
H-Index - 38
eISSN - 1939-0068
pISSN - 1939-5108
DOI - 10.1002/wics.1548
Subject(s) - persistent homology , topological data analysis , cluster analysis , computer science , computational topology , exploratory data analysis , time series , homology (biology) , series (stratigraphy) , theoretical computer science , biological data , data mining , algorithm , mathematics , machine learning , bioinformatics , biology , paleontology , gene , mathematical physics , biochemistry , scalar field
Topological data analysis (TDA) uses information from topological structures in complex data for statistical analysis and learning. This paper discusses persistent homology, a part of computational (algorithmic) topology that converts data into simplicial complexes and elicits information about the persistence of homology classes in the data. It computes and outputs the birth and death of such topologies via a persistence diagram. Data inputs for persistent homology are usually represented as point clouds or as functions, while the outputs depend on the nature of the analysis and commonly consist of either a persistence diagram, or persistence landscapes. This paper gives an introductory level tutorial on computing these summaries for time series using R, followed by an overview on using these approaches for time series classification and clustering. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Applications of Computational Statistics > Computational Mathematics