Persistence paths and signature features in topological data analysis

Ilya Chevyrev, Vidit Nanda, Harald Oberhauser

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in the tensor algebra of that vector space. The composition of these two operations - barcode to path, path to tensor series - results in a feature map that has several desirable properties for statistical learning, such as universality and characteristicness, and achieves state-of-the-art results on common classification benchmarks.
Original languageEnglish
Pages (from-to)192-202
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume42
Issue number1
Early online date7 Dec 2018
DOIs
Publication statusPublished - 1 Jan 2020

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