Persistence paths and signature features in topological data analysis

Ilya Chevyrev; Vidit Nanda; Harald Oberhauser

doi:10.1109/tpami.2018.2885516

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arXiv · 1806.00381

Persistence paths and signature features in topological data analysis

Ilya Chevyrev·Vidit Nanda·Harald Oberhauser

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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.

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BibTeX RIS

Ilya Chevyrev, Vidit Nanda, Harald Oberhauser. 2018-06-01. Persistence paths and signature features in topological data analysis. https://doi.org/10.1109/tpami.2018.2885516

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