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Talk

Persistence paths and signature features in topological data analysis

  • Ilya Chevyrev (University of Oxford, United Kingdom)
E1 05 (Leibniz-Saal)

Abstract

Persistent homology is a tool used to analyse topological features of data. In this talk, I will describe 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 high performance on several classification benchmarks.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail