Abstract for the talk on 25.07.2018 (10:00 h)Seminar on Nonlinear Algebra
Ilya Chevyrev (University of Oxford, United Kingdom)
Persistence paths and signature features in topological data analysis
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.