Conference abstracts

Session A4 - Computational Geometry and Topology

July 12, 19:00 ~ 19:25 - Room B7

Tropical Coordinates on the Space of Persistence Barcodes

Sara Kalisnik

Brown University / Max Planck Institute, USA / Germany   -

In the last two decades applied topologists have developed numerous methods for `measuring' and building combinatorial representations of the shape of the data. The most famous example of the former is persistent homology. This adaptation of classical homology assigns a barcode, i.e. a collection of intervals with endpoints on the real line, to a finite metric space. Unfortunately, barcodes are not well-adapted for use by practitioners in machine learning tasks. We can circumvent this problem by assigning numerical quantities to barcodes and these outputs can then be used as input to standard algorithms. I will talk about tropical functions that can be used as coordinates on the space of barcodes. All of these are stable with respect to the standard distance functions (bottleneck, Wasserstein) used on the barcode space.

View abstract PDF

FoCM 2017, based on a nodethirtythree design.