A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions

1 code implementation • NeurIPS 2023 • David Loiseaux, Mathieu Carrière, Andrew J. Blumberg

One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale.

Topological Data Analysis

Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures

2 code implementations • NeurIPS 2023 • David Loiseaux, Luis Scoccola, Mathieu Carrière, Magnus Bakke Botnan, Steve Oudot

Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space.