Generalized persistence analysis based on stable rank invariant

Abstract

We believe three ingredients are needed for further progress in persistence and its use: invariants not relying on decomposition theorems to go beyond 1-dimension, outcomes suitable for statistical analysis and a setup adopted for supervised and machine learning. Stable rank, a continuous invariant for multidimensional persistence, was introduced in W. Chacholski et al. - Multidimensional persistence and noise, 2017. In the current paper we continue this work by demonstrating how one builds an efficient computational pipeline around this invariant and uses it in inference in case of one parameter. We demonstrate some computational evidence of the statistical stability of stable rank. We also show how our framework can be used in supervised learning.