Metrics and stabilization in one parameter persistence

Abstract

We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between persistent vector spaces leads to stabilization of discrete invariants. We develop theory behind this stabilization and stable rank invariant. We give evidence of the usefulness of this approach in concrete data analysis.

32 pages, 10 figures, appearing in SIAM Journal on Applied Algebra and Geometry 4-1