# A persistence landscapes toolbox for topological statistics

arXiv: https://arxiv.org/abs/1501.00179 · HTML: https://mlsanity.com/paper/1501.00179/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2014.

## Built on by (most cited first, 16 of 16)

- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [On the effectiveness of persistent homology](https://mlsanity.com/paper/2206.10551/) (2022)
- [Mapping the Multiverse of Latent Representations](https://mlsanity.com/paper/2402.01514/) (2024)
- [Landslide Topology Uncovers Failure Movements](https://mlsanity.com/paper/2310.09631/) (2023)
- [A Topological Data Analysis Based Classifier](https://mlsanity.com/paper/2111.05214/) (2021)
- [TACO-Net: Topological Signatures Triumph in 3D Object Classification](https://mlsanity.com/paper/2509.24802/) (2025)
- [Transfer Learning for Autonomous Chatter Detection in Machining](https://mlsanity.com/paper/2204.05400/) (2022)
- [A topological classifier to characterize brain states: When shape matters more than variance](https://mlsanity.com/paper/2303.04231/) (2023)
- [Novel definition and quantitative analysis of branch structure with topological data analysis](https://mlsanity.com/paper/2402.07436/) (2024)
- [Topological descriptors of foot clearance gait dynamics improve differential diagnosis of Parkinsonism](https://mlsanity.com/paper/2603.06212/) (2026)
- [From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features](https://mlsanity.com/paper/2606.11911/) (2026)
- [A Mathematical Framework for Topological Causal Data Analysis](https://mlsanity.com/paper/2607.28161/) (2026)
- [Individual Topology Structure of Eye Movement Trajectories](https://mlsanity.com/paper/2205.10667/) (2022)
- [Machine learning and Topological data analysis identify unique features of human papillae in 3D scans](https://mlsanity.com/paper/2307.06255/) (2023)
- [Persistence Spheres: Bi-continuous Representations of Persistence Diagrams](https://mlsanity.com/paper/2509.16999/) (2025)
- [Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagrams](https://mlsanity.com/paper/2607.27126/) (2026)

## Abstract (arXiv)

Topological data analysis provides a multiscale description of the geometry and topology of quantitative data. The persistence landscape is a topological summary that can be easily combined with tools from statistics and machine learning. We give efficient algorithms for calculating persistence landscapes, their averages, and distances between such averages. We discuss an implementation of these algorithms and some related procedures. These are intended to facilitate the combination of statistics and machine learning with topological data analysis. We present an experiment showing that the low-dimensional persistence landscapes of points sampled from spheres (and boxes) of varying dimensions differ.