{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/statistical-topological-data-analysis-using","title":"Statistical topological data analysis using persistence landscapes","arxiv_id":"1207.6437","date":"2012-07-27","proceeding":null,"authors":["Peter Bubenik"],"abstract":"We define a new topological summary for data that we call the persistence landscape. Since this summary lies in a vector space, it is easy to combine with tools from statistics and machine learning, in contrast to the standard topological summaries. Viewed as a random variable with values in a Banach space, this summary obeys a strong law of large numbers and a central limit theorem. We show how a number of standard statistical tests can be used for statistical inference using this summary. We also prove that this summary is stable and that it can be used to provide lower bounds for the bottleneck and Wasserstein distances.","url_abs":"https://arxiv.org/abs/1207.6437v4","url_pdf":"https://arxiv.org/pdf/1207.6437v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"statistical-topological-data-analysis-using","repo_url":"https://github.com/aidos-lab/Presto","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1207.6437","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}