{"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/density-sensitive-bifiltered-dowker-complexes","title":"Density Sensitive Bifiltered Dowker Complexes via Total Weight","arxiv_id":"2405.15592","date":"2024-05-24","proceeding":null,"authors":["Niklas Hellmer","Jan Spaliński"],"abstract":"In this paper, we introduce new density-sensitive bifiltrations for data using the framework of Dowker complexes. Previously, Dowker complexes were studied to address directional or bivariate data whereas density-sensitive bifiltrations on \\v{C}ech and Vietoris--Rips complexes were suggested to make them more robust, while increasing computational complexity. We combine these two lines of research, noting that the superlevels of the total weight function of a Dowker complex can be identified as an instance of Sheehy's multicover filtration. We prove a version of Dowker duality that is compatible with this filtration and show that it corresponds to the multicover nerve theorem. As a consequence, we find that the subdivision intrinsic \\v{C}ech complex admits a smaller model. Moreover, regarding the total weight function as a counting measure, we generalize it to arbitrary measures and prove a density-sensitive stability theorem for the case of probability measures. As an application, we propose a robust landmark-based bifiltration which approximates the multicover bifiltration. Additionally, we provide an algorithm to calculate the appearances of simplices in our bifiltration and present computational examples.","url_abs":"https://arxiv.org/abs/2405.15592v2","url_pdf":"https://arxiv.org/pdf/2405.15592v2.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":"density-sensitive-bifiltered-dowker-complexes","repo_url":"https://github.com/nihell/pydowker","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}