{"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/differentially-private-topological-data","title":"Differentially Private Topological Data Analysis","arxiv_id":"2305.03609","date":"2023-05-05","proceeding":null,"authors":["Taegyu Kang","Sehwan Kim","Jinwon Sohn","Jordan Awan"],"abstract":"This paper is the first to attempt differentially private (DP) topological data analysis (TDA), producing near-optimal private persistence diagrams. We analyze the sensitivity of persistence diagrams in terms of the bottleneck distance, and we show that the commonly used \\v{C}ech complex has sensitivity that does not decrease as the sample size $n$ increases. This makes it challenging for the persistence diagrams of \\v{C}ech complexes to be privatized. As an alternative, we show that the persistence diagram obtained by the $L^1$-distance to measure (DTM) has sensitivity $O(1/n)$. Based on the sensitivity analysis, we propose using the exponential mechanism whose utility function is defined in terms of the bottleneck distance of the $L^1$-DTM persistence diagrams. We also derive upper and lower bounds of the accuracy of our privacy mechanism; the obtained bounds indicate that the privacy error of our mechanism is near-optimal. We demonstrate the performance of our privatized persistence diagrams through simulations as well as on a real dataset tracking human movement.","url_abs":"https://arxiv.org/abs/2305.03609v2","url_pdf":"https://arxiv.org/pdf/2305.03609v2.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":"abstracts"},"code_links":[{"paper_slug":"differentially-private-topological-data","repo_url":"https://github.com/jwsohn612/dptda","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"sensitivity","task_name":"Sensitivity"},{"task_slug":"topological-data-analysis","task_name":"Topological Data Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}