{"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/heat-diffusion-distance-processes-a","title":"Heat diffusion distance processes: a statistically founded method to analyze graph data sets","arxiv_id":"2109.13213","date":"2021-09-27","proceeding":null,"authors":["Etienne Lasalle"],"abstract":"We propose two multiscale comparisons of graphs using heat diffusion, allowing to compare graphs without node correspondence or even with different sizes. These multiscale comparisons lead to the definition of Lipschitz-continuous empirical processes indexed by a real parameter. The statistical properties of empirical means of such processes are studied in the general case. Under mild assumptions, we prove a functional central limit theorem, as well as a Gaussian approximation with a rate depending only on the sample size. Once applied to our processes, these results allow to analyze data sets of pairs of graphs. We design consistent confidence bands around empirical means and consistent two-sample tests, using bootstrap methods. Their performances are evaluated by simulations on synthetic data sets.","url_abs":"https://arxiv.org/abs/2109.13213v4","url_pdf":"https://arxiv.org/pdf/2109.13213v4.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":"heat-diffusion-distance-processes-a","repo_url":"https://github.com/elasalle/heatdistanceprocess","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}