{"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/heuristic-framework-for-multi-scale-testing","title":"Heuristic Framework for Multi-Scale Testing of the Multi-Manifold Hypothesis","arxiv_id":"1807.00349","date":"2018-07-01","proceeding":null,"authors":["F. Patricia Medina","Linda Ness","Melanie Weber","Karamatou Yacoubou Djima"],"abstract":"When analyzing empirical data, we often find that global linear models\noverestimate the number of parameters required. In such cases, we may ask\nwhether the data lies on or near a manifold or a set of manifolds (a so-called\nmulti-manifold) of lower dimension than the ambient space. This question can be\nphrased as a (multi-) manifold hypothesis. The identification of such intrinsic\nmultiscale features is a cornerstone of data analysis and representation and\nhas given rise to a large body of work on manifold learning. In this work, we\nreview key results on multi-scale data analysis and intrinsic dimension\nfollowed by the introduction of a heuristic, multiscale framework for testing\nthe multi-manifold hypothesis. Our method implements a hypothesis test on a set\nof spline-interpolated manifolds constructed from variance-based intrinsic\ndimensions. The workflow is suitable for empirical data analysis as we\ndemonstrate on two use cases.","url_abs":"http://arxiv.org/abs/1807.00349v1","url_pdf":"http://arxiv.org/pdf/1807.00349v1.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":"heuristic-framework-for-multi-scale-testing","repo_url":"https://github.com/MelWe/mm-hypothesis","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}