{"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/recursive-diffeomorphism-based-regression-for","title":"Recursive Diffeomorphism-Based Regression for Shape Functions","arxiv_id":"1610.03819","date":"2016-10-12","proceeding":null,"authors":["Jieren Xu","Haizhao Yang","Ingrid Daubechies"],"abstract":"This paper proposes a recursive diffeomorphism based regression method for\none-dimensional generalized mode decomposition problem that aims at extracting\ngeneralized modes $\\alpha_k(t)s_k(2\\pi N_k\\phi_k(t))$ from their superposition\n$\\sum_{k=1}^K \\alpha_k(t)s_k(2\\pi N_k\\phi_k(t))$. First, a one-dimensional\nsynchrosqueezed transform is applied to estimate instantaneous information,\ne.g., $\\alpha_k(t)$ and $N_k\\phi_k(t)$. Second, a novel approach based on\ndiffeomorphisms and nonparametric regression is proposed to estimate wave shape\nfunctions $s_k(t)$. These two methods lead to a framework for the generalized\nmode decomposition problem under a weak well-separation condition. Numerical\nexamples of synthetic and real data are provided to demonstrate the fruitful\napplications of these methods.","url_abs":"http://arxiv.org/abs/1610.03819v2","url_pdf":"http://arxiv.org/pdf/1610.03819v2.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":"recursive-diffeomorphism-based-regression-for","repo_url":"https://github.com/HaizhaoYang/DeCom","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}