{"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/geometry-based-data-generation","title":"Geometry-Based Data Generation","arxiv_id":"1802.04927","date":"2018-02-14","proceeding":null,"authors":["Ofir Lindenbaum","Jay S. Stanley III","Guy Wolf","Smita Krishnaswamy"],"abstract":"Many generative models attempt to replicate the density of their input data.\nHowever, this approach is often undesirable, since data density is highly\naffected by sampling biases, noise, and artifacts. We propose a method called\nSUGAR (Synthesis Using Geometrically Aligned Random-walks) that uses a\ndiffusion process to learn a manifold geometry from the data. Then, it\ngenerates new points evenly along the manifold by pulling randomly generated\npoints into its intrinsic structure using a diffusion kernel. SUGAR equalizes\nthe density along the manifold by selectively generating points in sparse areas\nof the manifold. We demonstrate how the approach corrects sampling biases and\nartifacts, while also revealing intrinsic patterns (e.g. progression) and\nrelations in the data. The method is applicable for correcting missing data,\nfinding hypothetical data points, and learning relationships between data\nfeatures.","url_abs":"http://arxiv.org/abs/1802.04927v4","url_pdf":"http://arxiv.org/pdf/1802.04927v4.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":"geometry-based-data-generation","repo_url":"https://github.com/KrishnaswamyLab/SUGAR","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1802.04927","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}