{"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/clustering-with-t-sne-provably","title":"Clustering with t-SNE, provably","arxiv_id":"1706.02582","date":"2017-06-08","proceeding":null,"authors":["George C. Linderman","Stefan Steinerberger"],"abstract":"t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and\nvisualization method proposed by van der Maaten & Hinton in 2008, has rapidly\nbecome a standard tool in a number of natural sciences. Despite its\noverwhelming success, there is a distinct lack of mathematical foundations and\nthe inner workings of the algorithm are not well understood. The purpose of\nthis paper is to prove that t-SNE is able to recover well-separated clusters;\nmore precisely, we prove that t-SNE in the `early exaggeration' phase, an\noptimization technique proposed by van der Maaten & Hinton (2008) and van der\nMaaten (2014), can be rigorously analyzed. As a byproduct, the proof suggests\nnovel ways for setting the exaggeration parameter $\\alpha$ and step size $h$.\nNumerical examples illustrate the effectiveness of these rules: in particular,\nthe quality of embedding of topological structures (e.g. the swiss roll)\nimproves. We also discuss a connection to spectral clustering methods.","url_abs":"http://arxiv.org/abs/1706.02582v1","url_pdf":"http://arxiv.org/pdf/1706.02582v1.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":"clustering-with-t-sne-provably","repo_url":"https://github.com/KlugerLab/pyFIt-SNE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"clustering-with-t-sne-provably","repo_url":"https://github.com/KlugerLab/t-SNE-Heatmaps","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[{"method_slug":"spectral-clustering","method_name":"Spectral Clustering"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1706.02582","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}