{"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/graph-drawing-by-stochastic-gradient-descent","title":"Graph Drawing by Stochastic Gradient Descent","arxiv_id":"1710.04626","date":"2017-10-12","proceeding":null,"authors":["Jonathan X. Zheng","Samraat Pawar","Dan F. M. Goodman"],"abstract":"A popular method of force-directed graph drawing is multidimensional scaling using graph-theoretic distances as input. We present an algorithm to minimize its energy function, known as stress, by using stochastic gradient descent (SGD) to move a single pair of vertices at a time. Our results show that SGD can reach lower stress levels faster and more consistently than majorization, without needing help from a good initialization. We then show how the unique properties of SGD make it easier to produce constrained layouts than previous approaches. We also show how SGD can be directly applied within the sparse stress approximation of Ortmann et al. [1], making the algorithm scalable up to large graphs.","url_abs":"http://arxiv.org/abs/1710.04626v3","url_pdf":"http://arxiv.org/pdf/1710.04626v3.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":"graph-drawing-by-stochastic-gradient-descent","repo_url":"https://github.com/jxz12/s_gd2","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"graph-drawing-by-stochastic-gradient-descent","repo_url":"https://github.com/Kursula/FeatureGraph","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"graph-drawing-by-stochastic-gradient-descent","repo_url":"https://github.com/Kursula/Feature_Graph","is_official":0,"mentioned_in_paper":0,"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}