{"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/stochastic-non-convex-ordinal-embedding-with","title":"Stochastic Non-convex Ordinal Embedding with Stabilized Barzilai-Borwein Step Size","arxiv_id":"1711.06446","date":"2017-11-17","proceeding":null,"authors":["Ke Ma","Jinshan Zeng","Jiechao Xiong","Qianqian Xu","Xiaochun Cao","Wei Liu","Yuan YAO"],"abstract":"Learning representation from relative similarity comparisons, often called\nordinal embedding, gains rising attention in recent years. Most of the existing\nmethods are batch methods designed mainly based on the convex optimization,\nsay, the projected gradient descent method. However, they are generally\ntime-consuming due to that the singular value decomposition (SVD) is commonly\nadopted during the update, especially when the data size is very large. To\novercome this challenge, we propose a stochastic algorithm called SVRG-SBB,\nwhich has the following features: (a) SVD-free via dropping convexity, with\ngood scalability by the use of stochastic algorithm, i.e., stochastic variance\nreduced gradient (SVRG), and (b) adaptive step size choice via introducing a\nnew stabilized Barzilai-Borwein (SBB) method as the original version for convex\nproblems might fail for the considered stochastic \\textit{non-convex}\noptimization problem. Moreover, we show that the proposed algorithm converges\nto a stationary point at a rate $\\mathcal{O}(\\frac{1}{T})$ in our setting,\nwhere $T$ is the number of total iterations. Numerous simulations and\nreal-world data experiments are conducted to show the effectiveness of the\nproposed algorithm via comparing with the state-of-the-art methods,\nparticularly, much lower computational cost with good prediction performance.","url_abs":"http://arxiv.org/abs/1711.06446v2","url_pdf":"http://arxiv.org/pdf/1711.06446v2.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":"stochastic-non-convex-ordinal-embedding-with","repo_url":"https://github.com/alphaprime/Stabilized_Stochastic_BB","is_official":1,"mentioned_in_paper":1,"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}