{"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/fast-matrix-factorization-with-non-uniform","title":"Fast Matrix Factorization with Non-Uniform Weights on Missing Data","arxiv_id":"1811.04411","date":"2018-11-11","proceeding":null,"authors":["Xiangnan He","Jinhui Tang","Xiaoyu Du","Richang Hong","Tongwei Ren","Tat-Seng Chua"],"abstract":"Matrix factorization (MF) has been widely used to discover the low-rank\nstructure and to predict the missing entries of data matrix. In many real-world\nlearning systems, the data matrix can be very high-dimensional but sparse. This\nposes an imbalanced learning problem, since the scale of missing entries is\nusually much larger than that of observed entries, but they cannot be ignored\ndue to the valuable negative signal. For efficiency concern, existing work\ntypically applies a uniform weight on missing entries to allow a fast learning\nalgorithm. However, this simplification will decrease modeling fidelity,\nresulting in suboptimal performance for downstream applications.\n  In this work, we weight the missing data non-uniformly, and more generically,\nwe allow any weighting strategy on the missing data. To address the efficiency\nchallenge, we propose a fast learning method, for which the time complexity is\ndetermined by the number of observed entries in the data matrix, rather than\nthe matrix size. The key idea is two-fold: 1) we apply truncated SVD on the\nweight matrix to get a more compact representation of the weights, and 2) we\nlearn MF parameters with element-wise alternating least squares (eALS) and\nmemorize the key intermediate variables to avoid repeating computations that\nare unnecessary. We conduct extensive experiments on two recommendation\nbenchmarks, demonstrating the correctness, efficiency, and effectiveness of our\nfast eALS method.","url_abs":"http://arxiv.org/abs/1811.04411v2","url_pdf":"http://arxiv.org/pdf/1811.04411v2.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":"fast-matrix-factorization-with-non-uniform","repo_url":"https://github.com/duxy-me/ext-als","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}