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Knowl. Discov. Data"],"published-print":{"date-parts":[[2026,1,31]]},"abstract":"<jats:p>Recommendation algorithms have been extensively applied in multiple areas. However, user-level uncertainty in implicit feedback introduce false-positive signals, misaligning interactions with true preferences and introducing noise. This makes it challenging for traditional recommendation methods to achieve both robust and accurate performance. In this manuscript, we propose a semi-supervised co-training algorithm for denoising learning in the recommender system, which incorporates both supervised learning and semi-supervised learning in a cooperative way. We first adopt a Gaussian Mixture Model as a confidence estimation module to partition the implicit feedback into two disjoint datasets: a reliable dataset and an unreliable dataset, based on the intrinsic features of the feedback. To achieve doubly robust learning, we design an iterative cross co-training module that consists of two key components: a two-stage reliable learning process and a cross-sample transmission mechanism. The two-stage reliable learning process enables semi-supervised training on both the reliable and unreliable datasets. Meanwhile, the cross-sample transmission mechanism iteratively transfers hard yet clean samples between dual networks, enhancing robustness through mutual supervision during joint learning. Extensive experiments are conducted using clean test sets extracted from four real-world explicit feedback datasets to validate our denoising method, which demonstrates superior effectiveness across all datasets.<\/jats:p>","DOI":"10.1145\/3773988","type":"journal-article","created":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T14:54:59Z","timestamp":1761836099000},"page":"1-25","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A Semi-supervised Co-training Algorithm for Robust Recommendation"],"prefix":"10.1145","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-1313-8340","authenticated-orcid":false,"given":"Yue","family":"Wu","sequence":"first","affiliation":[{"name":"School of Cyber Science and Technology, Sun Yat-sen University, Shenzhen, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-3741-3860","authenticated-orcid":false,"given":"Mingyu","family":"Zhao","sequence":"additional","affiliation":[{"name":"Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7695-5880","authenticated-orcid":false,"given":"Songming","family":"Zhang","sequence":"additional","affiliation":[{"name":"Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3049-0085","authenticated-orcid":false,"given":"Ziyu","family":"Lyu","sequence":"additional","affiliation":[{"name":"School of Cyber Science and Technology, Sun Yat-sen University, Shenzhen, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-6784-0170","authenticated-orcid":false,"given":"Dayong","family":"Peng","sequence":"additional","affiliation":[{"name":"Didi Chuxing, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-5753-1265","authenticated-orcid":false,"given":"Wanji","family":"Zheng","sequence":"additional","affiliation":[{"name":"Didi Chuxing, Beijing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3381-2526","authenticated-orcid":false,"given":"Hua","family":"Chai","sequence":"additional","affiliation":[{"name":"Didi Chuxing, Beijing, China"}]}],"member":"320","published-online":{"date-parts":[[2025,12,8]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2005.99"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.simpat.2021.102375"},{"issue":"11","key":"e_1_3_2_4_2","doi-asserted-by":"crossref","first-page":"15624","DOI":"10.1109\/TNNLS.2023.3288769","article-title":"Uncertainty-adjusted recommendation via matrix factorization with weighted losses","volume":"35","author":"Alves Rodrigo","year":"2023","unstructured":"Rodrigo Alves, Antoine Ledent, and Marius Kloft. 2023. Uncertainty-adjusted recommendation via matrix factorization with weighted losses. IEEE Transactions on Neural Networks and Learning Systems 35, 11 (2023), 15624\u201315637.","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"e_1_3_2_5_2","first-page":"233","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Arpit Devansh","year":"2017","unstructured":"Devansh Arpit, Stanis\u0142aw Jastrz\u0119bski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder S. Kanwal, Tegan Maharaj, Asja Fischer, Aaron Courville, Yoshua Bengio, et al. 2017. A closer look at memorization in deep networks. In Proceedings of the International Conference on Machine Learning. 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