{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:46:47Z","timestamp":1760233607259,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,1]],"date-time":"2021-02-01T00:00:00Z","timestamp":1612137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>Collaborative filtering (CF) is a widely used method in recommendation systems. Linear models are still the mainstream of collaborative filtering research methods, but non-linear probabilistic models are beyond the limit of linear model capacity. For example, variational autoencoders (VAEs) have been extensively used in CF, and have achieved excellent results. Aiming at the problem of the prior distribution for the latent codes of VAEs in traditional CF is too simple, which makes the implicit variable representations of users and items too poor. This paper proposes a variational autoencoder that uses a Gaussian mixture model for latent factors distribution for CF, GVAE-CF. On this basis, an optimization function suitable for GVAE-CF is proposed. In our experimental evaluation, we show that the recommendation performance of GVAE-CF outperforms the previously proposed VAE-based models on several popular benchmark datasets in terms of recall and normalized discounted cumulative gain (NDCG), thus proving the effectiveness of the algorithm.<\/jats:p>","DOI":"10.3390\/fi13020037","type":"journal-article","created":{"date-parts":[[2021,2,1]],"date-time":"2021-02-01T11:40:48Z","timestamp":1612179648000},"page":"37","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Collaborative Filtering Based on a Variational Gaussian Mixture Model"],"prefix":"10.3390","volume":"13","author":[{"given":"FengLei","family":"Yang","sequence":"first","affiliation":[{"name":"School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4094-7341","authenticated-orcid":false,"given":"Fei","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ShanShan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer Engineering and Science, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1145\/245108.245121","article-title":"Recommender systems","volume":"40","author":"Resnick","year":"1997","journal-title":"Commun. ACM"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Pazzani, M.J., and Billsus, D. (2007). Content-based recommendation systems. The Adaptive Web, Springer.","DOI":"10.1007\/978-3-540-72079-9_10"},{"key":"ref_3","unstructured":"Thomas, X. (2020). Content-Based Personalized Recommender System Using Entity Embeddings. arXiv."},{"key":"ref_4","unstructured":"Zarei, M.R., and Moosavi, M.R. (2019). An adaptive similarity measure to tune trust influence in memory-based collaborative filtering. arXiv."},{"key":"ref_5","unstructured":"Zhao, Z.D., and Shang, M.S. (2010, January 2\u20134). User-based collaborative-filtering recommendation algorithms on hadoop. Proceedings of the 2010 Third International Conference on Knowledge Discovery and Data Mining, IEEE, Jinggangshan, China."},{"key":"ref_6","unstructured":"Zhang, L., Liu, G., and Wu, J. (2019). Beyond Similarity: Relation Embedding with Dual Attentions for Item-based Recommendation. arXiv."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1145\/138859.138867","article-title":"Using collaborative filtering to weave an information tapestry","volume":"35","author":"Goldberg","year":"1992","journal-title":"Commun. ACM"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ding, X., Yu, W., Xie, Y., and Liu, S. (2020, January 9\u201311). Efficient model-based collaborative filtering with fast adaptive PCA. Proceedings of the 2020 IEEE 32nd International Conference on Tools with Artificial Intelligence (ICTAI), Baltimore, MD, USA.","DOI":"10.1109\/ICTAI50040.2020.00149"},{"key":"ref_9","unstructured":"Severinski, C., and Salakhutdinov, R. (2014). Bayesian Probabilistic Matrix Factorization: A User Frequency Analysis. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Chae, D.K., Kang, J.S., Kim, S.W., and Lee, J.T. (2018, January 22\u201326). Cfgan: A generic collaborative filtering framework based on generative adversarial networks. Proceedings of the 27th ACM International Conference on Information and Knowledge Management, Torino, Italy.","DOI":"10.1145\/3269206.3271743"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kang, W.C., Fang, C., Wang, Z., and McAuley, J. (2017, January 18\u201321). Visually-aware fashion recommendation and design with generative image models. Proceedings of the 2017 IEEE International Conference on Data Mining (ICDM), New Orleans, LA, USA.","DOI":"10.1109\/ICDM.2017.30"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Hu, Y., Koren, Y., and Volinsky, C. (2008, January 15\u201319). Collaborative filtering for implicit feedback datasets. Proceedings of the 2008 Eighth IEEE International Conference on Data Mining, Pisa, Italy.","DOI":"10.1109\/ICDM.2008.22"},{"key":"ref_13","unstructured":"Mnih, A., and Salakhutdinov, R.R. (2008). Probabilistic matrix factorization. Advances in Neural Information Processing Systems, MIT Press."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Liang, D., Krishnan, R.G., Hoffman, M.D., and Jebara, T. (2018, January 23\u201327). Variational autoencoders for collaborative filtering. Proceedings of the 2018 World Wide Web Conference, Lyon, France.","DOI":"10.1145\/3178876.3186150"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kim, D., and Suh, B. (2019, January 16\u201320). Enhancing VAEs for collaborative filtering: Flexible priors & gating mechanisms. Proceedings of the 13th ACM Conference on Recommender Systems, Copenhagen, Denmark.","DOI":"10.1145\/3298689.3347015"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Shenbin, I., Alekseev, A., Tutubalina, E., Malykh, V., and Nikolenko, S.I. (2020, January 3\u20137). RecVAE: A new variational autoencoder for top-N recommendations with implicit feedback. Proceedings of the 13th International Conference on Web Search and Data Mining, Houston, TX, USA.","DOI":"10.1145\/3336191.3371831"},{"key":"ref_17","unstructured":"Gopalan, P., Hofman, J.M., and Blei, D.M. (2013). Scalable Recommendation with Hierarchical Poisson Factorization. arXiv."},{"key":"ref_18","first-page":"46","article-title":"Learning collaborative information filters","volume":"Volume 98","author":"Billsus","year":"1998","journal-title":"Icml"},{"key":"ref_19","unstructured":"Alquier, P., Cottet, V., Chopin, N., and Rousseau, J. (2014). Bayesian matrix completion: Prior specification. arXiv."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1007\/s10618-017-0504-3","article-title":"Enhancing social collaborative filtering through the application of non-negative matrix factorization and exponential random graph models","volume":"31","author":"Alexandridis","year":"2017","journal-title":"Data Min. Knowl. Discov."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Liang, D., Altosaar, J., Charlin, L., and Blei, D.M. (2016). Factorization meets the item embedding: Regularizing matrix factorization with item co-occurrence. Proceedings of the 10th ACM Conference on Recommender Systems, ACM.","DOI":"10.1145\/2959100.2959182"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Lee, W., Song, K., and Moon, I.C. (2017). Augmented variational autoencoders for collaborative filtering with auxiliary information. Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, ACM.","DOI":"10.1145\/3132847.3132972"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Askari, B., Szlichta, J., and Salehi-Abari, A. (2020). Joint Variational Autoencoders for Recommendation with Implicit Feedback. arXiv.","DOI":"10.1145\/3404835.3462986"},{"key":"ref_24","unstructured":"Altosaar, J. (2021, January 30). Tutorial-What is a Variational Autoencoder. Available online: https:\/\/jaan.io\/what-is-variational-autoencoder-vae-tutorial\/."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","article-title":"Variational inference: A review for statisticians","volume":"112","author":"Blei","year":"2017","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_26","unstructured":"Kingma, D.P., and Welling, M. (2013). Auto-encoding variational bayes. arXiv."},{"key":"ref_27","unstructured":"Rezende, D.J., Mohamed, S., and Wierstra, D. (2014). Stochastic backpropagation and approximate inference in deep generative models. arXiv."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2827872","article-title":"The movielens datasets: History and context","volume":"5","author":"Harper","year":"2015","journal-title":"ACM Trans. Interact. Intell. Syst."},{"key":"ref_29","first-page":"35","article-title":"The netflix prize","volume":"Volume 2007","author":"Bennett","year":"2007","journal-title":"Proceedings of KDD Cup and Workshop"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Dong, X., Yu, L., Wu, Z., Sun, Y., Yuan, L., and Zhang, F. (2017, January 4\u20139). A hybrid collaborative filtering model with deep structure for recommender systems. Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, San Francisco, CA, USA.","DOI":"10.1609\/aaai.v31i1.10747"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Li, S., Kawale, J., and Fu, Y. (2015). Deep collaborative filtering via marginalized denoising auto-encoder. Proceedings of the 24th ACM International on Conference on Information and Knowledge Management, ACM.","DOI":"10.1145\/2806416.2806527"},{"key":"ref_32","unstructured":"Rendle, S., Freudenthaler, C., Gantner, Z., and Schmidt-Thieme, L. (2012). BPR: Bayesian personalized ranking from implicit feedback. arXiv."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Kabbur, S., Ning, X., and Karypis, G. (2013). Fism: Factored item similarity models for top-n recommender systems. Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM.","DOI":"10.1145\/2487575.2487589"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Yang, S.H., Long, B., Smola, A.J., Zha, H., and Zheng, Z. (2011, January 24\u201328). Collaborative competitive filtering: Learning recommender using context of user choice. Proceedings of the 34th International ACM SIGIR Conference on Research and Development in Information Retrieval, Beijing, China.","DOI":"10.1145\/2009916.2009959"},{"key":"ref_35","unstructured":"Croft, W.B., Metzler, D., and Strohman, T. (2010). Search Engines: Information Retrieval in Practice, Addison-Wesley Reading."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"20150202","DOI":"10.1098\/rsta.2015.0202","article-title":"Principal component analysis: A review and recent developments","volume":"374","author":"Jolliffe","year":"2016","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Ning, X., and Karypis, G. (2011, January 11\u201314). Slim: Sparse linear methods for top-n recommender systems. Proceedings of the 2011 IEEE 11th International Conference on Data Mining, Vancouver, BC, Canada.","DOI":"10.1109\/ICDM.2011.134"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Wu, Y., DuBois, C., Zheng, A.X., and Ester, M. (2016). Collaborative denoising auto-encoders for top-n recommender systems. Proceedings of the Ninth ACM International Conference on Web Search and Data Mining, ACM.","DOI":"10.1145\/2835776.2835837"}],"container-title":["Future Internet"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-5903\/13\/2\/37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:18:29Z","timestamp":1760159909000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-5903\/13\/2\/37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,1]]},"references-count":38,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["fi13020037"],"URL":"https:\/\/doi.org\/10.3390\/fi13020037","relation":{},"ISSN":["1999-5903"],"issn-type":[{"type":"electronic","value":"1999-5903"}],"subject":[],"published":{"date-parts":[[2021,2,1]]}}}