{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T22:09:01Z","timestamp":1769724541017,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,9]],"date-time":"2022-12-09T00:00:00Z","timestamp":1670544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2018YFC1503204"],"award-info":[{"award-number":["2018YFC1503204"]}]},{"name":"National Key Research and Development Program of China","award":["61972360"],"award-info":[{"award-number":["61972360"]}]},{"name":"National Key Research and Development Program of China","award":["62273290"],"award-info":[{"award-number":["62273290"]}]},{"name":"National Natural Science Foundation of China","award":["2018YFC1503204"],"award-info":[{"award-number":["2018YFC1503204"]}]},{"name":"National Natural Science Foundation of China","award":["61972360"],"award-info":[{"award-number":["61972360"]}]},{"name":"National Natural Science Foundation of China","award":["62273290"],"award-info":[{"award-number":["62273290"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Under the background of information overload, the recommendation system has attracted wide attention as one of the most important means for this problem. Feature interaction considers not only the impact of each feature but also the combination of two or more features, which has become an important research field in recommendation systems. There are two essential problems in current feature interaction research. One is that not all feature interactions can generate positive gains, and some may lead to an increase in noise. The other is that the process of feature interactions is implicit and uninterpretable. In this paper, a Hierarchical Dual-level Graph Feature Interaction (HDGFI) model is proposed to solve these problems in the recommendation system. The model regards features as nodes and edges as interactions between features in the graph structure. Interaction noise is filtered by beneficial interaction selection based on a hierarchical edge selection module. At the same time, the importance of interaction between nodes is modeled in two perspectives in order to learn the representation of feature nodes at a finer granularity. Experimental results show that the proposed HDGFI model has higher accuracy than the existing models.<\/jats:p>","DOI":"10.3390\/e24121799","type":"journal-article","created":{"date-parts":[[2022,12,9]],"date-time":"2022-12-09T06:14:00Z","timestamp":1670566440000},"page":"1799","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["HDGFI: Hierarchical Dual-Level Graph Feature Interaction Model for Personalized Recommendation"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6457-6207","authenticated-orcid":false,"given":"Xinxin","family":"Ma","sequence":"first","affiliation":[{"name":"School of Computer and Control Engineering, Yantai University, Yantai 264005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5503-1336","authenticated-orcid":false,"given":"Zhendong","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Computer and Control Engineering, Yantai University, Yantai 264005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"McMahan, H.B., Holt, G., Sculley, D., Young, M., Ebner, D., Grady, J., Nie, L., Phillips, T., Davydov, E., and Golovin, D. (2013, January 11\u201314). Ad click prediction: A view from the trenches. Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Chicago, IL, USA.","DOI":"10.1145\/2487575.2488200"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Su, Y., Zhang, J.D., Li, X., Zha, D., Xiang, J., Tang, W., and Gao, N. (2020, January 19\u201324). Fgrec: A fine-grained point-of-interest recommendation framework by capturing intrinsic influences. Proceedings of the 2020 International Joint Conference on Neural Networks (IJCNN), Glasgow, UK.","DOI":"10.1109\/IJCNN48605.2020.9207571"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wang, J., Huang, P., Zhao, H., Zhang, Z., Zhao, B., and Lee, D.L. (2018, January 19\u201323). Billion-scale commodity embedding for e-commerce recommendation in alibaba. Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, London, UK.","DOI":"10.1145\/3219819.3219869"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, X., He, X., Wang, M., Feng, F., and Chua, T.S. (2019, January 21\u201325). Neural graph collaborative filtering. Proceedings of the 42nd international ACM SIGIR conference on Research and development in Information Retrieval, Paris France.","DOI":"10.1145\/3331184.3331267"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Rendle, S. (2010, January 13\u201317). Factorization machines. Proceedings of the 2010 IEEE International Conference on Data Mining, Sydney, NSW, Australia.","DOI":"10.1109\/ICDM.2010.127"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Xiao, J., Ye, H., He, X., Zhang, H., Wu, F., and Chua, T.S. (2017). Attentional factorization machines: Learning the weight of feature interactions via attention networks. arXiv.","DOI":"10.24963\/ijcai.2017\/435"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Juan, Y., Zhuang, Y., Chin, W.S., and Lin, C.J. (2016, January 15\u201319). Field-aware factorization machines for CTR prediction. Proceedings of the 10th ACM Conference on Recommender Systems, Boston, MA, USA.","DOI":"10.1145\/2959100.2959134"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Guo, H., Tang, R., Ye, Y., Li, Z., and He, X. (2017). DeepFM: A factorization-machine based neural network for CTR prediction. arXiv.","DOI":"10.24963\/ijcai.2017\/239"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"He, X., and Chua, T.S. (2017, January 7\u201311). Neural factorization machines for sparse predictive analytics. Proceedings of the 40th International ACM SIGIR Conference on Research and Development in Information Retrieval, Tokyo, Japan.","DOI":"10.1145\/3077136.3080777"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Cheng, H.T., Koc, L., Harmsen, J., Shaked, T., Chandra, T., Aradhye, H., Anderson, G., Corrado, G., Chai, W., and Ispir, M. (2016, January 15). Wide & deep learning for recommender systems. Proceedings of the 1st Workshop on Deep Learning for Recommender Systems, Boston, MA, USA.","DOI":"10.1145\/2988450.2988454"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Song, W., Shi, C., Xiao, Z., Duan, Z., Xu, Y., Zhang, M., and Tang, J. (2019, January 3\u20137). Autoint: Automatic feature interaction learning via self-attentive neural networks. Proceedings of the 28th ACM International Conference on Information and Knowledge Management, Beijing, China.","DOI":"10.1145\/3357384.3357925"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Li, Z., Cheng, W., Chen, Y., Chen, H., and Wang, W. (2020, January 3\u20137). Interpretable click-through rate prediction through hierarchical attention. Proceedings of the 13th International Conference on Web Search and Data Mining, Houston, TX, USA.","DOI":"10.1145\/3336191.3371785"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Li, Z., Cui, Z., Wu, S., Zhang, X., and Wang, L. (2019, January 3\u20137). Fi-gnn: Modeling feature interactions via graph neural networks for ctr prediction. Proceedings of the 28th ACM International Conference on Information and Knowledge Management, Beijing, China.","DOI":"10.1145\/3357384.3357951"},{"key":"ref_14","unstructured":"Li, Z., Wu, S., Cui, Z., and Zhang, X. (2021). GraphFM: Graph Factorization Machines for Feature Interaction Modeling. arXiv."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zhang, W., Du, T., and Wang, J. (2016, January 20\u201323). Deep learning over multi-field categorical data. Proceedings of the European Conference on Information Retrieval, Padua, Italy.","DOI":"10.1007\/978-3-319-30671-1_4"},{"key":"ref_16","unstructured":"Shan, Y., Hoens, T.R., Jiao, J., Wang, H., Yu, D., and Mao, J.C. (2022, January 13\u201317). Deep crossing: Web-scale modeling without manually crafted combinatorial features. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Huang, T., Zhang, Z., and Zhang, J. (2019, January 16\u201320). FiBiNET: Combining feature importance and bilinear feature interaction for click-through rate prediction. Proceedings of the 13th ACM Conference on Recommender Systems, Copenhagen Denmark.","DOI":"10.1145\/3298689.3347043"},{"key":"ref_18","unstructured":"Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, \u0141., and Polosukhin, I. (2017, January 4\u20139). Attention is all you need. Proceedings of the Advances in Neural Information Processing Systems 2017, Long Beach, CA, USA."},{"key":"ref_19","unstructured":"Kipf, T.N., and Welling, M. (2016). Semi-supervised classification with graph convolutional networks. arXiv."},{"key":"ref_20","unstructured":"Hamilton, W., Ying, Z., and Leskovec, J. (2017, January 4\u20139). Inductive representation learning on large graphs. Proceedings of the Advances in Neural Information Processing Systems 2017, Long Beach, CA, USA."},{"key":"ref_21","unstructured":"Veli\u010dkovi\u0107, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., and Bengio, Y. (2017). Graph attention networks. arXiv."},{"key":"ref_22","unstructured":"Li, Y., Tarlow, D., Brockschmidt, M., and Zemel, R. (2015). Gated graph sequence neural networks. arXiv."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wang, X., He, X., Cao, Y., Liu, M., and Chua, T.S. (2019, January 4\u20138). Kgat: Knowledge graph attention network for recommendation. Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Anchorage, AK, USA.","DOI":"10.1145\/3292500.3330989"},{"key":"ref_24","unstructured":"Zhu, Y., Xu, W., Zhang, J., Du, Y., Zhang, J., Liu, Q., Yang, C., and Wu, S. (2021). A Survey on Graph Structure Learning: Progress and Opportunities. arXiv."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Li, R., Wang, S., Zhu, F., and Huang, J. (2018, January 2\u20137). Adaptive graph convolutional neural networks. Proceedings of the AAAI conference on Artificial Intelligence, New Orleans, LA, USA.","DOI":"10.1609\/aaai.v32i1.11691"},{"key":"ref_26","unstructured":"Chen, Y., Wu, L., and Zaki, M. (2020, January 6\u201312). Iterative deep graph learning for graph neural networks: Better and robust node embeddings. Proceedings of the Advances in Neural Information Processing Systems, virtual."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Jiang, B., Zhang, Z., Lin, D., Tang, J., and Luo, B. (2019, January 15\u201320). Semi-supervised learning with graph learning-convolutional networks. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.01157"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Luo, D., Cheng, W., Yu, W., Zong, B., Ni, J., Chen, H., and Zhang, X. (2021, January 8\u201312). Learning to drop: Robust graph neural network via topological denoising. Proceedings of the 14th ACM International Conference on Web Search and Data Mining, Virtual Event, Israel.","DOI":"10.1145\/3437963.3441734"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Gao, X., Hu, W., and Guo, Z. (2020, January 6\u201310). Exploring structure-adaptive graph learning for robust semi-supervised classification. Proceedings of the 2020 IEEE International Conference on Multimedia and Expo (ICME), London, UK.","DOI":"10.1109\/ICME46284.2020.9102726"},{"key":"ref_30","unstructured":"Zhao, G., Lin, J., Zhang, Z., Ren, X., Su, Q., and Sun, X. (2019). Explicit sparse transformer: Concentrated attention through explicit selection. arXiv."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Hu, J., Shen, L., and Sun, G. (2018, January 18\u201323). Squeeze-and-excitation networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00745"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Richardson, M., Dominowska, E., and Ragno, R. (2007, January 8). Predicting clicks: Estimating the click-through rate for new ads. Proceedings of the 16th International Conference on World Wide Web, Banff, AB, Canada.","DOI":"10.1145\/1242572.1242643"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1799\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:37:12Z","timestamp":1760146632000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1799"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,9]]},"references-count":32,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["e24121799"],"URL":"https:\/\/doi.org\/10.3390\/e24121799","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,9]]}}}