{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:58:42Z","timestamp":1760147922710,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,9]],"date-time":"2023-03-09T00:00:00Z","timestamp":1678320000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["52069014"],"award-info":[{"award-number":["52069014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Tri-training expands the training set by adding pseudo-labels to unlabeled data, which effectively improves the generalization ability of the classifier, but it is easy to mislabel unlabeled data into training noise, which damages the learning efficiency of the classifier, and the explicit decision mechanism tends to make the training noise degrade the accuracy of the classification model in the prediction stage. This study proposes the Tri-training algorithm for adaptive nearest neighbor density editing and cross-entropy evaluation (TTADEC), which is used to reduce the training noise formed during the classifier iteration and to solve the problem of inaccurate prediction by explicit decision mechanism. First, the TTADEC algorithm uses the nearest neighbor editing to label high-confidence samples. Then, combined with the relative nearest neighbor to define the local density of samples to screen the pre-training samples, and then dynamically expand the training set by adaptive technique. Finally, the decision process uses cross-entropy to evaluate the completed base classifier of training and assign appropriate weights to it to construct a decision function. The effectiveness of the TTADEC algorithm is verified on the UCI dataset, and the experimental results show that compared with the standard Tri-training algorithm and its improvement algorithm, the TTADEC algorithm has better classification performance and can effectively deal with the semi-supervised classification problem where the training set is insufficient.<\/jats:p>","DOI":"10.3390\/e25030480","type":"journal-article","created":{"date-parts":[[2023,3,10]],"date-time":"2023-03-10T02:30:33Z","timestamp":1678415433000},"page":"480","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Tri-Training Algorithm for Adaptive Nearest Neighbor Density Editing and Cross Entropy Evaluation"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3652-1903","authenticated-orcid":false,"given":"Jia","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Information Engineering, Nanchang Institute of Technology, Nanchang 330099, China"}]},{"given":"Yuhang","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Nanchang Institute of Technology, Nanchang 330099, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0951-2734","authenticated-orcid":false,"given":"Renbin","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"given":"Runxiu","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Nanchang Institute of Technology, Nanchang 330099, China"}]},{"given":"Tanghuai","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Nanchang Institute of Technology, Nanchang 330099, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chapelle, O., Scholkopf, B., and Zien, A. (2006). Semi-Supervised Learening, MIT Press.","DOI":"10.7551\/mitpress\/9780262033589.001.0001"},{"key":"ref_2","first-page":"1592","article-title":"Semi-Supervised Learning Methods","volume":"38","author":"Liu","year":"2015","journal-title":"Chin. J. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s10115-009-0209-z","article-title":"Semi-supervised learning by disagreement","volume":"24","author":"Zhou","year":"2010","journal-title":"Knowl. Inf. Syst."},{"key":"ref_4","first-page":"19","article-title":"Review of Semi-Supervised Learning Research","volume":"56","author":"Han","year":"2020","journal-title":"Comput. Eng. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"8583","DOI":"10.1109\/TGRS.2020.2988982","article-title":"Semi-Supervised PolSAR Image Classification Based on Improved Tri-Training with a Minimum Spanning Tree","volume":"58","author":"Wang","year":"2020","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1007\/s11517-020-02159-z","article-title":"Chronic gastritis classification using gastric X-ray images with a semi-supervised learning method based on tri-training","volume":"58","author":"Li","year":"2020","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3450285","article-title":"Improved Fake Reviews Detection Model Based on Vertical Ensemble Tri-Training and Active Learning","volume":"12","author":"Yin","year":"2021","journal-title":"ACM Trans. Intell. Syst. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1080\/23742917.2019.1623475","article-title":"Ensemble-based semi-supervised learning approach for a distributed intrusion detection system","volume":"3","author":"Khonde","year":"2019","journal-title":"J. Cyber Secur. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1871","DOI":"10.3724\/SP.J.1004.2013.01871","article-title":"Disagreement-based Semi-Supervised Learning","volume":"39","author":"Zhou","year":"2013","journal-title":"Acta Autom. Sin."},{"key":"ref_10","unstructured":"Miller, D.J., and Uyar, H.S. (1996, January 2\u20135). A mixture of experts classifier with learning based on both labeled and unlabeled data. Proceedings of the 9th International Conference on Neural Information Processing Systems, Denver, CO, USA."},{"key":"ref_11","unstructured":"Blum, A., and Chawla, S. (\u20131, January 28). Learning from labeled and unlabeled data using graph mincuts. Proceedings of the 18th International Conference on Machine Learning, Williams, CO, USA."},{"key":"ref_12","first-page":"203","article-title":"Optim\u1ea1zation techniques for semi- supervised support vector machines","volume":"9","author":"Chapelle","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Blum, A., and Mitchell, T. (1998, January 24\u201326). Combining labeled and unlabeled data with co-training. Proceedings of the 11th Annual Conference on Computational Learning Theory, Madison, WI, USA.","DOI":"10.1145\/279943.279962"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1109\/TKDE.2005.186","article-title":"Tri-training: Exploiting unlabeled data using three classifiers","volume":"17","author":"Zhou","year":"2005","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_15","first-page":"1213","article-title":"ADE-Tri-training: Tri-training with Adaptive Data Editing","volume":"30","author":"Deng","year":"2007","journal-title":"Chin. J. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4001","DOI":"10.3233\/JIFS-169722","article-title":"Safe semi-supervised classification algorithm combined with active learning sampling strategy","volume":"35","author":"Zhao","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Li, D.M., Mao, J.W., and Shen, F.K. (2019, January 3\u20135). A Novel Semi-supervised Adaboost Technique Based on Improved Tri-training. Proceedings of the 24th Australasian Conference on Information Security and Privacy, Christchurch, New Zealand.","DOI":"10.1007\/978-3-030-21548-4_39"},{"key":"ref_18","first-page":"331","article-title":"Semi-supervised patent text classification method based on improved Tri-training algorithm","volume":"54","author":"Hu","year":"2020","journal-title":"J. Zhejiang Univ. (Eng. Sci.)"},{"key":"ref_19","first-page":"2015","article-title":"Cross-Domain Trust Prediction Based on Tri-training and Extreme Learning Machine","volume":"59","author":"Wang","year":"2022","journal-title":"J. Comput. Res. Dev."},{"key":"ref_20","first-page":"60","article-title":"Safe Tri-training Algorithm Based on Cross Entropy","volume":"58","author":"Zhang","year":"2021","journal-title":"J. Comput. Res. Dev."},{"key":"ref_21","first-page":"2088","article-title":"Semi-supervised Classification Model Based on Ladder Network and Improved Tri-training","volume":"48","author":"Mo","year":"2022","journal-title":"Acta Autom. Sin."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/BF00116829","article-title":"Learning from noisy examples","volume":"2","author":"Angluin","year":"1988","journal-title":"Mach. Learn."},{"key":"ref_23","unstructured":"Zhao, J., Chen, L., Wu, R., Zhan, B., and Han, L. (2022). Density peaks clustering algorithm with K-nearest neighbors and weighted similarity. Control. Theory Appl., 1\u20139. Available online: http:\/\/kns.cnki.net\/kcms\/detail\/44.1240.TP.20220429.1633.024.html."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/s12539-019-00357-4","article-title":"Single-Cell Clustering Based on Shared Nearest Neighbor and Graph Partitioning","volume":"12","author":"Zhu","year":"2020","journal-title":"Interdiscip. Sci. Comput. Life Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"108938","DOI":"10.1016\/j.asoc.2022.108938","article-title":"Multi-strategy ensemble firefly algorithm with equilibrium of convergence and diversity","volume":"123","author":"Zhao","year":"2022","journal-title":"Appl. Soft Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1631\/FITEE.2000691","article-title":"Firefly algorithm with division of roles for complex optimal scheduling","volume":"22","author":"Zhao","year":"2021","journal-title":"Front. Info. Technol. Electro Engine."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1080\/10798587.2017.1316069","article-title":"Adaptive Intelligent Single Particle Optimizer Based Image De-noising in Shearlet Domain","volume":"23","author":"Zhao","year":"2017","journal-title":"Intell. Auto. Soft Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1762107","DOI":"10.34133\/2020\/1762107","article-title":"Flexible wolf pack algorithm for dynamic multidimensional knapsack problems","volume":"2020","author":"Wu","year":"2020","journal-title":"Research."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1356","DOI":"10.1631\/FITEE.1900437","article-title":"Uncertain bilevel knapsack problem based on improved binary wolf pack algorithm","volume":"21","author":"Wu","year":"2020","journal-title":"Front. Info. Technol. Electro Engine."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/S0377-2217(96)00385-2","article-title":"Optimization of computer simulation models with rare events","volume":"99","author":"Rubinstein","year":"1997","journal-title":"Eur. J. Oper. Res."},{"key":"ref_31","unstructured":"Dua, D., and G\u2019raff, C. (2019). UCI Machine Learning Repository, University of California, School of Information and Computer Science. Available online: http:\/\/archive.ics.uci.edu\/ml."},{"key":"ref_32","first-page":"1","article-title":"Statistical comparisons of classifiers over multiple data sets","volume":"7","year":"2006","journal-title":"J. Mach. Learn. Res."},{"key":"ref_33","first-page":"1","article-title":"Collective intelligence: Conception, research progress and application analysis","volume":"41","author":"Xiao","year":"2022","journal-title":"J. Nanchang Inst. Technol."},{"key":"ref_34","first-page":"1","article-title":"From swarm intelligence optimization to swarm intelligence evolution","volume":"42","author":"Xiao","year":"2023","journal-title":"J. Nanchang Inst. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"109406","DOI":"10.1016\/j.patcog.2023.109406","article-title":"Density Peaks Clustering Algorithm Based on Fuzzy Neighborhood and Weighted Shared Neighbor for Uneven Density Datasets","volume":"139","author":"Zhao","year":"2023","journal-title":"Pat. Rec."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/3\/480\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:52:07Z","timestamp":1760122327000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/3\/480"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,9]]},"references-count":35,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["e25030480"],"URL":"https:\/\/doi.org\/10.3390\/e25030480","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,3,9]]}}}