{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:19:13Z","timestamp":1760235553943,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,7]],"date-time":"2021-09-07T00:00:00Z","timestamp":1630972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key R&amp;D Program of China","award":["2018YFB0704300"],"award-info":[{"award-number":["2018YFB0704300"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Class imbalance, as a phenomenon of asymmetry, has an adverse effect on the performance of most machine learning and overlap is another important factor that affects the classification performance of machine learning algorithms. This paper deals with the two factors simultaneously, addressing the class overlap under imbalanced distribution. In this paper, a theoretical analysis is firstly conducted on the existing class overlap metrics. Then, an improved method and the corresponding metrics to evaluate the class overlap under imbalance distributions are proposed based on the theoretical analysis. A well-known collection of the imbalanced datasets is used to compare the performance of different metrics and the performance is evaluated based on the Pearson correlation coefficient and the \u03be correlation coefficient. The experimental results demonstrate that the proposed class overlap metrics outperform other compared metrics for the imbalanced datasets and the Pearson correlation coefficient with the AUC metric of eight algorithms can be improved by 34.7488% in average.<\/jats:p>","DOI":"10.3390\/sym13091649","type":"journal-article","created":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T02:41:07Z","timestamp":1631068867000},"page":"1649","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Addressing Class Overlap under Imbalanced Distribution: An Improved Method and Two Metrics"],"prefix":"10.3390","volume":"13","author":[{"given":"Zhuang","family":"Li","sequence":"first","affiliation":[{"name":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingyan","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7600-7231","authenticated-orcid":false,"given":"Xiaotong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"},{"name":"Shunde Graduate School, University of Science and Technology Beijing, Foshan 528000, China"},{"name":"Beijing Advanced Innovation Center for Materials Genome Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yadong","family":"Wan","sequence":"additional","affiliation":[{"name":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"},{"name":"Shunde Graduate School, University of Science and Technology Beijing, Foshan 528000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"429","DOI":"10.3233\/IDA-2002-6504","article-title":"The class imbalance problem: A systematic study","volume":"6","author":"Japkowicz","year":"2002","journal-title":"Intell. Data Anal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.eswa.2016.12.035","article-title":"Learning from class-imbalanced data: Review of methods and applications","volume":"73","author":"Guo","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1142\/S0218001409007326","article-title":"Classification of imbalanced data: A review","volume":"23","author":"Sun","year":"2009","journal-title":"Int. J. Pattern Recognit. Artif. Intell."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Dogo, E.M., Nwulu, N.I., Twala, B., and Aigbavboa, C. (2021). Accessing Imbalance Learning Using Dynamic Selection Approach in Water Quality Anomaly Detection. Symmetry, 13.","DOI":"10.3390\/sym13050818"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Bejjanki, K.K., Gyani, J., and Gugulothu, N. (2020). Class Imbalance Reduction (CIR): A Novel Approach to Software Defect Prediction in the Presence of Class Imbalance. Symmetry, 12.","DOI":"10.3390\/sym12030407"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1109\/TKDE.2008.239","article-title":"Learning from Imbalanced Data","volume":"21","author":"He","year":"2009","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Xiong, H., Wu, J., and Liu, L. (2010, January 19\u201321). Classification with Class Overlapping: A Systematic Study. Proceedings of the 1st International Conference on E-Business Intelligence (ICEBI 2010), Guangzhou, China.","DOI":"10.2991\/icebi.2010.43"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s10032-008-0069-1","article-title":"Partial discriminative training for classification of overlapping classes in document analysis","volume":"11","author":"Liu","year":"2008","journal-title":"Int. J. Doc. Anal. Recognit."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.compbiomed.2010.12.006","article-title":"A new dataset evaluation method based on category overlap","volume":"41","author":"Oh","year":"2011","journal-title":"Comput. Biol. Med."},{"key":"ref_10","first-page":"220","article-title":"Overlap versus imbalance","volume":"Volume 6085","author":"Farzindar","year":"2010","journal-title":"Advances in Artificial Intelligence"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.eswa.2018.01.008","article-title":"An overlap-sensitive margin classifier for imbalanced and overlapping data","volume":"98","author":"Lee","year":"2018","journal-title":"Expert Syst. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1016\/j.asoc.2017.04.037","article-title":"A string grammar fuzzy-possibilistic c-medians","volume":"57","author":"Klomsae","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.compbiomed.2012.11.010","article-title":"RFS: Efficient feature selection method based on R-value","volume":"43","author":"Lee","year":"2013","journal-title":"Comput. Biol. Med."},{"key":"ref_14","unstructured":"Wang, X., Lin, X., Huang, X., and Yang, Y. (2015, January 15\u201317). Ensemble unsupervised feature selection based on permutation and R-value. Proceedings of the 2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), Zhangjiajie, China."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Li, Z., He, J., Zhang, X., He, J., and Qin, J. (2020, January 16\u201319). Toward high accuracy and visualization: An interpretable feature extraction method based on genetic programming and non-overlap degree. Proceedings of the 2020 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), Seoul, Korea.","DOI":"10.1109\/BIBM49941.2020.9313182"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"5","DOI":"10.3233\/IDA-194477","article-title":"Balanced Training\/Test Set Sampling for Proper Evaluation of Classification Models","volume":"24","author":"Kang","year":"2020","journal-title":"Intell. Data Anal."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/s10044-016-0583-6","article-title":"Dealing with overlap and imbalance: A new metric and approach","volume":"21","author":"Borsos","year":"2018","journal-title":"Pattern Anal. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"103906","DOI":"10.1016\/j.chemolab.2019.103906","article-title":"Feature selection and classification by minimizing overlap degree for class-imbalanced data in metabolomics","volume":"196","author":"Fu","year":"2020","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"28101","DOI":"10.1109\/ACCESS.2021.3056285","article-title":"Minimizing the overlapping degree to improve class-imbalanced learning under sparse feature selection. Application to fraud detection","volume":"9","author":"Fatima","year":"2021","journal-title":"IEEE Access"},{"key":"ref_20","first-page":"451","article-title":"Information Retrieval Perspective to Nonlinear Dimensionality Reduction for Data Visualization","volume":"11","author":"Venna","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1016\/S0031-3203(96)00142-2","article-title":"The use of the area under the roc curve in the evaluation of machine learning algorithms","volume":"30","author":"Bradley","year":"1997","journal-title":"Pattern Recognit."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Luque, A., Carrasco, A., Mart\u00edn, A., and Lama, J.R. (2019). Exploring Symmetry of Binary Classification Performance Metrics. Symmetry, 11.","DOI":"10.3390\/sym11010047"},{"key":"ref_23","first-page":"2825","article-title":"Scikit-learn: Machine Learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.ins.2013.07.007","article-title":"An insight into classification with imbalanced data: Empirical results and current trends on using data intrinsic characteristics","volume":"250","author":"Palade","year":"2013","journal-title":"Inform. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1098\/rspl.1895.0041","article-title":"Notes on Regression and Inheritance in the Case of Two Parents","volume":"58","author":"Pearson","year":"1895","journal-title":"Proc. R. Soc. Lond."},{"key":"ref_26","unstructured":"Sourav, C. (2020). A New Coefficient of Correlation. J. Am. Stat. Assoc., 1\u201314."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/9\/1649\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:58:21Z","timestamp":1760165901000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/9\/1649"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,7]]},"references-count":26,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["sym13091649"],"URL":"https:\/\/doi.org\/10.3390\/sym13091649","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,9,7]]}}}