Noisy label relabeling by nonparallel support vector machine

Document Type : Research Article


1 Department of Applied Mathematics, Faculty of Mathematical Sciences, Rasht, Iran.

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.


In machine learning, models are derived from labeled training data where labels signify classes and features define sample attributes. However, noise from data collection can impair the algorithm’s performance. Blanco, Japón, and Puerto proposed mixed-integer programming (MIP) models within support vector machines (SVM) to handle label noise in training datasets. Nonetheless, it is imperative to underscore that their models demonstrate an observable escalation in the number of variables as sample size increases. The nonparallel support vector machine (NPSVM) is a bi-nary classification method that merges the strengths of both SVM and twin SVM. It accomplishes this by determining two nonparallel hyperplanes by solving two optimization problems. Each hyperplane is strategically po-sitioned to be closer to one of the classes while maximizing its distance from the other class. In this paper, to take advantage of NPSVM’s fea-tures, NPSVM-based relabeling (RENPSVM) MIP models are developed to deal with the label noises in the dataset. The proposed model adjusts observation labels and seeks optimal solutions while minimizing compu-tational costs by selectively focusing on class-relevant observations within an ϵ-intensive tube. Instances exhibiting similarities to the other class are excluded from this ϵ-intensive tube. Experiments on 10 UCI datasets show that the proposed NPSVM-based MIP models outperform their counter-parts in accuracy and learning time on the majority of datasets.


Main Subjects

[1] Abdi, A., Nabi, R.M., Sardasht, M. and Mahmood R. Multiclass clas-sifiers for stock price prediction: A comparison study, J. Harbin Inst. Technol. 54(3) (2022), 32–39.
[2] Angluin, D. and Laird, P. Learning from noisy examples, Mach. Learn. 2 (1988), 343–370.
[3] Bertsimas, D., Dunn, J., Pawlowski, C. and Zhuo, Y.D. Robust classifi-cation, INFORMS Journal on Optimization 1(1) (2019), 2–34.
[4] Biggio, B., Nelson, B. and Laskov, P. Support vector machines under adversarial label noise, Asian conference on machine learning (2011), 97–112.
[5] Blanco, V., Japón, A. and Puerto, J. Robust optimal classification trees under noisy labels, Adv. Data Anal. Classif. 16(1) (2022), 155–179.
[6] Blanco, V., Japón, A. and Puerto, J. A mathematical programming ap-proach to SVM-based classification with label noise, Comput. Ind. Eng. 172 (2022), 108611.
[7] Chen, Z., Song, A., Wang, Y., Huang, X. and Kong, Y. A noise rate estimation method for image classification with label noise, J. Phys. Conf. Ser. IOP Publishing 2433(1) (2023), 012039.
[8] Cortes, C. and Vapnik, V.N. Support vector networks, Mach. Learn. 20(3) (1995), 273–297.
[9] Demsar, J. Statistical comparisons of classifiers over multiple data sets, J. Mach. Learn Res. 7 (2006), 1–30.
[10] Deng, N., Tian, Y. and Zhang, C. Support vector machines: Optimiza-tion based theory, algorithms, and extensions, CRC press, 2012.
[11] Ding, S., Zhang, N., Zhang, X. and Wu, F. Twin support vector ma-chine: Theory, algorithm and applications, Neural Comput. Appl. 28(11) (2017), 3119–3130.
[12] Ding, S., Zhao, X., Zhang, J., Zhang, X. and Xue, Y. A review on multi-class TWSVM, Artif. Intell. Rev. 52(2) (2019), 775–801.
[13] Duan, Y. and Wu, O. Learning with auxiliary less-noisy labels, IEEE Trans. Neural Netw. Learn. Syst. 28(7) (2018), 1716–1721.
[14] Duda, R.O., Hart, P.E. and Stork, D.G. Pattern Classification, John Wiley & Sons, 2012.
[15] Ekambaram, R., Fefilatyev, S., Shreve, M., Kramer, K., Hall, L.O. and Goldgof, D.B. Active cleaning of label noise, Pattern Recognit. 51 (2016), 463–480.
[16] Grant, M., Boyd, S. and Ye, Y. Cvx: Matlab software for disciplined convex programming, version 2.0 beta, 2013.
[17] Hassani, S.F., Eskandari, S. and Salahi, M. CInf-FS: An efficient infi-nite feature selection method using K-means clustering to partition large feature spaces, Pattern Anal. Appl. (2023), 1–9.
[18] Iman, R.L. and Davenport, J.M. Approximations of the critical region of the fbietkan statistic, Commun. Stat. Theory Methods 9 (6) (1980), 571–595.
[19] Jayadeva, Khemchandani, R. and Chandra, S. Twin support vector ma-chines for pattern classification, Trans. Pattern Anal. Mach. Intell. 29(5) (2007), 905–910.
[20] Jimenez-Castano, C., Alvarez-Meza, A. and Orozco-Gutierrez, A. En-hanced automatic twin support vector machine for imbalanced data clas-sification, Pattern Recognit. 107 (2020), 107442.
[21] Keerthi, S.S., Shevade, S.K., Bhattacharyya, C. and Murthy, K.R.K. Improvements to platt’s SMO algorithm for SVM classifier design, Neu-ral Comput. 13(3) (2001), 637–649.
[22] Kshirsagar, A.P. and Shakkeera, L. Recognizing Abnormal Activity Us-ing MultiClass SVM Classification Approach in Tele-health Care, IOT with Smart Systems: Proceedings of ICTIS 2021, Springer Singapore, 2 (2022), 739–750.
[23] Lachenbruch, P.A. Discriminant analysis when the initial samples are misclassified, Technometrics 8(4) (1966), 657–662.
[24] Lachenbruch, P.A. Note on initial misclassification effects on the quadratic discriminant function, Technometrics 21(1) (1979), 129–132.
[25] McLachlan, G.J. Asymptotic results for discriminant analysis when the initial samples are misclassified, Technometrics 14(2) (1972), 415–422.
[26] Nasiri, J.A. and Mir, A.M. An enhanced KNN-based twin support vector machine with stable learning rules, Neural Comput. Appl. 16 (2020), 12949–12969.
[27] Okamoto, S. and Yugami, N. An average-case analysis of the k-nearest neighbor classifier for noisy domains, 15th International Joint Confer-ence on Artificial Intelligence (IJCAI) (1997), 238–245.
[28] Platt, J. Fast Training of Support Vector Machines using Sequential Minimal Optimization, MIT Press, 1998.
[29] Sahleh, A., Salahi, M. and Eskandari, S. Multi-class nonparallel support vector machine, Prog. Artif. Intell. (2023), 1–15.
[30] Tanveer, M., Rajani, T., Rastogi, R., Shao, Y.H. and Ganaie, M.A. Comprehensive review on twin support vector machines, Ann. Oper. Res. (2022), 1–46.
[31] Thulasidasan, S., Bhattacharya, T., Bilmes, J., Chennupati, G., and Mohd-Yusof, J. Combating label noise in deep learning using abstention, arXiv preprint arXiv, (2019), 1905.10964.
[32] Tian, Y. and Qi, Z. Review on: twin support vector machines, Ann. Data Sci. 1 (2014), 253–277.
[33] Tian,Y., Qi, Z., Ju, X., Shi, Y. and Liu, X. Nonparallel support vector machines for pattern classification, IEEE Trans. Cybern. 44(7) (2014), 1067–1079.
[34] Vapnik, V.N. The Nature of Statistical Learning Theory, Springer, New York, 1996.
[35] Vapnik, V.N. Statistical Learning Theory, John Wiley & Sons, New York, 1998.
[36] Witoonchart, P. and Chongstitvatana, P. Application of structured sup-port vector machine backpropagation to a convolutional neural network for human pose estimation, Neural Networks 92 (2017), 39–46.
[37] Wolsey, L.A. and Nemhauser, G.L. Integer and combinatorial optimiza-tion, John Wiley & Sons, 55, 1999.
[38] Xiao, H., Biggio, B., Nelson, B., Xiao, H., Eckert, C. and Roli, F. Support vector machines under adversarial label contamination, Neurocomputing 160 (2015), 53–62.