Journal of the Operations Research Society of China >

2022 , Vol. 10 >Issue 1: 89 - 112

DOI: https://doi.org/10.1007/s40305-021-00354-9

Intuitionistic Fuzzy Laplacian Twin Support Vector Machine for Semi-supervised Classification

Expand
  • 1 Department of Mathematics, Shanghai University, Shanghai 200444, China;
    2 Delft Institute of Applied Mathematics, Delft University of Technology, Delft 2600 GA, The Netherlands

Received date: 2020-11-04

  Revised date: 2021-04-16

  Online published: 2022-03-23

Fold

Abstract

In general, data contain noises which come from faulty instruments, flawed measurements or faulty communication. Learning with data in the context of classification or regression is inevitably affected by noises in the data. In order to remove or greatly reduce the impact of noises, we introduce the ideas of fuzzy membership functions and the Laplacian twin support vector machine (Lap-TSVM). A formulation of the linear intuitionistic fuzzy Laplacian twin support vector machine (IFLap-TSVM) is presented. Moreover, we extend the linear IFLap-TSVM to the nonlinear case by kernel function. The proposed IFLap-TSVM resolves the negative impact of noises and outliers by using fuzzy membership functions and is a more accurate reasonable classifier by using the geometric distribution information of labeled data and unlabeled data based on manifold regularization. Experiments with constructed artificial datasets, several UCI benchmark datasets and MNIST dataset show that the IFLap-TSVM has better classification accuracy than other state-of-the-art twin support vector machine (TSVM), intuitionistic fuzzy twin support vector machine (IFTSVM) and Lap-TSVM.

Key words： Twin support vector machine; Semi-supervised classification; Intuitionistic fuzzy; Manifold regularization; Noisy data

Cite this article

Jia-Bin Zhou, Yan-Qin Bai, Yan-Ru Guo, Hai-Xiang Lin . Intuitionistic Fuzzy Laplacian Twin Support Vector Machine for Semi-supervised Classification[J]. Journal of the Operations Research Society of China, 2022 , 10(1) : 89 -112 . DOI: 10.1007/s40305-021-00354-9

References

[1] Cortes, C., Vapnik, V.:Support-vector networks. Mach. Learn. 20(3), 273-297(1995)
[2] Joachims,T.:Text categorization with support vector machines:learning with many relevant features. In:Proceedings of Conference on Machine Learning (1998) https://doi.org/10.1007/BFb0026683
[3] Li, X., Chen, G.:Face recognition based on PCA and SVM. In:IEEE Photonics and Optoelectronics, pp. 1-4(2012), https://doi.org/10.1109/SOPO.2012.6270973
[4] Sun, J., Shang, Z., Li, H.:Imbalance-oriented SVM methods for financial distress prediction:a comparative study among the new SB-SVM-ensemble method and traditional methods. J. Oper. Res. Soc. 65(12), 1905-1919(2014)
[5] Chen,L.,Zhou,M.,Wu,M.,etal.:Three-layerweightedfuzzysupportvectorregressionforemotional intentionunderstandinginhuman-robotinteraction.IEEETrans.FuzzySyst. 26(5),2524-2538(2018)
[6] Zhang, M., Zhen, Y., Hui, G., Chen, G.:Accurate multisteps traffic flow prediction based on SVM. Math. Probl. Eng. 1-8(2013)
[7] Bai, Y., Han, X., Chen, T., Yu, H.:Quadratic kernel-free least squares support vector machine for target diseases classification. J. Combin. Optim. 30(4), 850-870(2015)
[8] Fung, G., Mangasarian, O.:Proximal support vector machine classifiers. In:ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 77-86. Assoc. Comput. Mach., New York (2001)
[9] Bai, Y., Zhu, Z., Yan, W.:Sparse proximal support vector machine with a specialized interior-point method. J. Oper. Res. Soc. China 3, 1-15(2015)
[10] Mangasarian, O.L., Wild, E.W.:Multisurface proximal support vector machine classification via generalized eigenvalues. IEEE Trans. Pattern Anal. Mach. Intell. 28(1), 69-74(2006)
[11] Jayadeva, R.K., Khemchandani, R., Chandra, S.:Twin support vector machines for pattern classification. IEEE Trans. Pattern Anal. Mach. Intell. 29(5), 905-910(2007)
[12] Shao, Y., Chen, W., Zhang, J., et al.:An efficient weighted Lagrangian twin support vector machine for imbalanced data classification. Pattern Recognit. 47(9), 3158-3167(2014)
[13] Tian, Y., Ju, X.:Nonparallel support vector machine based on one optimization problem for pattern recognition. J. Oper. Res. Soc. China 3, 499-519(2015)
[14] Gao, Q., Bai, Y., Zhan, Y.:Quadratic kernel-free least square twin support vector machine for binary classification problems. J. Oper. Res. Soc. China 7, 539-559(2019)
[15] Zhu, X., Goldber, A.:Introduction to semi-supervised learning. Morgan & Claypool (2009)
[16] Yan, X., Bai, Y., Fang, S., Luo, J.:A kernel-free quadratic surface support vector machine for semisupervised learning. J. Oper. Res. Soc. 67(7), 1001-1011(2016)
[17] Zhan, Y., Bai, Y., Zhang, W., Ying, S.:A P-ADMM for sparse quadratic kernel-free least squares semi-supervised support vector machine. Neurocomputing. 306, 37-50(2018)
[18] Belkin, M., Niyogi, P., Sindhwani, V.:Manifold regularization:a geometric framework for learning from labeled and unlabeled examples. J. Mach. Learn. Res. 7, 2399-2434(2006)
[19] Chen, W., Shao, Y., Xu, D., Fu, Y.:Manifold proximal support vector machine for semi-supervised classification. Appl. Intell. 40(4), 623-638(2014)
[20] Qi, Z., Tian, Y., Shi, Y.:Laplacian twin support vector machine for semi-supervised classification. Neural Netw. 35, 46-53(2012)
[21] Rastogi,R.,Pal,A.:Fuzzysemi-supervisedweightedlinearlosstwinsupportvectorclustering.Knowl. Based Syst. 165, 132-148(2019)
[22] Dong, H., Yang, L., Wang, X.:Robust semi-supervised support vector machines with Laplace kernelinduced correntropy loss functions. Appl. Intell. 51(21), 1-15(2021)
[23] Lin, C., Wang, S.:Fuzzy support vector machines. IEEE Trans. Neural Netw. 13(2), 464-471(2002)
[24] Revani, S., Wang, X., Pourpanah, F.:Intuitionistic fuzzy twin support vector machines. IEEE Trans. Fuzzy Syst. 27(11), 2140-2151(2019)
[25] Tikhonov, A.:Regularization of incorrectly posed problems. Sov. Math. Doklady. 4, 1624-1627(1963)
[26] Gantmacher, F.R.:Matrix Theory. Chelsea, New York (1990)
[27] Zadeh, L.A.:Fuzzy sets. Inf. Control 8, 338-353(1965)
[28] Atanssov, K.:Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87-96(1986)
[29] Ha, M., Wang, C., Chen, J.:The support vector machine based on intuitionistic fuzzy number and kernel function. Soft Comput. 17(4), 635-641(2013)
[30] Deng, N., Tian, Y., Zhang, C.:Support Vector Machines:Theory, Algorithms, and Extensions. CRC Press, Philadelphia (2013)
[31] Asuncion, A., Newman, D.:UCI machine learning repository (2007) https://archive.ics.uci.edu/ml/index.php
[32] Chen, W., Shao, Y., Deng, N., Feng, Z.:Laplacian least squares twin support vector machine for semi-supervised classification. Neurocomputing 145, 465-476(2014)
Options
Outlines

/

〈 〉

Copyright © Operations Research Society of China, The Periodicals Agency of Shanghai University , and Springer-Verlag Berlin Heidelberg 2016