Skip to main content
SpringerLink
Log in

Robust statistics-based support vector machine and its variants: a survey

  • Review Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Support vector machines (SVMs) are versatile learning models which are used for both classification and regression. Several authors have reported successful applications of SVM in a wide range of fields. With the continuous growth and development in machine learning using SVM, it was observed that SVM also has some limitations. This paper focuses on limitation regarding its boundary, i.e., sensitivity to noise or outliers in the dataset. Researchers have proposed many variants and extensions of SVM to make it robust. This paper gives an overview of the developments in the field of robust statistics in support vector machines and its variants. This paper includes an up to date survey of the research development in the field of robustness in SVM and its extensions. It also includes a discussion part which not only discusses the pros and cons of the proposed approaches but also highlights some important future directions in it. This paper would be helpful for researchers working in the field of robust statistics as well as supervised machine learning. This study would also encourage the researchers to work further in the development of SVM and even its variants to improve them.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. An W, Liang M (2013) Fuzzy support vector machine based on within-class scatter for classification problems with outliers or noises. Neurocomputing 110:101–110

    Google Scholar 

  2. Angulo C, Parra X, Catala A (2003) K-SVCR a support vector machine for multi-class classification. Neurocomputing 55(1–2):57–77

    Google Scholar 

  3. Bamakan SMH, Wang H, Shi Y (2017) Ramp loss k-support vector classification-regression; a robust and sparse multi-class approach to the intrusion detection problem. Knowl Based Syst 126:113–126

    Google Scholar 

  4. Barnett V, Lewis T (1974) Outliers in statistical data. Wiley, Hoboken

    MATH  Google Scholar 

  5. Batuwita R, Palade V (2010) Fsvm-cil: fuzzy support vector machines for class imbalance learning. IEEE Trans Fuzzy Syst 18(3):558–571

    Google Scholar 

  6. Ben-Hur A, Horn D, Siegelmann HT, Vapnik V (2001) Support vector clustering. J Mach Learn Res 2(Dec):125–137

    MATH  Google Scholar 

  7. Bhukra MJ, Sharma KK (2018) Rician noise reduction with SVM, IMRD and iterative bilateral filter in different type of medical images using digital image processing

  8. Bicego M, Figueiredo MA (2009) Soft clustering using weighted one-class support vector machines. Pattern Recognit 42(1):27–32

    MATH  Google Scholar 

  9. Biggio B, Nelson B, Laskov P (2011) Support vector machines under adversarial label noise. In: Asian conference on machine learning, pp 97–112

  10. Cevikalp H, Franc V (2017) Large-scale robust transductive support vector machines. Neurocomputing 235:199–209

    Google Scholar 

  11. Chapelle O (2007) Training a support vector machine in the primal. Neural Comput 19(5):1155–1178

    MathSciNet  MATH  Google Scholar 

  12. Chen C, Li Y, Yan C, Guo J, Liu G (2017) Least absolute deviation-ased robust support vector regression. Knowl Based Syst 131:183–194

    Google Scholar 

  13. Chen G, Zhang X, Wang ZJ, Li F (2015) Robust support vector data description for outlier detection with noise or uncertain data. Knowl Based Syst 90:129–137

    Google Scholar 

  14. Chen J, Ji G (2010) Weighted least squares twin support vector machines for pattern classification. In: 2010 The 2nd international conference on computer and automation engineering (ICCAE), IEEE, vol 2, pp 242–246

  15. Chen X, Yang J, Liang J, Ye Q (2010) Robust and sparse twin support vector regression via linear programming. In: 2010 Chinese conference on pattern recognition (CCPR), IEEE, pp 1–6

  16. Chen X, Yang J, Chen L (2014) An improved robust and sparse twin support vector regression via linear programming. Soft Comput 18(12):2335–2348

    MATH  Google Scholar 

  17. Chen Y, Wang W, Zhang X (2018) Randomizing svm against adversarial attacks under uncertainty. In: Pacific-Asia conference on knowledge discovery and data mining, Springer, pp 556–568

  18. Choi YS (2009) Least squares one-class support vector machine. Pattern Recognit Lett 30(13):1236–1240

    Google Scholar 

  19. Chuang CC (2007) Fuzzy weighted support vector regression with a fuzzy partition. IEEE Trans Syst Man Cybern Part B (Cybern) 37(3):630–640

    Google Scholar 

  20. Chuang CC, Lee ZJ (2011) Hybrid robust support vector machines for regression with outliers. Appl Soft Comput 11(1):64–72

    Google Scholar 

  21. Chuang CC, Su SF, Jeng JT, Hsiao CC (2002) Robust support vector regression networks for function approximation with outliers. IEEE Trans Neural Netw 13(6):1322–1330

    Google Scholar 

  22. Collobert R, Sinz F, Weston J, Bottou L (2006) Trading convexity for scalability. In: Proceedings of the 23rd international conference on Machine learning, ACM, pp 201–208

  23. Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297

    MATH  Google Scholar 

  24. David M (2001) Tax one-class classification; concept-learning in the absence of counter-examples. ASCI dissertation series, 65

  25. Du H, Zhao S, Zhang D, Wu J (2016) Novel clustering-based approach for local outlier detection. In: 2016 IEEE conference on computer communications workshops (INFOCOM WKSHPS), IEEE, pp 802–811

  26. Dufrenois F, Noyer JC (2015) Generalized eigenvalue proximal support vector machines for outlier description. In: 2015 International joint conference on neural networks (IJCNN), IEEE, pp 1–9

  27. Erfani SM, Rajasegarar S, Karunasekera S, Leckie C (2016) High-dimensional and large-scale anomaly detection using a linear one-class svm with deep learning. Pattern Recognit 58:121–134

    Google Scholar 

  28. Goel V, Raj H, Muthigi K, Kumar SS, Prasad D, Nath V (2019) Development of human detection system for security and military applications. In: Proceedings of the 3rd international conference on microelectronics, computing and communication systems, Springer, pp 195–200

  29. Guarracino MR, Cifarelli C, Seref O, Pardalos PM (2007) A classification method based on generalized eigenvalue problems. Optim Methods Softw 22(1):73–81

    MathSciNet  MATH  Google Scholar 

  30. Gupta G, Ghosh J (2005) Robust one-class clustering using hybrid global and local search. In: Proceedings of the 22nd international conference on machine learning, ACM, pp 273–280

  31. Gurumurthy S, Sushama C, Ramu M, Nikhitha KS (2019) Design and implementation of intelligent system to detect malicious facebook posts using support vector machine (SVM). In: Soft computing and medical bioinformatics, Springer, pp 17–24

  32. Hao PY et al (2008) Fuzzy one-class support vector machines. Fuzzy Sets Syst 159(18):2317–2336

    MathSciNet  MATH  Google Scholar 

  33. Heo G, Gader P (2009) Fuzzy svm for noisy data: A robust membership calculation method. In: IEEE international conference on fuzzy systems, 2009. FUZZ-IEEE 2009. IEEE, pp 431–436

  34. Huang H, Wei X, Zhou Y (2016) A sparse method for least squares twin support vector regression. Neurocomputing 211:150–158

    Google Scholar 

  35. Huang X, Shi L, Suykens JA (2014) Ramp loss linear programming support vector machine. J Mach Learn Res 15(1):2185–2211

    MathSciNet  MATH  Google Scholar 

  36. Huang X, Shi L, Suykens JA (2014) Support vector machine classifier with pinball loss. IEEE Trans Pattern Anal Mach Intell 36(5):984–997

    Google Scholar 

  37. Jeragh M, AlSulaimi M (2018) Combining auto encoders and one class support vectors machine for fraudulant credit card transactions detection. In: 2018 Second world conference on smart trends in systems, security and sustainability (WorldS4), IEEE, pp 178–184

  38. Jiang J, Wu C, Song C et al (2006) Adaptive and iterative gene selection based on least squares support vector regression. J Inf Comput Sci 3(4):443–451

    Google Scholar 

  39. Jordaan EM, Smits GF (2004) Robust outlier detection using SVM regression. IEEE Int Jt Conf Neural Netw 3:2017–2022

    Google Scholar 

  40. Joshi A, Krishnapuram R (1998) Robust fuzzy clustering methods to support web mining. In: Proceedings of workshop in data mining and knowledge discovery, SIGMOD, Citeseer, pp 1–15

  41. Kaya D (2019) Optimization of SVM parameters with hybrid CS-PSO algorithms for Parkinson’s disease in labview environment. Parkinson’s Disease 2019

  42. Khemchandani R, Sharma S (2016) Robust least squares twin support vector machine for human activity recognition. Appl Soft Comput 47:33–46

    Google Scholar 

  43. Khemchandani R, Chandra S et al (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905–910

    MATH  Google Scholar 

  44. Kumar MA, Gopal M (2008) Application of smoothing technique on twin support vector machines. Pattern Recognit Lett 29(13):1842–1848

    Google Scholar 

  45. Kumar MA, Gopal M (2009) Least squares twin support vector machines for pattern classification. Expert Syst Appl 36(4):7535–7543

    Google Scholar 

  46. Kwak N (2008) Principal component analysis based on l1-norm maximization. IEEE Trans Pattern Anal Mach Intell 30(9):1672–1680

    Google Scholar 

  47. Le HM, Le Thi HA, Nguyen MC (2015) Sparse semi-supervised support vector machines by DC programming and DCA. Neurocomputing 153:62–76

    Google Scholar 

  48. Le Thi Hoai A, Tao PD (1997) Solving a class of linearly constrained indefinite quadratic problems by dc algorithms. J Glob Optim 11(3):253–285

    MATH  Google Scholar 

  49. Lee G, Taur J, Tao C (2006) A robust fuzzy support vector machine for two-class pattern classification. Int J Fuzzy Syst 8(2):76–86

    Google Scholar 

  50. Li CN, Shao YH, Deng NY (2016) Robust l1-norm non-parallel proximal support vector machine. Optimization 65(1):169–183

    MathSciNet  MATH  Google Scholar 

  51. Li Q, Li X, Ba W (2015) Sparse least squares support vector machine with l 0-norm in primal space. In: 2015 IEEE international conference on information and automation, IEEE, pp 2778–2783

  52. Li Y, Wang Y, Bi C, Jiang X (2018) Revisiting transductive support vector machines with margin distribution embedding. Knowl Based Syst 152:200–214

    Google Scholar 

  53. Lin CF, Wang SD (2002) Fuzzy support vector machines. IEEE Trans Neural Netw 13(2):464–471

    Google Scholar 

  54. Lin Cf, Wang Sd (2005) Fuzzy support vector machines with automatic membership setting. Theory Appl Support Vector Mach 177:233–254

    Google Scholar 

  55. Lin CF et al (2004) Training algorithms for fuzzy support vector machines with noisy data. Pattern Recognit Lett 25(14):1647–1656

    Google Scholar 

  56. Lin CT, Liang SF, Yeh CM, Fan KW (2005) Fuzzy neural network design using support vector regression for function approximation with outliers. In: 2005 IEEE international conference on systems, man and cybernetics, IEEE, vol 3, pp 2763–2768

  57. Liu CY, Sun L, Zhou ZJ (2013) Weighted support vector machine based on association rules. In: 2013 International conference on machine learning and cybernetics (ICMLC), IEEE, vol 1, pp 381–386

  58. Liu D, Shi Y, Tian Y, Huang X (2016) Ramp loss least squares support vector machine. J Comput Sci 14:61–68

    MathSciNet  Google Scholar 

  59. Liu T, Tao D (2016) Classification with noisy labels by importance reweighting. IEEE Trans Pattern Anal Mach Intell 38(3):447–461

    Google Scholar 

  60. Liu W, Pokharel PP, Príncipe JC (2007) Correntropy: properties and applications in non-Gaussian signal processing. IEEE Trans Signal Process 55(11):5286–5298

    MathSciNet  MATH  Google Scholar 

  61. Ma Y, Li L, Huang X, Wang S (2011) Robust support vector machine using least median loss penalty. IFAC Proc Vol 44(1):11208–11213

    Google Scholar 

  62. Mangasarian OL, Wild EW (2001) Proximal support vector machine classifiers. In: Proceedings KDD-2001: knowledge discovery and data mining, Citeseer

  63. Mangasarian OL, Wild EW (2006) Multisurface proximal support vector machine classification via generalized eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69–74

    Google Scholar 

  64. Mehrkanoon S, Huang X, Suykens JA (2014) Non-parallel support vector classifiers with different loss functions. Neurocomputing 143:294–301

    Google Scholar 

  65. Mohdiwale S, Sahu TP, Chaurasia RK, Nagwani NK, Verma S (2018) Detection and classification of noise using bark domain features. In: Proceedings of the 6th international conference on communications and broadband networking, ACM, pp 18–21

  66. Mourão-Miranda J, Hardoon DR, Hahn T, Marquand AF, Williams SC, Shawe-Taylor J, Brammer M (2011) Patient classification as an outlier detection problem: an application of the one-class support vector machine. Neuroimage 58(3):793–804

    Google Scholar 

  67. Nasiri JA, Charkari NM, Mozafari K (2014) Energy-based model of least squares twin support vector machines for human action recognition. Signal Process 104:248–257

    Google Scholar 

  68. Ning K, Liu M, Dong M, Wu Z (2014) Robust ls-svr based on variational bayesian and its applications. In: 2014 International joint conference on neural networks (IJCNN), IEEE, pp 2920–2926

  69. Niu J, Chen J, Xu Y (2017) Twin support vector regression with huber loss. J Intell Fuzzy Syst 32(6):4247–4258

    MATH  Google Scholar 

  70. Oliva JT, Rosa JLG (2017) The use of one-class classifiers for differentiating healthy from epileptic EEQ segments. In: 2017 International joint conference on neural networks (IJCNN), IEEE, pp 2956–2963

  71. Oza P, Patel VM (2019) One-class convolutional neural network. IEEE Signal Process Lett 26(2):277–281

    Google Scholar 

  72. Park SY, Liu Y (2011) Robust penalized logistic regression with truncated loss functions. Can J Stat 39(2):300–323

    MathSciNet  MATH  Google Scholar 

  73. Peng X (2010) A \(\nu\)-twin support vector machine (\(\nu\)-tsvm) classifier and its geometric algorithms. Inf Sci 180(20):3863–3875

    MathSciNet  MATH  Google Scholar 

  74. Peng X (2010) Primal twin support vector regression and its sparse approximation. Neurocomputing 73(16–18):2846–2858

    Google Scholar 

  75. Peng X (2010) TSVR: an efficient twin support vector machine for regression. Neural Netw 23(3):365–372

    MATH  Google Scholar 

  76. Peng X (2011) TPMSVM: a novel twin parametric-margin support vector machine for pattern recognition. Pattern Recognit 44(10–11):2678–2692

    MATH  Google Scholar 

  77. Rajalaxmi R, Vidhya E (2019) A mutated salp swarm algorithm for optimization of support vector machine parameters. In: 2019 5th International conference on advanced computing & communication systems (ICACCS), IEEE, pp 979–983

  78. Rakhe SS, Vaidya AS (2015) A survey on different unsupervised techniques to detect outliers. Int Res J Eng Technol (IRJET) 2

  79. Roy A, Singha J, Devi SS, Laskar RH (2016) Impulse noise removal using svm classification based fuzzy filter from grayscale images. Signal Process 128:262–273

    Google Scholar 

  80. Ruff L, Görnitz N, Deecke L, Siddiqui SA, Vandermeulen R, Binder A, Müller E, Kloft M (2018) Deep one-class classification. In: International conference on machine learning, pp 4390–4399

  81. Rustam Z, Pandelaki J, Siahaan A, et al. (2019) Kernel spherical k-means and support vector machine for acute sinusitis classification. In: IOP conference series: materials science and engineering, IOP Publishing, vol 546, p 052011

  82. Saeedi J, Ahadi SM, Faez K (2015) Robust voice activity detection directed by noise classification. Signal Image Video Process 9(3):561–572

    Google Scholar 

  83. Shao YH, Deng NY, Chen WJ, Wang Z (2013) Improved generalized eigenvalue proximal support vector machine. IEEE Signal Process Lett 20(3):213–216

    Google Scholar 

  84. Shao YH, Zhang CH, Yang ZM, Jing L, Deng NY (2013) An \(\varepsilon\)-twin support vector machine for regression. Neural Comput Appl 23(1):175–185

    Google Scholar 

  85. Shen X, Niu L, Qi Z, Tian Y (2017) Support vector machine classifier with truncated pinball loss. Pattern Recognit 68:199–210

    Google Scholar 

  86. Shi Y, Zhang L (2011) Coid: a cluster-outlier iterative detection approach to multi-dimensional data analysis. Knowl Inf Syst 28(3):709–733

    Google Scholar 

  87. Shin HJ, Eom DH, Kim SS (2005) One-class support vector machines-an application in machine fault detection and classification. Comput Ind Eng 48(2):395–408

    Google Scholar 

  88. Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14(3):199–222

    MathSciNet  Google Scholar 

  89. Song Q, Hu W, Xie W (2002) Robust support vector machine with bullet hole image classification. IEEE Trans Syst Man Cybern Part C (Appl Rev) 32(4):440–448

    Google Scholar 

  90. Sun XQ, Chen YJ, Shao YH, Li CN, Wang CH (2018) Robust nonparallel proximal support vector machine with lp-norm regularization. IEEE Access 6:20334–20347

    Google Scholar 

  91. Suykens JA, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Process Lett 9(3):293–300

    Google Scholar 

  92. Suykens JA, De Brabanter J, Lukas L, Vandewalle J (2002) Weighted least squares support vector machines: robustness and sparse approximation. Neurocomputing 48(1–4):85–105

    MATH  Google Scholar 

  93. Takruri M, Mahmoud A, Khaled M, Al-Jumaily A (2019) PSO-SVM hybrid system for melanoma detection from histo-pathological images. Int J Electr Comput Eng 2088–8708:9

    Google Scholar 

  94. Tang L, Tian Y, Yang C, Pardalos PM (2018) Ramp-loss nonparallel support vector regression: robust, sparse and scalable approximation. Knowl Based Syst 147:55–67

    Google Scholar 

  95. Tao PD et al (2005) The dc (difference of convex functions) programming and dca revisited with dc models of real world nonconvex optimization problems. Ann Oper Res 133(1–4):23–46

    MathSciNet  MATH  Google Scholar 

  96. Tao Q, Wang J (2004) A new fuzzy support vector machine based on the weighted margin. Neural Process Lett 20(3):139–150

    Google Scholar 

  97. Tao Z, Huiling L, Wenwen W, Xia Y (2019) Ga-svm based feature selection and parameter optimization in hospitalization expense modeling. Appl Soft Comput 75:323–332

    Google Scholar 

  98. Tax DM, Duin RP (2004) Support vector data description. Mach Learn 54(1):45–66

    MATH  Google Scholar 

  99. Tian Y, Mirzabagheri M, Bamakan SMH, Wang H, Qu Q (2018) Ramp loss one-class support vector machine; a robust and effective approach to anomaly detection problems. Neurocomputing 310:223–235

    Google Scholar 

  100. Tomar D, Agarwal S (2014) Feature selection based least square twin support vector machine for diagnosis of heart disease. Int J Bio-Sci Bio-Technol 6(2):69–82

    Google Scholar 

  101. Tuba E, Strumberger I, Bacanin N, Jovanovic R, Tuba M (2019) Bare bones fireworks algorithm for feature selection and SVM optimization. In: 2019 IEEE congress on evolutionary computation (CEC), IEEE, pp 2207–2214

  102. Vapnik VN (1998) Adaptive and learning systems for signal processing communications, and control. Stat Learn Theory

  103. Vijayalakshmi V, Babu MS, Lakshmi RP (2018) Kfcm algorithm for effective brain stroke detection through SVM classifier. In: 2018 IEEE international conference on system, computation, automation and networking (ICSCA), IEEE, pp 1–6

  104. Wang JS, Chiang JC (2008) A cluster validity measure with outlier detection for support vector clustering. IEEE Trans Syst Man Cybern Part B (Cybern) 38(1):78–89

    Google Scholar 

  105. Wang K, Zhong P (2014) Robust non-convex least squares loss function for regression with outliers. Knowl Based Syst 71:290–302

    Google Scholar 

  106. Wang L, Jia H, Li J (2008) Training robust support vector machine with smooth ramp loss in the primal space. Neurocomputing 71(13–15):3020–3025

    Google Scholar 

  107. Wang R, Li W, Li R, Zhang L (2019) Automatic blur type classification via ensemble svm. Signal Process Image Commun 71:24–35

    Google Scholar 

  108. Wang T-Y, Chiang H-M (2007) Fuzzy support vector machine for multi-class text categorization. Inf Process Manag 43(4):914–929

    Google Scholar 

  109. Wang Y, Wang S, Lai KK (2005) A new fuzzy support vector machine to evaluate credit risk. IEEE Trans Fuzzy Syst 13(6):820–831

    Google Scholar 

  110. Wang YF, Jiong Y, Su GP, Qian YR (2019) A new outlier detection method based on optics. Sustain Cities Soc 45:197–212

    Google Scholar 

  111. Wang Z, Shao YH, Bai L, Deng NY (2015) Twin support vector machine for clustering. IEEE Trans Neural Netw Learn Syst 26(10):2583–2588

    MathSciNet  Google Scholar 

  112. Wang Z, Chen X, Li CN, Shao YH (2018) Ramp-based twin support vector clustering. arXiv preprint arXiv:181203710

  113. Wang Z, Wang S, Kong D, Liu S (2019) Methane detection based on improved chicken algorithm optimization support vector machine. Appl Sci 9(9):1761

    Google Scholar 

  114. Wu Q, Law R (2010) Fuzzy support vector regression machine with penalizing gaussian noises on triangular fuzzy number space. Expert Syst Appl 37(12):7788–7795

    Google Scholar 

  115. Wu Y, Liu Y (2007) Robust truncated hinge loss support vector machines. J Am Stat Assoc 102(479):974–983

    MathSciNet  MATH  Google Scholar 

  116. Wu Y, Liu Y (2013) Adaptively weighted large margin classifiers. J Comput Graph Stat 22(2):416–432

    MathSciNet  Google Scholar 

  117. Xiao J (2019) SVM and KNN ensemble learning for traffic incident detection. Phys A Stat Mech Appl 517:29–35

    Google Scholar 

  118. Xiao Y, Wang H, Xu W, Zhou J (2016) Robust one-class SVM for fault detection. Chemom Intell Lab Syst 151:15–25

    Google Scholar 

  119. Xiao Y, Wang H, Xu W (2017) Ramp loss based robust one-class SVM. Pattern Recognit Lett 85:15–20

    Google Scholar 

  120. Xing HJ, Ji M (2018) Robust one-class support vector machine with rescaled hinge loss function. Pattern Recognit 84:152–164

    Google Scholar 

  121. Xu G, Cao Z, Hu BG, Principe JC (2017) Robust support vector machines based on the rescaled hinge loss function. Pattern Recognit 63:139–148

    MATH  Google Scholar 

  122. Xu H, Caramanis C, Mannor S (2009) Robust regression and lasso. In: Advances in neural information processing systems, pp 1801–1808

  123. Xu L, Crammer K, Schuurmans D (2006) Robust support vector machine training via convex outlier ablation. AAAI 6:536–542

    Google Scholar 

  124. Xu Y, Guo R (2014) An improved \(\nu\)-twin support vector machine. Appl Intell 41(1):42–54

    Google Scholar 

  125. Xu Y, Wang L (2012) A weighted twin support vector regression. Knowl Based Syst 33:92–101

    Google Scholar 

  126. Xu Y, Lv X, Wang Z, Wang L (2014) A weighted least squares twin support vector machine. J Inf Sci Eng 30(6):1773–1787

    MathSciNet  Google Scholar 

  127. Xu Y, Yang Z, Pan X (2017) A novel twin support-vector machine with pinball loss. IEEE Trans Neural Netw Learn Syst 28(2):359–370

    MathSciNet  Google Scholar 

  128. Yang HY, Wang XY, Niu PP, Liu YC (2014) Image denoising using nonsubsampled shearlet transform and twin support vector machines. Neural Netw 57:152–165

    Google Scholar 

  129. Yang J, Deng T, Sui R (2016) An adaptive weighted one-class svm for robust outlier detection. In: Proceedings of the 2015 Chinese intelligent systems conference, Springer, pp 475–484

  130. Yang L, Dong H (2018) Support vector machine with truncated pinball loss and its application in pattern recognition. Chemom Intell Lab Syst 177:89–99

    Google Scholar 

  131. Yang L, Zhang S (2016) A sparse extreme learning machine framework by continuous optimization algorithms and its application in pattern recognition. Eng Appl Artif Intell 53:176–189

    Google Scholar 

  132. Yang L, Ren Z, Wang Y, Dong H (2017) A robust regression framework with laplace kernel-induced loss. Neural Comput 29(11):3014–3039

    MathSciNet  MATH  Google Scholar 

  133. Yang X, Song Q, Wang Y (2007) A weighted support vector machine for data classification. Int J Pattern Recognit Artif Intell 21(05):961–976

    Google Scholar 

  134. Yang X, Tan L, He L (2014) A robust least squares support vector machine for regression and classification with noise. Neurocomputing 140:41–52

    Google Scholar 

  135. Yang X, Han L, Li Y, He L (2015) A bilateral-truncated-loss based robust support vector machine for classification problems. Soft Comput 19(10):2871–2882

    MATH  Google Scholar 

  136. YangX W, ZhangG Q et al (2011) A kernel fuzzy c-means clustering-based fuzzy support vector machine algorithm for classification problems with outliers or noises. IEEE Trans FuzzySyst 19(1):105–115

    Google Scholar 

  137. Ye Q, Zhao H, Li Z, Yang X, Gao S, Yin T, Ye N (2018) L1-norm distance minimization-based fast robust twin support vector \(k\)-plane clustering. IEEE Trans Neural Netw Learn Syst 29(9):4494–4503

    Google Scholar 

  138. Ye YF, Shao YH, Deng NY, Li CN, Hua XY (2017) Robust lp-norm least squares support vector regression with feature selection. Appl Math Comput 305:32–52

    MathSciNet  MATH  Google Scholar 

  139. Yin S, Zhu X, Jing C (2014) Fault detection based on a robust one class support vector machine. Neurocomputing 145:263–268

    Google Scholar 

  140. You L, Jizhen L, Yaxin Q (2011) A new robust least squares support vector machine for regression with outliers. Procedia Eng 15:1355–1360

    Google Scholar 

  141. Yuille AL, Rangarajan A (2003) The concave–convex procedure. Neural Comput 15(4):915–936

    MATH  Google Scholar 

  142. Zhang Y, Xie F, Huang D, Ji M (2010) Support vector classifier based on fuzzy c-means and mahalanobis distance. J Intell Inf Syst 35(2):333–345

    Google Scholar 

  143. Zhao Y, Sun J (2008) Robust support vector regression in the primal. Neural Netw 21(10):1548–1555

    MATH  Google Scholar 

  144. Zhao YP, Zhao J, Zhao M (2013) Twin least squares support vector regression. Neurocomputing 118:225–236

    Google Scholar 

  145. Zhong P, Xu Y, Zhao Y (2012) Training twin support vector regression via linear programming. Neural Comput Appl 21(2):399–407

    Google Scholar 

  146. Zhu F, Yang J, Gao C, Xu S, Ye N, Yin T (2016) A weighted one-class support vector machine. Neurocomputing 189:1–10

    Google Scholar 

  147. Zhu W, Song Y, Xiao Y (2018) A new support vector machine plus with pinball loss. J Classif 35(1):52–70

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments that have resulted in the significant improvement of the paper. The first author would like to thank IIT BHU for providing the research fellowship.

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, India

    Manisha Singla & K. K. Shukla

Authors
  1. Manisha Singla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. K. Shukla
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manisha Singla.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singla, M., Shukla, K.K. Robust statistics-based support vector machine and its variants: a survey. Neural Comput & Applic 32, 11173–11194 (2020). https://doi.org/10.1007/s00521-019-04627-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-019-04627-6

Keywords

Search

Navigation