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Intuitionistic fuzzy proximal support vector machine for multicategory classification problems

  • Mathematical methods in data science
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Abstract

Fuzzy support vector machine and their variants are prominent classification techniques that reduce the adverse effects of noises and outliers as compare to classical support vector machine. However, in these methods, only the distance between the training pattern and the class center is considered, and hence, the edge support vectors cannot be distinguished from noises and outliers properly. These limitations are overcome by intuitionistic fuzzy-based support vector machine which allocate two parameters (membership and non-membership degrees) to each pattern of a dataset and hence define score number based on the importance of a pattern. In this paper, an intuitionistic fuzzy proximal support vector machine for multi-category classification problems is proposed. The method significantly reduces the impacts of noises and outliers present in the dataset by assigning the intuitionistic fuzzy score function to each training point based on its location and surroundings. Moreover, the method is computationally efficient as the robust classifiers are obtained by solving the system of linear equations instead of large size quadratic programming problems. In the proposed method, using polynomial and Gaussian kernels, the hyperplanes are also developed in the feature space. The geometrical advantages of the suggested method over the existing techniques are ascertained using the simulated two-dimensional artificial dataset having three target classes. Further, extensive experimental studies on ten UCI benchmark datasets have been performed which demonstrate that the proposed algorithm predicts more precisely about future data as comparison to some well-established algorithms. Figures are also illustrated by varying different parameters involved in the model which confirms the performance of the method over the existing algorithms. Moreover, the analysis of the predictive behavior of the proposed approach is done using the Friedman test, a nonparametric alternative to the analysis of variance test at \(5\%\) significance level. Further, the proposed method has also been applied to image classification and gesture-phase segmentation problems which confirms the efficiency and handling capabilities of the proposed algorithm in practical applications.

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References

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

    Article  Google Scholar 

  • Blake CL, Merz CJ (1998) UCI repository for machine learning databases. Department of Information and Computer Sciences University of California Irvine http://www.ics.uci.edu/~mlearn/MLRepository.html

  • Blumer A, Ehrenfeucht A, Haussler D, Warmuth MK (1989) Learnability and the Vapnik-Chervonenkis dimension. J ACM 36(4):929–965

    Article  MathSciNet  MATH  Google Scholar 

  • Bradley PS, Mangasarian OL (2000) Massive data discrimination via linear support vector machines. Optim Methods Softw 13(1):1–10

    Article  MathSciNet  MATH  Google Scholar 

  • Burges CJC (1998) A tutorial on support vector machines for pattern recognition. Data Min Knowl Disc 2:121–167

    Article  Google Scholar 

  • Charalampous K, Kostavelis I, Gasteratos A (2015) Thorough robot navigation based on SVM local planning. Robot Auton Syst 70:166–180

    Article  Google Scholar 

  • Chen ZS, Liu XL, Chin KS, Pedrycz W, Tsui KL, Skibniewski MJ (2021) Online-review analysis based large-scale group decision-making for determining passenger demands and evaluating passenger satisfaction: Case study of high-speed rail system in China. Inf Fusion 69:22–39

    Article  Google Scholar 

  • Chen ZS, Zhang X, Rodríguez RM, Pedrycz W, Martínez L (2021) Expertise-based bid evaluation for construction-contractor selection with generalized comparative linguistic ELECTRE III. Autom Constr 125:103578

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Cristianini N, Taylor JS (2000) An introduction to support vector machines and other kernel-based learning methods. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • de Carvalho AC, Freitas AA (2009) A tutorial on multi-label classification techniques. In: Abraham A, Hassanien AE, Snašel V Foundations of Computational Intelligence 5:177-195 Studies in Computational Intelligence 205 Springer Berlin Heidelberg

  • Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30

    MathSciNet  MATH  Google Scholar 

  • Deng W, Liu H, Xu J, Zhao H, Song Y (2020a) An improved quantum-inspired differential evolution algorithm for deep belief network. IEEE Trans Instrum Meas 69(10):7319–7327

    Article  Google Scholar 

  • Deng W, Xu J, Gao XZ, Zhao H (2020b) An enhanced MSIQDE algorithm with novel multiple strategies for global optimization problems. IEEE Trans Syst Man Cybern : Syst. https://doi.org/10.1109/TSMC.2020.3030792

  • Deng W, Xu J, Zhao H, Song Y (2020c) A novel gate resource allocation method using improved PSO-based QEA. IEEE Trans Intell Transp Syst. https://doi.org/10.1109/TITS.2020.3025796

  • Deng W, Xu J, Song Y, Zhao H (2021) Differential evolution algorithm with wavelet basis function and optimal mutation strategy for complex optimization problem. Appl Soft Comput 100:106724

    Article  Google Scholar 

  • Deng W, Yao R, Zhao H, Yang X, Li G (2019) A novel intelligent diagnosis method using optimal LS-SVM with improved PSO algorithm. Soft Comput 23:2445–2462

    Article  Google Scholar 

  • Dong S (2021) Multi class SVM algorithm with active learning for network traffic classification. Expert Syst Appl 176:114885

    Article  Google Scholar 

  • Faris H, Hassonah MA, AlaM AZ, Mirjalili S, Aljarah I (2018) A multi-verse optimizer approach for feature selection and optimizing SVM parameters based on a robust system architecture. Neural Comput Appl 30:2355–2369

    Article  Google Scholar 

  • Foody GM, Mathur A (2004) A relative evaluation of multiclass image classification by support vector machines. IEEE Trans Geosci Remote Sens 42(6):1335–1343

    Article  Google Scholar 

  • Fung GM, Mangasarian OL (2005) Multicategory proximal support vector machine classifiers. Mach Learn 59:77–97

    Article  MATH  Google Scholar 

  • Golub GH, Loan CFV (1996) Matrix computations, 3rd edn. The Johns Hopkins University Press, Baltimore

    MATH  Google Scholar 

  • Goudjil M, Koudil M, Bedda M, Ghoggali N (2018) A novel active learning method using SVM for text classification. Int J Autom Comput 15(3):290–298

    Article  Google Scholar 

  • Graf ABA, Smola AJ, Borer S (2003) Classification in a normalized feature spaces using support vector machines. IEEE Trans Neural Netw 14(3):597–605

    Article  Google Scholar 

  • Graf HP, Cosatto E, Bottou L, Dourdanovic I, Vapnik V (2005) Parallel support vector machines: the cascade svm. Adv NIPS 17:521–528

    Google Scholar 

  • Guo B, Gunn SR, Damper RI, Nelson JDB (2008) Customizing kernel functions for SVM-based hyperspectral image classification. IEEE Trans Image Process 17(4):622–629

    Article  MathSciNet  Google Scholar 

  • Gupta D, Richhariya B, Borah P (2019) A fuzzy twin support vector machine based on information entropy for class imbalance learning. Neural Comput Appl 31:7153–7164

    Article  Google Scholar 

  • Ha M, Wang C, Chen J (2013) The support vector machine based on intuitionistic fuzzy number and kernel function. Soft Comput 17:635–641

    Article  MATH  Google Scholar 

  • Ha MH, Huang S, Wang C, Wang XL (2011) Intuitionistic fuzzy support vector machine. J Hebei Univ (Nat Sci Edn) 3:225–229

    Google Scholar 

  • Hassoun MH (1995) Fundamentals of artificial neural networks. MIT Press, Cambridge

    MATH  Google Scholar 

  • Herbrich R, Weston J (1999) Adaptive margin support vector machines for classification. In: Proceedings of the 9th ICANN 2:880-885

  • Hu L, Cui J (2019) Digital image recognition based on Fractional-order-PCA-SVM coupling algorithm. Measurement 145:150–159

    Article  Google Scholar 

  • Huang CL, Dun JF (2008) A distributed PSO-SVM hybrid system with feature selection and parameter optimization. Appl Soft Comput 8(4):1381–1391

    Article  Google Scholar 

  • Huang S, Cai N, Pacheco PP, Narrandes S, Wang Y, Xu W (2018) Applications of support vector machine (SVM) learning in cancer genomics. Cancer Genomics-Proteomics 15:41–51

    Google Scholar 

  • Jayadeva, Khemchandani R, Chandra S (2005) Fuzzy linear proximal support vector machines for multicategory data classification. Neurocomputing 67:426–435

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Keerthi SS, Shevade SK, Bhattacharyya C, Murthy KRK (2001) Improvements to Platts SMO algorithm for SVM classifier design. Neural Comput 13:637–649

    Article  MATH  Google Scholar 

  • Khemchandani R, Jayadeva, Chandra S (2009) Knowledge based proximal support vector machines. Eur J Oper Res 195:914–923

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Kreßel UHG, Schölkopf B, Burges CJC, Smola AJ (1999) Pairwise classification and support vector machines, Advances in kernel methods: support vector learning. MIT Press Cambridge 255–268

  • Kuo BC, Ho HH, Li CH, Hung CC, Taur JS (2014) A kernel-based feature selection method for SVM with RBF kernel for hyperspectral image classification. IEEE J Sel Top Appl Earth Obs Remote Sens 7(1):317–326

    Article  Google Scholar 

  • Laxmi S, Gupta SK (2020) Intuitionistic fuzzy proximal support vector machines for pattern classification. Neural Process Lett 51:2701–2735

    Article  Google Scholar 

  • Li K, Zhou G, Yang Y, Li F, Jiao Z (2020) A novel prediction method for favorable reservoir of oil field based on grey wolf optimizer and twin support vector machine. J Petrol Sci Eng 189:106952

    Article  Google Scholar 

  • Li S, Wu H, Wan D, Zhu J (2011) An effective feature selection method for hyperspectral image classification based on genetic algorithm and support vector machine. Knowl-Based Syst 24(1):40–48

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Liu P, Choo KKR, Wang L, Huang F (2017) SVM or deep learning? A comparative study on remote sensing image classification. Soft Comput 21:7053–7065

    Article  Google Scholar 

  • Lu Y, Boukharouba K, Boonært J, Fleury A, Lecoeuche S (2014) Application of an incremental SVM algorithm for on-line human recognition from video surveillance using texture and color features. Neurocomputing 126:132–140

    Article  Google Scholar 

  • Madeo RCB, Peres SM, de Moraes Lima CA (2016) Gesture phase segmentation using support vector machines. Expert Syst Appl 56:100–115

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Mercer J (1909) Functions of positive and negative type and their connection with the theory of integral equations. Philos Trans R Soc Lond A 209:415–446

    Article  MATH  Google Scholar 

  • Prakash KA, Suresh M, Vengataasalam S (2016) A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept. Math Sci 10(4):177–184

    Article  MathSciNet  MATH  Google Scholar 

  • Rahman MM, Antani SK, Thoma GR (2011) A learning-based similarity fusion and filtering approach for biomedical image retrieval using SVM classification and relevance feedback. IEEE Trans Inf Technol Biomed 15(4):640–646

    Article  Google Scholar 

  • Safavian SR, Landgrebe D (1991) A survey of decision tree classifier methodology. IEEE Trans Syst Man Cybern 21(3):660–674

    Article  MathSciNet  Google Scholar 

  • Schmidhuber J (2015) Deep learning in neural networks: an overview. Neural Netw 61:85–117

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Tran C, Doshi A, Trivedi MM (2012) Modeling and prediction of driver behavior by foot gesture analysis. Comput Vision Image Underst 116(3):435–445

    Article  Google Scholar 

  • Turk M (2014) Multimodal interaction: a review. Pattern Recognit Lett 36:189–195

    Article  Google Scholar 

  • Vapnik V (1995) The nature of statistical learning theory. Springer, Berlin

    Book  MATH  Google Scholar 

  • Vapnik VN (1999) An overview of statistical learning theory. IEEE Trans Neural Netw 10(5):988–999

    Article  Google Scholar 

  • Wang H, Zheng B, Yoon SW, Ko HS (2018) A support vector machine-based ensemble algorithm for breast cancer diagnosis. Eur J Oper Res 267(2):687–699

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • Yan X, Bai Y, Fang SC, Luo J (2018) A proximal quadratic surface support vector machine for semi-supervised binary classification. Soft Comput 22:6905–6919

    Article  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  • Zhang X (1999) Using class-center vectors to build support vector machines. In: Neural Networks for Signal Processing IX: Proceedings of the IEEE Signal Processing Society Workshop (Cat. No. 98TH8468) IEEE 3-11

  • Zhiqiang G, Huaiqing W, Quan L (2013) Financial time series forecasting using LPP and SVM optimized by PSO. Soft Comput 17:805–818

    Article  Google Scholar 

  • Zhou MM, Li L, Lu YL (2009) Fuzzy support vector machine based on density with dual membership. Int Conf Mach Learn Cybern IEEE 2:674–678

    Google Scholar 

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Acknowledgements

The authors sincerely thank the reviewers for the recommendation, valuable comments and the interesting suggestions which have considerably improved the presentation of the paper. The first author is also grateful to the Ministry of Human Resource Development, India, for financial support, to carry out this work.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247 667, India

    Scindhiya Laxmi & S. K. Gupta

  2. Indian Institute of Management Udaipur, Udaipur, 313001, India

    Sumit Kumar

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  1. Scindhiya Laxmi
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  2. S. K. Gupta
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Correspondence to S. K. Gupta.

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Laxmi, S., Gupta, S.K. & Kumar, S. Intuitionistic fuzzy proximal support vector machine for multicategory classification problems. Soft Comput 25, 14039–14057 (2021). https://doi.org/10.1007/s00500-021-06193-3

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