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A structural information-based twin-hypersphere support vector machine classifier

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Abstract

Twin-hypersphere support vector machine (THSVM) for binary pattern recognition aims at generating two hyperspheres in the feature space such that each hypersphere contains as many as possible samples in one class and is as far as possible from the other one. THSVM has a fast learning speed since it solves two small sized support vector machine (SVM)-type quadratic programming problems (QPPs). However, it only simply considers the prior class-based structural information in the optimization problems. In this paper, a structural information-based THSVM (STHSVM) classifier for binary classification is presented. This proposed STHSVM focuses on the cluster-based structural information of the corresponding class in each optimization problem, which is vital for designing a good classifier in different real-world problems. In addition, it also leads to a fast learning speed since this STHSVM solves a series of smaller-sized QPPs compared with THSVM. Experimental results demonstrate that STHSVM is superior in generalization performance to other classifiers.

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References

  1. Boser B, Guyon L, Vapnik VN (1992) A training algorithm for optimal margin classifiers. In: Proceedings of the 5th Annual Workshop on Computational Learning Theory, ACM Press, Pittsburgh, 1992, pp 144–152

  2. Vapnik VN (1995) The natural of statistical learning theory. Springer, New York

    Book  MATH  Google Scholar 

  3. Vapnik VN (1998) Statistical learning theory. Wiley, New York

    MATH  Google Scholar 

  4. He Q, Wu C (2011) Separating theorem of samples in Banach space for support vector machine learning. Int J Mach Learn Cybernet 2(1):49–54

    Article  Google Scholar 

  5. Wang X, He Q, Chen D, Yeung D (2005) A genetic algorithm for solving the inverse problem of support vector machines. Neurocomputing 68:225–238

    Article  Google Scholar 

  6. Wang X, Lu S, Zhai J (2008) Fast fuzzy multi-category SVM based on support vector domain description. Int J Pattern Recognit Artif Intell 22(1):109–120

    Article  Google Scholar 

  7. Osuna E, Freund R, Girosi F (1997) Training support vector machines: an application to face detection. In: Proceedings of IEEE Computer Vision and Pattern Recognition, San Juan, Puerto Rico, 1997, pp 130–136

  8. El-Naqa I, Yang Y, Wernik M, Galatsanos NP, Nishikawa RM (2002) A support vector machine approach for detection of microclassification. IEEE Trans Med Imaging 21(12):1552–1563

    Article  Google Scholar 

  9. Schölkopf B, Tsuda K, Vert J-P (2004) Kernel methods in computational biology. MIT Press, Cambridge

    Google Scholar 

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

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

    Article  Google Scholar 

  12. Ghorai S, Mukherjee A, Dutta PK (2009) Nonparallel plane proximal classifier. Signal Process 89(4):510–522

    Article  MATH  Google Scholar 

  13. Peng X (2010) A \(\nu\)-twin support vector machine (\(\nu\)-TSVM) classifier and its geometric algorithms. Inform Sci 180(15):3863–3875

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  15. Chen X, Yang J, Ye Q, Liang J (2011) Recursive projection twin support vector machine via within-class variance minimization. Pattern Recognit 44(10–11):2643–2655

    Article  MATH  Google Scholar 

  16. Shao YH, Chen WJ, Deng NY (2014) Nonparallel hyperplane support vector machine for binary classification problems. Inform Sci 263:22–35

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  18. Peng X (2012) Efficient twin parametric insensitive support vector regression model. Neurocomputing 79:26–38

    Article  Google Scholar 

  19. Peng X, Xu D (2013) A twin-hypersphere support vector machine classifier and the fast learning algorithm. Inform Sci 221(1):12–27

    Article  MathSciNet  MATH  Google Scholar 

  20. Yeung D, Wang D, Ng W, Tsang E, Zhao X (2007) Structured large margin machines: sensitive to data distributions. Mach Learn 68(2):171–200

    Article  Google Scholar 

  21. Belkin M, Niyogi P, Sindhwani V (2004) Manifold regularization: a geometric framework for learning from examples, Dept. Comput. Sci., Univ. Chicago, Chicago, IL, Techique report, TR-2004-06, Aug 2004

  22. Chen WJ, Shao YH, Hong N (2014) Laplacian smooth twin support vector machine for semi-supervised classification. Int J Mach Learn Cybernet 5(3):459–468

    Article  Google Scholar 

  23. Rigollet P (2007) Generalization error bounds in semi-supervised classification under the cluster assumption. J Mach Learn Res 8:1369–1392

    MathSciNet  MATH  Google Scholar 

  24. Shivaswamy PK, Jebara T (2007) Ellipsoidal kernel machines. In: Proceeding of 12th International Workshop on Artificial Intelligence Statistic, 2007, pp 1–8

  25. Lanckriet GRG, Ghaoui LE, Bhattacharyya C, Jordan MI (2002) A robust minimax approach to classfication. J Mach Learn Res 3:555–582

    MATH  Google Scholar 

  26. Huang K, Yang H, King I, Lyu MR (2008) Maxi–min margin machine-learning large margin classifiers locally and globally. IEEE Trans Neural Netw 19:260–272

    Article  Google Scholar 

  27. Xue H, Chen S, Yang Q (2011) Structural regularized support vector machine: a framework for structural large margin classifier. IEEE Trans Neural Netw 22:573–587

    Article  Google Scholar 

  28. Peng X, Xu D (2014) Structural regularized projection twin support vector machine for data classification. Inform Sci 279:416–432

    Article  Google Scholar 

  29. Hartigan JA, Wong MA (1979) A \(k\)-means clustering algorithm. Appl Stat 28(1):100–108

    Article  MATH  Google Scholar 

  30. Lu S-Y, Fu KS (1978) A sentence-to-sentence clustering procedure for pattern analysis. IEEE Trans Syst Man Cybernet 8(5):381–389

    Article  MathSciNet  MATH  Google Scholar 

  31. Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353

    Article  MathSciNet  MATH  Google Scholar 

  32. Ward JH (1963) Hierarchical grouping to optimize an objective function. J Am Stat Assoc 58(301):236–244

    Article  MathSciNet  Google Scholar 

  33. Salvador S, Chan P (2004) Determining the number of clusters/segments in hierarchical clustering/segmentation algorithms. In: Proc. 16th IEEE Int. Conf. Tools Artif. Intell., Nov 2004, pp 576584

  34. Rätsch G (2000) Benchmark repository, datasets available at http://ida.first.fhg.de/projects/bench/benchmarks.htm

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Acknowledgments

The authors would like to genuinely thank the anonymous reviewers for their constructive comments and suggestions. This work is partly supported by the National Natural Science Foundation of China (61202156), the National Natural Science Foundation of Shanghai (12ZR1447100), and the program of Shanghai Normal University (DZL121).

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Xinjun Peng, Lingyan Kong & Dongjing Chen

  2. Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, 200234, China

    Xinjun Peng

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  1. Xinjun Peng
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  2. Lingyan Kong
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  3. Dongjing Chen
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Correspondence to Xinjun Peng.

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Peng, X., Kong, L. & Chen, D. A structural information-based twin-hypersphere support vector machine classifier. Int. J. Mach. Learn. & Cyber. 8, 295–308 (2017). https://doi.org/10.1007/s13042-014-0323-4

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  • DOI: https://doi.org/10.1007/s13042-014-0323-4

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