Parallel Learning Algorithms of Local Support Vector Regression for Dealing with Large Datasets

  • Thanh-Nghi DoEmail author
  • Le-Diem Bui
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11390)


New parallel algorithms of local support vector regression (local SVR), called kSVR, krSVR are proposed in this paper to efficiently handle the prediction task for large datasets. The learning strategy of kSVR performs the regression task with two main steps. The first one is to partition the training data into k clusters, followed which the second one is to learn the SVR model from each cluster to predict the data locally in the parallel way on multi-core computers. The krSVR learning algorithm trains an ensemble of T random kSVR models for improving the generalization capacity of the kSVR alone. The performance analysis in terms of the algorithmic complexity and the generalization capacity illustrates that our kSVR and krSVR algorithms are faster than the standard SVR for the non-linear regression on large datasets while maintaining the high correctness in the prediction. The numerical test results on five large datasets from UCI repository showed that proposed kSVR and krSVR algorithms are efficient compared to the standard SVR. Typically, the average training time of kSVR and krSVR are 183.5 and 43.3 times faster than the standard SVR; kSVR and krSVR also improve 62.10%, 63.70% of the relative prediction correctness compared to the standard SVR, respectively.


Support vector regression (SVR) Local support vector regression (local SVR) Ensemble learning Large datasets 


  1. 1.
    Lyman, P., et al.: How much information (2003)Google Scholar
  2. 2.
    National Research Council, Division on Engineering and Physical Sciences, Board on Mathematical Sciences and Their Applications, Committee on the Analysis of Massive Data, Committee on Applied and Theoretical Statistics: Frontiers in Massive Data Analysis. The National Academies Press (2013)Google Scholar
  3. 3.
    Vapnik, V.: The Nature of Statistical Learning Theory. Springer, Heidelberg (1995). Scholar
  4. 4.
    Guyon, I.: Web page on SVM applications (1999).
  5. 5.
    Bui, L.D., Tran-Nguyen, M.T., Kim, Y.G., Do, T.N.: Parallel algorithm of local support vector regression for large datasets. In: Proceedings of Future Data and Security Engineering - 4th International Conference, FDSE 2017, pp. 139–153, Ho Chi Minh City, Vietnam, 29 November–1 December (2017)CrossRefGoogle Scholar
  6. 6.
    Chang, C.C., Lin, C.J.: LIBSVM : a library for support vector machines. ACM Trans. Intell. Syst. Technol. 2(27), 1–27 (2011)CrossRefGoogle Scholar
  7. 7.
    MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297. University of California Press, Berkeley, January 1967Google Scholar
  8. 8.
    Lichman, M.: UCI machine learning repository (2013)Google Scholar
  9. 9.
    Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines: And Other Kernel-based Learning Methods. Cambridge University Press, New York (2000)zbMATHCrossRefGoogle Scholar
  10. 10.
    Platt, J.: Fast training of support vector machines using sequential minimal optimization. In: Schölkopf, B., Burges, C., Smola, A. (eds.) Advances in Kernel Methods - Support Vector Learning, pp. 185–208 (1999)Google Scholar
  11. 11.
    OpenMP Architecture Review Board: OpenMP application program interface version 3.0 (2008)Google Scholar
  12. 12.
    Bi, J., Bennett, K.P.: A geometric approach to support vector regression. Neurocomputing 55(1–2), 79–108 (2003)CrossRefGoogle Scholar
  13. 13.
    Vapnik, V.: Principles of risk minimization for learning theory. In: Advances in Neural Information Processing Systems 4, NIPS Conference, Denver, Colorado, USA, 2–5 December 1991, pp. 831–838 (1991)Google Scholar
  14. 14.
    Bottou, L., Vapnik, V.: Local learning algorithms. Neural Comput. 4(6), 888–900 (1992)CrossRefGoogle Scholar
  15. 15.
    Vapnik, V., Bottou, L.: Local algorithms for pattern recognition and dependencies estimation. Neural Comput. 5(6), 893–909 (1993)CrossRefGoogle Scholar
  16. 16.
    Do, T.N., Poulet, F.: Parallel learning of local SVM algorithms for classifying large datasets. T. Large-Scale Data-Knowl.-Cent. Syst. 31, 67–93 (2016)Google Scholar
  17. 17.
    Do, T.N., Poulet, F.: Latent-lSVM classification of very high-dimensional and large-scale multi-class datasets. Concurr. Comput.: Pract. Exp. 0(0), e4224Google Scholar
  18. 18.
    Vapnik, V.: The Nature of Statistical Learning Theory, 2nd edn. Springer, Heidelberg (2000). Scholar
  19. 19.
    Breiman, L.: Bagging predictors. Mach. Learn. 24(2), 123–140 (1996)zbMATHGoogle Scholar
  20. 20.
    Breiman, L.: Random forests. Mach. Learn. 45(1), 5–32 (2001)zbMATHCrossRefGoogle Scholar
  21. 21.
    Breiman, L.: Arcing classifiers. Ann. Stat. 26(3), 801–849 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Dietterich, T.G.: Ensemble methods in machine learning. In: Kittler, J., Roli, F. (eds.) MCS 2000. LNCS, vol. 1857, pp. 1–15. Springer, Heidelberg (2000). Scholar
  23. 23.
    Whaley, R., Dongarra, J.: Automatically tuned linear algebra software. In: Ninth SIAM Conference on Parallel Processing for Scientific Computing, CD-ROM Proceedings (1999)Google Scholar
  24. 24.
    Lin, C.: A practical guide to support vector classification (2003)Google Scholar
  25. 25.
    Boser, B., Guyon, I., Vapnik, V.: An training algorithm for optimal margin classifiers. In: Proceedings of 5th ACM Annual Workshop on Computational Learning Theory of 5th ACM Annual Workshop on Computational Learning Theory, pp. 144–152. ACM (1992)Google Scholar
  26. 26.
    Osuna, E., Freund, R., Girosi, F.: An improved training algorithm for support vector machines. In: Gile, L., Morgan, N., Wilson, E. (eds.) Neural Networks for Signal Processing VII, Jose Principe, pp. 276–285 (1997)Google Scholar
  27. 27.
    Shalev-Shwartz, S., Singer, Y., Srebro, N.: Pegasos: primal estimated sub-gradient solver for SVM. In: Proceedings of the Twenty-Fourth International Conference Machine Learning, pp. 807–814 (2007). ACMGoogle Scholar
  28. 28.
    Bottou, L., Bousquet, O.: The tradeoffs of large scale learning. In: Platt, J., Koller, D., Singer, Y., Roweis, S. (eds.) Advances in Neural Information Processing Systems, vol. 20, pp. 161–168. NIPS Foundation (2008).
  29. 29.
    Do, T.N.: Parallel multiclass stochastic gradient descent algorithms for classifying million images with very-high-dimensional signatures into thousands classes. Vietnam. J. Comput. Sci. 1(2), 107–115 (2014)CrossRefGoogle Scholar
  30. 30.
    Do, T.N., Poulet, F.: Parallel multiclass logistic regression for classifying large scale image datasets. In: Advanced Computational Methods for Knowledge Engineering - Proceedings of 3rd International Conference on Computer Science, Applied Mathematics and Applications - ICCSAMA 2015, Metz, France, 11–13 May 2015, pp. 255–266 (2015)CrossRefGoogle Scholar
  31. 31.
    Do, T.-N., Tran-Nguyen, M.-T.: Incremental parallel support vector machines for classifying large-scale multi-class image datasets. In: Dang, T.K., Wagner, R., Küng, J., Thoai, N., Takizawa, M., Neuhold, E. (eds.) FDSE 2016. LNCS, vol. 10018, pp. 20–39. Springer, Cham (2016). Scholar
  32. 32.
    Yuan, G., Ho, C., Lin, C.: Recent advances of large-scale linear classification. Proc. IEEE 100(9), 2584–2603 (2012)CrossRefGoogle Scholar
  33. 33.
    Fan, R.E., Chang, K.W., Hsieh, C.J., Wang, X.R., Lin, C.J.: LIBLINEAR: a library for large linear classification. J. Mach. Learn. Res. 9(4), 1871–1874 (2008)zbMATHGoogle Scholar
  34. 34.
    Ho, C., Lin, C.: Large-scale linear support vector regression. J. Mach. Learn. Res. 13, 3323–3348 (2012)MathSciNetzbMATHGoogle Scholar
  35. 35.
    Zaharia, M., Chowdhury, M., Franklin, M.J., Shenker, S., Stoica, I.: Spark: cluster computing with working sets. In: Proceedings of the 2nd USENIX Conference on Hot Topics in Cloud Computing, HotCloud 2010, p. 10. USENIX Association, Berkeley (2010)Google Scholar
  36. 36.
    Lin, C., Tsai, C., Lee, C., Lin, C.: Large-scale logistic regression and linear support vector machines using spark. In: 2014 IEEE International Conference on Big Data, Big Data 2014, Washington, DC, USA, 27–30 October 2014, pp. 519–528 (2014)Google Scholar
  37. 37.
    Zhuang, Y., Chin, W., Juan, Y., Lin, C.: Distributed Newton methods for regularized logistic regression. In: Proceedings Advances in Knowledge Discovery and Data Mining - 19th Pacific-Asia Conference, PAKDD 2015, Part II, Ho Chi Minh City, Vietnam, 19–22 May 2015, pp. 690–703 (2015)CrossRefGoogle Scholar
  38. 38.
    Chiang, W., Lee, M., Lin, C.: Parallel dual coordinate descent method for large-scale linear classification in multi-core environments. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, 13–17 August 2016, pp. 1485–1494 (2016)Google Scholar
  39. 39.
    Tsai, C., Lin, C., Lin, C.: Incremental and decremental training for linear classification. In: The 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2014, New York, NY, USA, 24–27 August 2014, pp. 343–352 (2014)Google Scholar
  40. 40.
    Huang, H., Lin, C.: Linear and kernel classification: when to use which? In: Proceedings of the SIAM International Conference on Data Mining 2016 (2016)Google Scholar
  41. 41.
    Jacobs, R.A., Jordan, M.I., Nowlan, S.J., Hinton, G.E.: Adaptive mixtures of local experts. Neural Comput. 3(1), 79–87 (1991)CrossRefGoogle Scholar
  42. 42.
    Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B 39(1), 1–38 (1977)MathSciNetzbMATHGoogle Scholar
  43. 43.
    Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)zbMATHGoogle Scholar
  44. 44.
    Collobert, R., Bengio, S., Bengio, Y.: A parallel mixture of SVMs for very large scale problems. Neural Comput. 14(5), 1105–1114 (2002)zbMATHCrossRefGoogle Scholar
  45. 45.
    Gu, Q., Han, J.: Clustered support vector machines. In: Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, AISTATS 2013, Scottsdale, AZ, USA, 29 April–1 May 2013, Volume 31 of JMLR Proceedings, pp. 307–315 (2013)Google Scholar
  46. 46.
    Do, T.-N.: Non-linear classification of massive datasets with a parallel algorithm of local support vector machines. In: Le Thi, H.A., Nguyen, N.T., Do, T.V. (eds.) Advanced Computational Methods for Knowledge Engineering. AISC, vol. 358, pp. 231–241. Springer, Cham (2015). Scholar
  47. 47.
    Do, T.-N., Poulet, F.: Random local SVMs for classifying large datasets. In: Dang, T.K., Wagner, R., Küng, J., Thoai, N., Takizawa, M., Neuhold, E. (eds.) FDSE 2015. LNCS, vol. 9446, pp. 3–15. Springer, Cham (2015). Scholar
  48. 48.
    Chang, F., Guo, C.Y., Lin, X.R., Lu, C.J.: Tree decomposition for large-scale SVM problems. J. Mach. Learn. Res. 11, 2935–2972 (2010)MathSciNetzbMATHGoogle Scholar
  49. 49.
    Chang, F., Liu, C.C.: Decision tree as an accelerator for support vector machines. In: Ding, X. (ed.) Advances in Character Recognition. InTech (2012)Google Scholar
  50. 50.
    Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann, San Mateo (1993)Google Scholar
  51. 51.
    Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.: Classification and Regression Trees. Wadsworth International, Kennett Square (1984)zbMATHGoogle Scholar
  52. 52.
    Vincent, P., Bengio, Y.: K-local hyperplane and convex distance nearest neighbor algorithms. In: Advances in Neural Information Processing Systems, pp. 985–992. The MIT Press (2001)Google Scholar
  53. 53.
    Zhang, H., Berg, A., Maire, M., Malik, J.: SVM-KNN: discriminative nearest neighbor classification for visual category recognition. In: 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 2126–2136 (2006)Google Scholar
  54. 54.
    Yang, T., Kecman, V.: Adaptive local hyperplane classification. Neurocomputing 71(13–15), 3001–3004 (2008)CrossRefGoogle Scholar
  55. 55.
    Segata, N., Blanzieri, E.: Fast and scalable local kernel machines. J. Mach. Learn. Res. 11, 1883–1926 (2010)MathSciNetzbMATHGoogle Scholar
  56. 56.
    Beygelzimer, A., Kakade, S., Langford, J.: Cover trees for nearest neighbor. In: Proceedings of the 23rd International Conference on Machine Learning, pp. 97–104. ACM (2006)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Information TechnologyCan Tho UniversityCanthoVietnam
  2. 2.UMI UMMISCO 209 (IRD/UPMC)UPMC, Sorbonne University, Pierre and Marie Curie UniversityParis 6France
  3. 3.AI Lab, Computer Science DepartmentGyeongsang National UniversityJinjuKorea

Personalised recommendations