Multiconlitron: A general piecewise linear classifier

IEEE Transactions on Neural Networks

Volumn 22, Issue 2, 2011, Pages 276-289

  Yujian, Li ^a   Bo, Liu ^a   Xinwu, Yang ^a   Yaozong, Fu ^a   Houjun, Li ^a  

^a BEIJING UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Conlitron; cross distance minimization algorithm; multiconlitron; piecewise linear classifier; piecewise linear learning; support conlitron algorithm; support multiconlitron algorithm; support vector machine

Indexed keywords

CONLITRON; CROSS DISTANCE MINIMIZATION ALGORITHM; MULTICONLITRON; PIECEWISE LINEAR; PIECEWISE-LINEAR CLASSIFIER;

CLASSIFIERS; EXPERIMENTS; GEARS; OPTIMIZATION; PIECEWISE LINEAR TECHNIQUES; RADIAL BASIS FUNCTION NETWORKS; SUPPORT VECTOR MACHINES;

LEARNING ALGORITHMS;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; ARTIFICIAL NEURAL NETWORK; AUTOMATED PATTERN RECOGNITION; CLASSIFICATION; COMPUTER PROGRAM; COMPUTER SIMULATION; DATA BASE; INFORMATION PROCESSING; MATHEMATICAL PHENOMENA; METHODOLOGY; STANDARD; STATISTICAL MODEL;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; AUTOMATIC DATA PROCESSING; CLASSIFICATION; COMPUTER SIMULATION; DATABASES AS TOPIC; LINEAR MODELS; MATHEMATICAL CONCEPTS; NEURAL NETWORKS (COMPUTER); PATTERN RECOGNITION, AUTOMATED; SOFTWARE DESIGN;

EID: 79951670257     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2010.2094624     Document Type: Article

References (58)

1. V. N. Vapnik, Statistical Learning Theory. New York: Wiley, 1998.
2. S. Theodoridis and K. Koutroumbas, Pattern Recognition, 3rd ed. New York: Academic, 2006.
3. V. N. Vapnik, The Nature of Statistical Learning Theory. Berlin, Germany: Springer-Verlag, 1995.
4. C. Cortes and V. N. Vapnik, "Support-vector networks," Mach. Learn., vol. 20, no. 3, pp. 273-297, 1995.
5. I. El-Naqa, Y. Yang, M. Wernik, N. Galatsanos, and R. Nishikawa, "A support vector machine approach for detection of microcalcifications," IEEE Trans. Med. Imag., vol. 21, no. 12, pp. 1552-1563, Dec. 2002.
6. T. Joachims, "Text categorization with support vector machines: Learning with many relevant features," in Proc. 10th Eur. Conf. Mach. Learn., Chemnitz, Germany, 1998, pp. 137-142. (Pubitemid 128067178)
7. E. Osuna, R. Freund, and F. Girosi, "Training support vector machines: An application to face detection," in Proc. IEEE Conf. Comput. Vis. Pattern Recognit., San Juan, Puerto Rico, Jun. 1997, pp. 130-136.
8. M. P. S. Brown, W. N. Grundy, D. Lin, N. Cristianini, C. W. Sugnet, T. S. Furey, M. Ares, Jr., and D. Haussler, "Knowledge-based analysis of microarray gene expression data by using support vector machines," in Proc. Nat. Acad. Sci., vol. 97. Jan. 2000, pp. 262-267. (Pubitemid 30055819)
9. A. Navia-Vasquez, F. Perez-Cruz, and A. Artes-Rodriguez, "Weighted least squares training of support vector classifiers leading to compact and adaptive schemes," IEEE Trans. Neural Netw., vol. 12, no. 5, pp. 1047-1059, Sep. 2001. (Pubitemid 32981747)
10. D. J. Sebald and J. A. Buklew, "Support vector machine techniques for nonlinear equalization," IEEE Trans. Signal Process., vol. 48, no. 11, pp. 3217-3226, Nov. 2000. (Pubitemid 32027347)
11. J. C. Platt, "Fast training of support vector machines using sequential minimal optimization," in Advances in Kernel Methods: Support Vector Machines, B. Schölkopf, C. J. C. Burges, and A. Smola, Eds. Cambridge, MA: MIT Press, 1998, pp. 185-208.
12. S. S. Keerthi, S. K. Shevade, C. Bhattachayya, and K. R. K. Murth, "Improvements to Platt's SMO algorithm for SVM classifier design," Neural Comput., vol. 13, no. 3, pp. 637-649, Mar. 2001. (Pubitemid 33595014)
13. J.-X. Dong, A. Krzyzak, and C. Y. Suen, "Fast SVM training algorithm with decomposition on very large data sets," IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no. 4, pp. 603-618, Apr. 2005. (Pubitemid 40556114)
14. A. Bordes, L. Bottou, and P. Gallinari, "SGD-QN: Careful quasi-Newton stochastic gradient descent," J. Mach. Learn. Res., vol. 10, pp. 1737- 1754, Jul. 2009.
15. S. Shalev-Shwartz, Y. Singer, and N. Srebro, "Pegasos: Primal estimated sub-gradient solver for SVM," in Proc. 24th Int. Conf. Mach. Learn., Corvalis, OR, 2007, pp. 807-814.
16. O. Chapelle, "Training a support vector machine in the primal," Neural Comput., vol. 19, no. 5, pp. 1155-1178, Mar. 2007.
17. G. Fung and O. L. Mangasarian, "Proximal support vector machine classifiers," in Proc. Knowl. Discovery Data Mining, San Francisco, CA, Aug. 2001, pp. 77-86.
18. O. L. Mangasarian and E. W. Wild, "Multisurface proximal support vector classification via generalized eigenvalues," IEEE Trans. Pattern Anal. Mach. Intell., vol. 28, no. 1, pp. 69-74, Jan. 2006. (Pubitemid 46395305)
19. R. J. Khemchandani and S. Chandra, "Twin support vector machines for pattern classification," IEEE Trans. Pattern Anal. Mach. Intell., vol. 29, no. 5, pp. 905-910, May 2007. (Pubitemid 46534787)
20. J. Suykens and J. Vandewalle, "Least squares support vector machine classifiers," Neural Process. Lett., vol. 9, no. 3, pp. 293-300, Jun. 1999.
21. K.-M. Lin and C.-J. Lin, "A study on reduced support vector machines," IEEE Trans. Neural Netw., vol. 14, no. 6, pp. 1449-1459, Nov. 2003.
22. O. L. Mangasarian and D. R. Musicant, "Lagrangian support vector machines," J. Mach. Learn. Res., vol. 1, no. 3, pp. 161-177, 2001. (Pubitemid 33687201)
23. M. E. Tipping, "Sparse Bayesian learning and the relevance vector machine," J. Mach. Learn. Res., vol. 1, no. 3, pp. 211-244, Jun. 2001. (Pubitemid 33687203)
24. H. Chen, P. Tino, and X. Yao, "Probabilistic classification vector machines," IEEE Trans. Neural Netw., vol. 20, no. 6, pp. 901-914, Jun. 2009.
25. K.-R. Müller, S. Mika, G. Rätsch, K. Tsuda, and B. Schölkopf, "An introduction to kernel-based learning algorithms," IEEE Trans. Neural Netw., vol. 12, no. 2, pp. 181-202, Mar. 2001.
26. J. Shawe-Taylor and N. Cristianini, Kernel Methods for Pattern Analysis. Cambridge, U.K.: Cambridge Univ. Press, 2004.
27. S. Sonnenburg, G. Rätsch, and C. Schäfer, "A general and efficient multiple kernel learning algorithm," in Neural Information Processing Systems, vol. 15. Cambridge, MA: MIT Press, 2005, pp. 1273-1280.
28. S. Sonnenburg, G. Rätsch, C. Schäfer, and B. Schölkopf, "Large scale multiple kernel learning," J. Mach. Learn. Res., vol. 7, pp. 1531-1565, Jul. 2006. (Pubitemid 44373694)
29. Z. Wang, S. Chen, and T. Sun, "MultiK-MHKS: A novel multiple kernel learning algorithm," IEEE Trans. Pattern Anal. Mach. Intell., vol. 30, no. 2, pp. 348-353, Feb. 2008.
30. S. S. Keerthi, S. K. Shevade, C. Bhattacharyya, and K. R. K. Murthy, "A fast iterative nearest point algorithm for support vector machine classifier design," IEEE Trans. Neural Netw., vol. 11, no. 1, pp. 124-136, Jan. 2000.
31. Y. Li and P. M. Long, "The relaxed online maximum margin algorithm," in Advances in Neural Information Processing Systems, vol. 12, S. A. Solla, T. K. Leen, and K. R. Müller, Eds. Cambridge, MA: MIT Press, 2000, pp. 498-504.
32. V. Franc and V. Hlaváč, "An iterative algorithm learning the maximal margin classifier," Pattern Recognit., vol. 36, no. 9, pp. 1985-1996, Sep. 2003. (Pubitemid 36726818)
33. M. E. Mavroforakis and S. Theodoridis, "A geometric approach to support vector machine (SVM) classification," IEEE Trans. Neural Netw., vol. 17, no. 3, pp. 671-682, May 2006.
34. P.Williams, S. Li, J. Feng, and S.Wu, "A geometrical method to improve performance of the support vector machine," IEEE Trans. Neural Netw., vol. 18, no. 3, pp. 942-947, May 2007. (Pubitemid 46773761)
35. M. E. Mavroforakis, M. Sdralis, and S. Theodoridis, "A geometric nearest point algorithm for the efficient solution of the SVM classification task," IEEE Trans. Neural Netw., vol. 18, no. 5, pp. 1545-1549, Sep. 2007. (Pubitemid 47408556)
36. M. Doumpos, C. Zopounidis, and V. Golfinopoulou, "Additive support vector machines for pattern classification," IEEE Trans. Syst., Man, Cybern., Part B: Cybern., vol. 37, no. 3, pp. 540-550, Jun. 2007. (Pubitemid 46784590)
37. O. Pujol and D. Masip, "Geometry-based ensembles: Toward a structural characterization of the classification boundary," IEEE Trans. Pattern Anal. Mach. Intell., vol. 31, no. 6, pp. 1140-1146, Jun. 2009.
38. J. Sklansky and L. Michelotti, "Locally trained piecewise linear classifiers," IEEE Trans. Pattern Anal. Mach. Intell., vol. 2, no. 2, pp. 101- 111, Mar. 1980. (Pubitemid 10484989)
39. Y. Park and J. Sklansky, "Automated design of multiple-class piecewise linear classifiers," J. Classification, vol. 6, no. 1, pp. 195-222, Dec. 1989.
40. H. Tenmoto, M. Kudo, and M. Shimbo, "Piecewise linear classifiers with an appropriate number of hyperplances," Pattern Recognit., vol. 31, no. 11, pp. 1627-1634, Nov. 1998.
41. O. L. Mangasarian, R. Setono, and W. H. Wolberg, "Pattern recognition via linear programming: Theory and applications to medical diagnosis," in Large-Scale Numerical Optimization, T. F. Coleman and Y. Li, Eds. Philadelphia, PA: SIAM, 1990, pp. 22-31.
42. G. T. Herman and K. T. D. Yeung, "On piecewise-linear classification," IEEE Trans. Pattern Anal. Mach. Intell., vol. 14, no. 7, pp. 782-786, Jul. 1992.
43. B.-B. Chai, T. Huang, X. Zhuang, Y. Zhao, and J. Sklansky, "Piecewise linear classifiers using binary tree structure and genetic algorithm," Pattern Recognit., vol. 29, no. 11, pp. 1905-1917, Nov. 1996. (Pubitemid 126383977)
44. A. Kostin, "A simple and fast multi-class piecewise linear pattern classifier," Pattern Recognit., vol. 39, no. 11, pp. 1949-1962, Nov. 2006. (Pubitemid 44202541)
45. M. Kudo, I. Takigawa, and A. Nakamura, "Classification by reflective convex hulls," in Proc. 19th Int. Conf. Pattern Recognit., Tampa, FL, Dec. 2008, pp. 1-4.
46. N. Cristianini and J. Shawe-Taylor, An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods. Cambridge, U.K.: Cambridge Univ. Press, 2000.
47. K. P. Bennett and E. J. Bredensteiner, "Geometry in learning," in Geometry at Work, C. Gorini, E. Hart, W. Meyer, and T. Phillips, Eds. Washington D.C.: MAA, 1998.
48. N. K. Sancheti and S. S. Keerthi, "Computation of certain measures of proximity between convex polytopes: A complexity viewpoint," in Proc. IEEE Int. Conf. Robot. Automat., vol. 3. Nice, France, May 1992, pp. 2508-2513. (Pubitemid 23615275)
49. D. Naiyang and T. Yingjie, New Methods in Data Mining: Support Vector Machines. Duluth, GA: Science Press, 2004.
50. C. P. Bennett and E. J. Bredensteiner, "Duality and geometry in SVM classifiers," in Proc. 17th Int. Conf. Mach. Learn., San Francisco, CA, 2000, pp. 57-64.
51. O. L. Mangasarian, "Polyhedral boundary projection," SIAM J. Optim., vol. 9, no. 4, pp. 1128-1134, Apr. 1999. (Pubitemid 129489320)
52. UCI Repository of Machine Learning Databases [Online]. Available: http://www.ics.uci.edu/?excl;?mlearn/MLRepository.html
53. C. C. Chang and C. J. Lin. LIBSVM: A Library for Support Vector Machines [Online]. Available: http://www.csie.ntu.edu.tw/?excl;?cjlin/libsvm
54. C.-W. Hsu, C.-C. Chang, and C.-J. Lin. A Practical Guide to Support Vector Classification [Online]. Available: http://www.csie.ntu.edu.tw/?excl;? cjlin/papers/guide/guide.pdf
55. C. J. C. Burges, "A tutorial on support vector machines for pattern recognition," Data Mining Knowl. Discovery, vol. 2, no. 2, pp. 121- 167, Jun. 1998. (Pubitemid 128695475)
56. R.-E. Fan, P.-H. Chen, and C.-J. Lin, "Working set selection using second order information for training SVM," J. Mach. Learn. Res., vol. 6, pp. 1889-1918, Dec. 2005. (Pubitemid 41798130)
57. T. Joachins, "Training linear SVMs in linear time," in Proc. 12th ACM SIGKDD Int. Conf. Knowl. Discovery Data Mining, Philadelphia, PA, 2006, pp. 217-226.
58. C.-W. Hsu and C.-J. Lin, "A comparison of methods for multiclass support vector machines," IEEE Trans. Neural Netw., vol. 13, no. 2, pp. 415-425, Mar. 2002. (Pubitemid 34475042)