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Volumn 22, Issue 10, 2011, Pages 1613-1625

Nonlinear regularization path for quadratic loss support vector machines

Author keywords

Parametric programming; rational approximation; support vector machines

Indexed keywords

ALGORITHM PERFORMANCE; BREAK-POINTS; LEARNING MACHINES; MACHINE-LEARNING; MODEL SELECTION PROBLEM; PARAMETRIC PROGRAMMING; PATH ALGORITHM; PENALTY TERM; PIECE-WISE; PIECEWISE LINEAR; PREDICTOR CORRECTOR; QUADRATIC CONVERGENCE; QUADRATIC LOSS; RATIONAL APPROXIMATIONS; RATIONAL EQUATIONS; REAL DATA SETS; REGULARIZATION PARAMETERS; SOLUTION PATH; SUPPORT VECTOR;

EID: 80053646089     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2011.2164265     Document Type: Article
Times cited : (18)

References (43)
  • 1
    • 84925605946 scopus 로고    scopus 로고
    • The entire regularization path for the support vector machine
    • Oct.
    • T. Hastie, S. Rosset, R. Tibshirani, and J. Zhu, "The entire regularization path for the support vector machine," J. Mach. Learn. Res., vol. 5, pp. 1391-1415, Oct. 2004.
    • (2004) J. Mach. Learn. Res. , vol.5 , pp. 1391-1415
    • Hastie, T.1    Rosset, S.2    Tibshirani, R.3    Zhu, J.4
  • 2
    • 84971957489 scopus 로고
    • Continuation and path following
    • E. L. Allgower and K. Georg, "Continuation and path following," Acta Numer., vol. 2, pp. 1-64, 1993.
    • (1993) Acta Numer. , vol.2 , pp. 1-64
    • Allgower, E.L.1    Georg, K.2
  • 4
    • 33747350759 scopus 로고    scopus 로고
    • Considering cost asymmetry in learning classifiers
    • Aug.
    • F. Bach, D. Heckerman, and E. Horvitz, "Considering cost asymmetry in learning classifiers," J. Mach. Learn. Res., vol. 7, pp. 1713-1741, Aug. 2006.
    • (2006) J. Mach. Learn. Res. , vol.7 , pp. 1713-1741
    • Bach, F.1    Heckerman, D.2    Horvitz, E.3
  • 5
    • 80052866161 scopus 로고    scopus 로고
    • Incremental and decremental support vector machine learning
    • T. K. Leen, T. G. Dietterich, and V. Tresp, Eds. Cambridge, MA: MIT Press
    • G. Cauwenberghs and T. Poggio, "Incremental and decremental support vector machine learning," in Advances in Neural Information Processing Systems, vol. 13, T. K. Leen, T. G. Dietterich, and V. Tresp, Eds. Cambridge, MA: MIT Press, 2001, pp. 409-415.
    • (2001) Advances in Neural Information Processing Systems , vol.13 , pp. 409-415
    • Cauwenberghs, G.1    Poggio, T.2
  • 6
    • 34249726632 scopus 로고    scopus 로고
    • Efficient computation and model selection for the support vector regression
    • Jun.
    • L. Gunter and J. Zhu, "Efficient computation and model selection for the support vector regression," Neural Comput., vol. 19, no. 6, pp. 1633-1655, Jun. 2007.
    • (2007) Neural Comput. , vol.19 , Issue.6 , pp. 1633-1655
    • Gunter, L.1    Zhu, J.2
  • 7
    • 80053620586 scopus 로고    scopus 로고
    • Multiple incremental decremental learning of support vector machines
    • Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams, and A. Culotta, Eds. Cambridge, MA: MIT Press
    • M. Karasuyama and I. Takeuchi, "Multiple incremental decremental learning of support vector machines," in Advances in Neural Information Processing Systems 22, Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams, and A. Culotta, Eds. Cambridge, MA: MIT Press, 2009, pp. 907-915.
    • (2009) Advances in Neural Information Processing Systems , vol.22 , pp. 907-915
    • Karasuyama, M.1    Takeuchi, I.2
  • 8
    • 33745777639 scopus 로고    scopus 로고
    • Incremental support vector learning: Analysis, implementation and applications
    • P. Laskov, C. Gehl, S. Kruger, and K.-R. Muller, "Incremental support vector learning: Analysis, implementation and applications," J. Mach. Learn. Res., vol. 7, pp. 1909-1936, Sep. 2006. (Pubitemid 44477117)
    • (2006) Journal of Machine Learning Research , vol.7 , pp. 1909-1936
    • Laskov, P.1    Gehl, C.2    Kruger, S.3    Muller, K.-R.4
  • 9
    • 0141765796 scopus 로고    scopus 로고
    • Accurate On-line Support Vector Regression
    • DOI 10.1162/089976603322385117
    • J. Ma and J. Theiler, "Accurate on-line support vector regression," Neural Comput., vol. 15, no. 11, pp. 2683-2703, Nov. 2003. (Pubitemid 37206931)
    • (2003) Neural Computation , vol.15 , Issue.11 , pp. 2683-2703
    • Ma, J.1    Theiler, J.2    Perkins, S.3
  • 11
    • 77649273984 scopus 로고    scopus 로고
    • An improved algorithm for the solution of the regularization path of support vector machine
    • Mar.
    • C.-J. Ong, S. Shao, and J. Yang, "An improved algorithm for the solution of the regularization path of support vector machine," IEEE Trans. Neural Netw., vol. 21, no. 3, pp. 451-462, Mar. 2010.
    • (2010) IEEE Trans. Neural Netw. , vol.21 , Issue.3 , pp. 451-462
    • Ong, C.-J.1    Shao, S.2    Yang, J.3
  • 12
    • 67650329813 scopus 로고    scopus 로고
    • Nonparametric conditional density estimation using piecewise-linear solution path of kernel quantile regression
    • Feb.
    • I. Takeuchi, K. Nomura, and T. Kanamori, "Nonparametric conditional density estimation using piecewise-linear solution path of kernel quantile regression," Neural Comput., vol. 21, no. 2, pp. 533-559, Feb. 2009.
    • (2009) Neural Comput. , vol.21 , Issue.2 , pp. 533-559
    • Takeuchi, I.1    Nomura, K.2    Kanamori, T.3
  • 13
    • 54349106864 scopus 로고    scopus 로고
    • A new solution path algorithm in support vector regression
    • Oct.
    • G. Wang, D.-Y. Yeung, F. H. Lochovsky, "A new solution path algorithm in support vector regression," IEEE Trans. Neural Netw., vol. 19, no. 10, pp. 1753-1767, Oct. 2008.
    • (2008) IEEE Trans. Neural Netw. , vol.19 , Issue.10 , pp. 1753-1767
    • Wang, G.1    Yeung, D.-Y.2    Lochovsky, F.H.3
  • 15
    • 34548452938 scopus 로고    scopus 로고
    • Piecewise linear regularized solution paths
    • S. Rosset and J. Zhu, "Piecewise linear regularized solution paths," Ann. Stat., vol. 35, no. 3, pp. 1012-1030, 2007.
    • (2007) Ann. Stat. , vol.35 , Issue.3 , pp. 1012-1030
    • Rosset, S.1    Zhu, J.2
  • 16
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • R. Tibshirani, "Regression shrinkage and selection via the lasso," J. Royal Stat. Soc. Ser. B: Methodol., vol. 58, no. 1, pp. 267-288, 1996.
    • (1996) J. Royal Stat. Soc. Ser. B: Methodol. , vol.58 , Issue.1 , pp. 267-288
    • Tibshirani, R.1
  • 17
    • 0343441845 scopus 로고
    • On parametric linear and quadratic programming problems
    • K. Ritter, "On parametric linear and quadratic programming problems," in Proc. Int. Congr. Math. Program., 1984, pp. 307-335.
    • (1984) Proc. Int. Congr. Math. Program. , pp. 307-335
    • Ritter, K.1
  • 18
    • 84898952043 scopus 로고    scopus 로고
    • Computing regularization paths for learning multiple kernels
    • L. K. Saul, Y. Weiss, and L. Bottou, Eds. Cambridge, MA: MIT Press
    • F. R. Bach, R. Thibaux, and M. I. Jordan, "Computing regularization paths for learning multiple kernels," in Advances in Neural Information Processing Systems 17, L. K. Saul, Y. Weiss, and L. Bottou, Eds. Cambridge, MA: MIT Press, 2005, pp. 73-80.
    • (2005) Advances in Neural Information Processing Systems , vol.17 , pp. 73-80
    • Bach, F.R.1    Thibaux, R.2    Jordan, M.I.3
  • 20
    • 34547849507 scopus 로고    scopus 로고
    • L1-regularization path algorithm for generalized linear models
    • M. Park and T. Hastie, "L1-regularization path algorithm for generalized linear models," J. Royal Stat. Soc.: Ser. B: Stat. Methodol., vol. 69, no. 4, pp. 659-677, 2007.
    • (2007) J. Royal Stat. Soc.: Ser. B: Stat. Methodol. , vol.69 , Issue.4 , pp. 659-677
    • Park, M.1    Hastie, T.2
  • 21
    • 84898950954 scopus 로고    scopus 로고
    • Following curved regularized optimization solution paths
    • L. K. Saul, Y. Weiss, and L. Bottou, Eds. Cambridge, MA: MIT Press
    • S. Rosset, "Following curved regularized optimization solution paths," in Advances in Neural Information Processing Systems 17, L. K. Saul, Y. Weiss, and L. Bottou, Eds. Cambridge, MA: MIT Press, 2005, pp. 1153-1160.
    • (2005) Advances in Neural Information Processing Systems , vol.17 , pp. 1153-1160
    • Rosset, S.1
  • 23
    • 4644257995 scopus 로고    scopus 로고
    • Statistical behavior and consistency of classification methods based on convex risk minimization
    • DOI 10.1214/aos/1079120130
    • T. Zhang, "Statistical behavior and consistency of classification methods based on convex risk minimization," Ann. Stat., vol. 32, no. 1, pp. 56-134, 2004. (Pubitemid 41449305)
    • (2004) Annals of Statistics , vol.32 , Issue.1 , pp. 56-134
    • Zhang, T.1
  • 24
    • 34247849152 scopus 로고    scopus 로고
    • Training a support vector machine in the primal
    • May
    • O. Chapelle, "Training a support vector machine in the primal," Neural Comput., vol. 19, no. 5, pp. 1155-1178, May 2007.
    • (2007) Neural Comput. , vol.19 , Issue.5 , pp. 1155-1178
    • Chapelle, O.1
  • 25
    • 34247596518 scopus 로고    scopus 로고
    • Sparseness vs estimating conditional probabilities: Some asymptotic results
    • P. L. Bartlett and A. Tewari, "Sparseness versus estimating conditional probabilities: Some asymptotic results," J. Mach. Learn. Res., vol. 8, pp. 775-790, Apr. 2007. (Pubitemid 46677047)
    • (2007) Journal of Machine Learning Research , vol.8 , pp. 775-790
    • Bartlett, P.L.1    Tewari, A.2
  • 26
    • 34247216124 scopus 로고    scopus 로고
    • Recursive finite newton algorithm for support vector regression in the primal
    • Apr.
    • L. Bo, L. Wang, and L. Jiao, "Recursive finite newton algorithm for support vector regression in the primal," Neural Comput., vol. 19, no. 4, pp. 1082-1096, Apr. 2007.
    • (2007) Neural Comput. , vol.19 , Issue.4 , pp. 1082-1096
    • Bo, L.1    Wang, L.2    Jiao, L.3
  • 27
    • 21844461582 scopus 로고    scopus 로고
    • A modified finite Newton method for fast solution of large scale linear SVMs
    • Mar.
    • S. S. Keerthi and D. DeCoste, "A modified finite Newton method for fast solution of large scale linear SVMs," J. Mach. Learn. Res., vol. 6, pp. 341-361, Mar. 2005.
    • (2005) J. Mach. Learn. Res. , vol.6 , pp. 341-361
    • Keerthi, S.S.1    Decoste, D.2
  • 28
    • 0002316189 scopus 로고
    • Rank-one modification of the symmetric eigenproblem
    • J. Bunch, C. Nielsen, and D. Sorensen, "Rank-one modification of the symmetric eigenproblem," Numer. Math., vol. 31, no. 1, pp. 31-48, 1979.
    • (1979) Numer. Math. , vol.31 , Issue.1 , pp. 31-48
    • Bunch, J.1    Nielsen, C.2    Sorensen, D.3
  • 29
    • 1242331293 scopus 로고    scopus 로고
    • Bayesian support vector regression using a unified loss function
    • Jan.
    • W. Chu, S. S. Keerthi, and C. J. Ong, "Bayesian support vector regression using a unified loss function," IEEE Trans. Neural Netw., vol. 15, no. 1, pp. 29-44, Jan. 2004.
    • (2004) IEEE Trans. Neural Netw. , vol.15 , Issue.1 , pp. 29-44
    • Chu, W.1    Keerthi, S.S.2    Ong, C.J.3
  • 30
    • 56749090853 scopus 로고
    • Dept. Comput. Sci., Stanford Univ., Stanford, CA, Tech. Rep. SU326 P30-11, Aug.
    • G. H. Golub, "Some modified eigenvalue problems," Dept. Comput. Sci., Stanford Univ., Stanford, CA, Tech. Rep. SU326 P30-11, Aug. 1971.
    • (1971) Some Modified Eigenvalue Problems
    • Golub, G.H.1
  • 32
    • 0003120218 scopus 로고    scopus 로고
    • Fast training of support vector machines using sequential minimal optimization
    • B. Schölkopf, C. J. C. Burges, and A. J. Smola, Eds. Cambridge, MA: MIT Press
    • J. C. Platt, "Fast training of support vector machines using sequential minimal optimization," in Advances in Kernel Methods: Support Vector Learning, B. Schölkopf, C. J. C. Burges, and A. J. Smola, Eds. Cambridge, MA: MIT Press, 1999, pp. 185-208.
    • (1999) Advances in Kernel Methods: Support Vector Learning , pp. 185-208
    • Platt, J.C.1
  • 33
    • 3543134928 scopus 로고    scopus 로고
    • Inst. Automatic Control, Technische Universität Darmstadt, Darmstadt, Germany, Tech. Rep.
    • M. Vogt, "SMO algorithms for support vector machines without bias term," Inst. Automatic Control, Technische Universität Darmstadt, Darmstadt, Germany, Tech. Rep., 2002.
    • (2002) SMO Algorithms for Support Vector Machines Without Bias Term
    • Vogt, M.1
  • 37
    • 42249094907 scopus 로고    scopus 로고
    • Support vector machine solvers
    • L. Bottou, O. Chapelle, D. DeCoste, and J. Weston, Eds. Cambridge, MA: MIT Press
    • L. Bottou and C.-J. Lin, "Support vector machine solvers," in Large Scale Kernel Machines, L. Bottou, O. Chapelle, D. DeCoste, and J. Weston, Eds. Cambridge, MA: MIT Press, 2007, pp. 301-320.
    • (2007) Large Scale Kernel Machines , pp. 301-320
    • Bottou, L.1    Lin, C.-J.2
  • 38
    • 33646023117 scopus 로고    scopus 로고
    • An introduction to ROC analysis
    • Jun.
    • T. Fawcett, "An introduction to ROC analysis," Pattern Recognit. Lett., vol. 27, no. 8, pp. 861-874, Jun. 2006.
    • (2006) Pattern Recognit. Lett. , vol.27 , Issue.8 , pp. 861-874
    • Fawcett, T.1
  • 39
    • 0037382208 scopus 로고    scopus 로고
    • Evaluation of simple performance measures for tuning SVM hyperparameters
    • DOI 10.1016/S0925-2312(02)00601-X, PII S092523120200601X
    • K. Duan, S. S. Keerthi, and A. N. Poo, "Evaluation of simple performance measures for tuning SVM hyperparameters," Neurocomputing, vol. 51, pp. 41-59, Apr. 2003. (Pubitemid 36367224)
    • (2003) Neurocomputing , vol.51 , pp. 41-59
    • Duan, K.1    Keerthi, S.S.2    Poo, A.N.3
  • 40
    • 0034264380 scopus 로고    scopus 로고
    • Bounds on error expectation for support vector machines
    • Sep.
    • V. N. Vapnik and O. Chapelle, "Bounds on error expectation for support vector machines," Neural Comput., vol. 12, no. 9, pp. 2013-2036, Sep. 2000.
    • (2000) Neural Comput. , vol.12 , Issue.9 , pp. 2013-2036
    • Vapnik, V.N.1    Chapelle, O.2
  • 41
    • 79951675527 scopus 로고    scopus 로고
    • Logistic regression by means of evolutionary radial basis function neural networks
    • Feb.
    • P. Gutiérrez, C. Hervás-Martines, and F. Martinez-Estudillo, "Logistic regression by means of evolutionary radial basis function neural networks," IEEE Trans. Neural Netw., vol. 22, no. 2, pp. 246-263, Feb. 2011.
    • (2011) IEEE Trans. Neural Netw. , vol.22 , Issue.2 , pp. 246-263
    • Gutiérrez, P.1    Hervás-Martines, C.2    Martinez-Estudillo, F.3
  • 42
    • 79955824877 scopus 로고    scopus 로고
    • Reduced hyperBF networks: Regularization by explicit complexity reduction and scaled rprop-based training
    • May
    • R. Mahdi and E. Rouchka, "Reduced hyperBF networks: Regularization by explicit complexity reduction and scaled rprop-based training," IEEE Trans. Neural Netw., vol. 22, no. 5, pp. 673-686, May 2011.
    • (2011) IEEE Trans. Neural Netw. , vol.22 , Issue.5 , pp. 673-686
    • Mahdi, R.1    Rouchka, E.2
  • 43
    • 76749105659 scopus 로고    scopus 로고
    • Feature extraction using constrained approximation and suppression
    • Feb.
    • Y. Washizawa, "Feature extraction using constrained approximation and suppression," IEEE Trans. Neural Netw., vol. 21, no. 2, pp. 201-210, Feb. 2010.
    • (2010) IEEE Trans. Neural Netw. , vol.21 , Issue.2 , pp. 201-210
    • Washizawa, Y.1


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