메뉴 건너뛰기




Volumn 40, Issue 4, 2010, Pages 1128-1144

Framelet Kernels with applications to support vector regression and regularization networks

Author keywords

Framelet; kernel; multiresolution analysis (MRA); regularization networks (RNs); support vector regression (SVR)

Indexed keywords

APPROXIMATE FUNCTION; APPROXIMATION PROPERTIES; FEATURE SPACE; FRAMELETS; GAUSSIAN KERNELS; HARD PROBLEMS; INPUT SPACE; KERNEL FUNCTION; KERNEL METHODS; LEARNING MACHINES; MULTI-SCALE STRUCTURES; OVERFITTING; REGRESSION PROBLEM; REGULARIZATION NETWORKS; SAMPLE DATA; SPARSE DATA; SUPPORT VECTOR REGRESSIONS; TIGHT WAVELET FRAMES;

EID: 77954762258     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2009.2034993     Document Type: Article
Times cited : (19)

References (44)
  • 2
    • 4043137356 scopus 로고    scopus 로고
    • A tutorial on support vector regression
    • Aug.
    • A. Smola and B. Schölkopf, "A tutorial on support vector regression," Stat. Comput., vol.14, no.3, pp. 199-222, Aug. 2004.
    • (2004) Stat. Comput. , vol.14 , Issue.3 , pp. 199-222
    • Smola, A.1    Schölkopf, B.2
  • 3
    • 33846092558 scopus 로고    scopus 로고
    • Reduced support vector machines: A statistical theory
    • Jan.
    • Y. J. Lee and S. Y. Huang, "Reduced support vector machines: A statistical theory," IEEE Trans. Neural Netw., vol.18, no.1, pp. 1-13, Jan. 2007.
    • (2007) IEEE Trans. Neural Netw. , vol.18 , Issue.1 , pp. 1-13
    • Lee, Y.J.1    Huang, S.Y.2
  • 4
    • 33746899028 scopus 로고    scopus 로고
    • Multidimensional vector regression for accurate and low-cost location estimation in pervasive computing
    • Sep.
    • J. J. Pan, J. T. Kwok, Q. Yang, and Y. Q. Chen, "Multidimensional vector regression for accurate and low-cost location estimation in pervasive computing," IEEE Trans. Knowl. Data Eng., vol.18, no.9, pp. 1181-1193, Sep. 2006.
    • (2006) IEEE Trans. Knowl. Data Eng. , vol.18 , Issue.9 , pp. 1181-1193
    • Pan, J.J.1    Kwok, J.T.2    Yang, Q.3    Chen, Y.Q.4
  • 5
    • 33847712243 scopus 로고    scopus 로고
    • Kernel regression for image processing and reconstruction
    • Feb.
    • H. Takeda, S. Farsiu, and P. Milanfar, "Kernel regression for image processing and reconstruction," IEEE Trans. Image Process., vol.16, no.2, pp. 349-366, Feb. 2007.
    • (2007) IEEE Trans. Image Process. , vol.16 , Issue.2 , pp. 349-366
    • Takeda, H.1    Farsiu, S.2    Milanfar, P.3
  • 6
    • 2142643698 scopus 로고    scopus 로고
    • A support vector machine with a hybrid kernel and minimal Vapnik-Chervonenkis dimension
    • Apr.
    • Y. Tan and J. Wang, "A support vector machine with a hybrid kernel and minimal Vapnik-Chervonenkis dimension," IEEE Trans. Knowl. Data Eng., vol.16, no.4, pp. 385-395, Apr. 2004.
    • (2004) IEEE Trans. Knowl. Data Eng. , vol.16 , Issue.4 , pp. 385-395
    • Tan, Y.1    Wang, J.2
  • 9
    • 0025490985 scopus 로고
    • Networks for approximation and learning
    • Sep.
    • T. Poggio and F. Girosi, "Networks for approximation and learning," Proc. IEEE, vol.78, no.9, pp. 1481-1497, Sep. 1990.
    • (1990) Proc. IEEE , vol.78 , Issue.9 , pp. 1481-1497
    • Poggio, T.1    Girosi, F.2
  • 10
    • 0001219859 scopus 로고
    • Regularization theory and neural networks architectures
    • Mar.
    • F. Girosi, M. Jones, and T. Poggio, "Regularization theory and neural networks architectures," Neural Comput., vol.7, no.2, pp. 219-269, Mar. 1995.
    • (1995) Neural Comput , vol.7 , Issue.2 , pp. 219-269
    • Girosi, F.1    Jones, M.2    Poggio, T.3
  • 11
    • 0034419669 scopus 로고    scopus 로고
    • Regularization networks and support vector machines
    • Apr.
    • T. Evgeniou, M. Pontil, and T. Poggio, "Regularization networks and support vector machines," Adv. Comput. Math., vol.13, no.1, pp. 1-50, Apr. 2000.
    • (2000) Adv. Comput. Math. , vol.13 , Issue.1 , pp. 1-50
    • Evgeniou, T.1    Pontil, M.2    Poggio, T.3
  • 12
    • 0032098361 scopus 로고    scopus 로고
    • The connection between regularization operators and support vector kernels
    • Jun.
    • A. J. Smola, B. Schölkopf, and K. R. Müller, "The connection between regularization operators and support vector kernels," Neural Netw., vol.11, no.4, pp. 637-649, Jun. 1998.
    • (1998) Neural Netw , vol.11 , Issue.4 , pp. 637-649
    • Smola, A.J.1    Schölkopf, B.2    Müller, K.R.3
  • 15
    • 33846063532 scopus 로고    scopus 로고
    • Kernel classifier construction using orthogonal forward selection and boosting with fisher ratio class separability measure
    • DOI 10.1109/TNN.2006.881487
    • S. Chen, X. X. Wang, X. Hong, and C. J. Harris, "Kernel classifier construction using orthogonal forward selection and boosting with fisher ratio class separability measure," IEEE Trans. Neural Netw., vol.17, no.6, pp. 1652-1656, Nov. 2006. (Pubitemid 44824278)
    • (2006) IEEE Transactions on Neural Networks , vol.17 , Issue.6 , pp. 1652-1656
    • Chen, S.1    Wang, X.X.2    Hong, X.3    Harris, C.J.4
  • 16
    • 33645988196 scopus 로고    scopus 로고
    • From sample similarity to ensemble similarity: Probabilistic distance measures in reproducing kernel Hilbert space
    • Jun.
    • S. K. Zhou and R. Chellappa, "From sample similarity to ensemble similarity: Probabilistic distance measures in reproducing kernel Hilbert space," IEEE Trans. Pattern Anal. Mach. Intell., vol.28, no.6, pp. 917-929, Jun. 2006.
    • (2006) IEEE Trans. Pattern Anal. Mach. Intell. , vol.28 , Issue.6 , pp. 917-929
    • Zhou, S.K.1    Chellappa, R.2
  • 18
    • 33846086864 scopus 로고    scopus 로고
    • Nonlinear knowledge in kernel approximation
    • Jan.
    • O. L. Mangasarian and E. W. Wild, "Nonlinear knowledge in kernel approximation," IEEE Trans. Neural Netw., vol.18, no.1, pp. 300-306, Jan. 2007.
    • (2007) IEEE Trans. Neural Netw. , vol.18 , Issue.1 , pp. 300-306
    • Mangasarian, O.L.1    Wild, E.W.2
  • 19
    • 33750379440 scopus 로고    scopus 로고
    • Non-flat function estimation with a multi-scale support vector regression
    • Dec.
    • D. N. Zheng, J. X. Wang, and Y. N. Zhao, "Non-flat function estimation with a multi-scale support vector regression," Neurocomputing, vol.70, no.1-3, pp. 420-429, Dec. 2006.
    • (2006) Neurocomputing , vol.70 , Issue.1-3 , pp. 420-429
    • Zheng, D.N.1    Wang, J.X.2    Zhao, Y.N.3
  • 20
    • 34547938101 scopus 로고    scopus 로고
    • Finding numerical derivatives for unstructured and noisy data by multiscale kernels
    • L. V. Ling, "Finding numerical derivatives for unstructured and noisy data by multiscale kernels," SIAM J. Numer. Anal., vol.44, no.4, pp. 1780-1800, 2006.
    • (2006) SIAM J. Numer. Anal. , vol.44 , Issue.4 , pp. 1780-1800
    • Ling, L.V.1
  • 21
    • 33646732403 scopus 로고    scopus 로고
    • Multiscale kernels
    • Nov.
    • R. Opfer, "Multiscale kernels," Adv. Comput. Math., vol.25, no.4, pp. 357-380, Nov. 2006.
    • (2006) Adv. Comput. Math. , vol.25 , Issue.4 , pp. 357-380
    • Opfer, R.1
  • 22
    • 33644555212 scopus 로고    scopus 로고
    • Wavelet kernel penalized estimation for non-equispaced design regression
    • Mar.
    • U. Amato, A. Antoniadis, and M. Pensky, "Wavelet kernel penalized estimation for non-equispaced design regression," Stat. Comput., vol.16, no.1, pp. 37-55, Mar. 2006.
    • (2006) Stat. Comput. , vol.16 , Issue.1 , pp. 37-55
    • Amato, U.1    Antoniadis, A.2    Pensky, M.3
  • 24
    • 17444391661 scopus 로고    scopus 로고
    • Non-parametric regression with wavelet kernels
    • Mar.
    • A. Rakotomamonjy, X. Mary, and S. Canu, "Non-parametric regression with wavelet kernels," Appl. Stoch. Models Bus. Ind., vol.21, no.2, pp. 153-163, Mar. 2005.
    • (2005) Appl. Stoch. Models Bus. Ind. , vol.21 , Issue.2 , pp. 153-163
    • Rakotomamonjy, A.1    Mary, X.2    Canu, S.3
  • 26
    • 0035461049 scopus 로고    scopus 로고
    • On a class of support vector kernels based on frames in function Hilbert spaces
    • Sep.
    • J. B. Gao, C. J. Harris, and S. R. Gunn, "On a class of support vector kernels based on frames in function Hilbert spaces," Neural Comput., vol.13, no.9, pp. 1975-1994, Sep. 2001.
    • (2001) Neural Comput , vol.13 , Issue.9 , pp. 1975-1994
    • Gao, J.B.1    Harris, C.J.2    Gunn, S.R.3
  • 27
    • 25444533296 scopus 로고    scopus 로고
    • Frames, reproducing kernels, regularization and learning
    • Dec.
    • A. Rakotomamonjy and S. Canu, "Frames, reproducing kernels, regularization and learning," J. Mach. Learn. Res., vol.6, pp. 1485-1515, Dec. 2005.
    • (2005) J. Mach. Learn. Res. , vol.6 , pp. 1485-1515
    • Rakotomamonjy, A.1    Canu, S.2
  • 28
    • 33646112177 scopus 로고    scopus 로고
    • Tight frame expansions of multiscale reproducing kernels in Sobolev spaces
    • R. Opfer, "Tight frame expansions of multiscale reproducing kernels in Sobolev spaces," Appl. Comput. Harmon. Anal., vol.20, no.3, pp. 357-374, 2006.
    • (2006) Appl. Comput. Harmon. Anal. , vol.20 , Issue.3 , pp. 357-374
    • Opfer, R.1
  • 29
    • 1842715640 scopus 로고    scopus 로고
    • On approximation with spline generated framelets
    • R. Gribonval and M. Nielsen, "On approximation with spline generated framelets," Constr. Approx., vol.20, no.2, pp. 207-232, 2004.
    • (2004) Constr. Approx. , vol.20 , Issue.2 , pp. 207-232
    • Gribonval, R.1    Nielsen, M.2
  • 30
    • 33750998519 scopus 로고    scopus 로고
    • Symmetric interplatory framelets and their erasure recovery properties
    • Berlin, Germany: Springer-Verlag
    • O. Amrani, A. Z. Averbuch, and V. A. Zheludev, Symmetric Interplatory Framelets and Their Erasure Recovery Properties, vol.4105, Lecture Notes in Computer Science. Berlin, Germany: Springer-Verlag, 2006, pp. 643-649.
    • (2006) Lecture Notes in Computer Science , vol.4105 , pp. 643-649
    • Amrani, O.1    Averbuch, A.Z.2    Zheludev, V.A.3
  • 32
  • 33
    • 38049125745 scopus 로고    scopus 로고
    • On a new class of framelet kernels for support vector regression and regularization networks
    • Berlin, Germany: Springer-Verlag
    • W. F. Zhang, D. Q. Dai, and H. Yan, On a New Class of Framelet Kernels for Support Vector Regression and Regularization Networks, vol.4426, Lecture Notes in Artificial Intelligence. Berlin, Germany: Springer-Verlag, 2007, pp. 355-366.
    • (2007) Lecture Notes in Artificial Intelligence , vol.4426 , pp. 355-366
    • Zhang, W.F.1    Dai, D.Q.2    Yan, H.3
  • 37
    • 0040709212 scopus 로고    scopus 로고
    • Construction of compactly supported affine frames in L2(R)
    • A. Ron and Z. Shen, "Construction of compactly supported affine frames in L2(R)," Math. Comput., vol.67, pp. 191-207, 1998.
    • (1998) Math. Comput. , vol.67 , pp. 191-207
    • Ron, A.1    Shen, Z.2
  • 40
    • 0036161011 scopus 로고    scopus 로고
    • Choosing multiple parameters for support vector machines
    • DOI 10.1023/A:1012450327387
    • O. Chapelle, V. Vapnik, O. Bousquet, and S. Mukherjee, "Choosing multiple parameters for support vector machines," Mach. Learn., vol.46, no.1-3, pp. 131-159, Jan. 2002. (Pubitemid 34129966)
    • (2002) Machine Learning , vol.46 , Issue.1-3 , pp. 131-159
    • Chapelle, O.1    Vapnik, V.2    Bousquet, O.3    Mukherjee, S.4
  • 41
    • 0036436325 scopus 로고    scopus 로고
    • Best choices for regularization parameters in learning theory: On the bias-variance problem
    • F. Cuker and S. Smale, "Best choices for regularization parameters in learning theory: On the bias-variance problem," Found. Comput. Math., vol.2, no.4, pp. 413-428, 2002.
    • (2002) Found. Comput. Math. , vol.2 , Issue.4 , pp. 413-428
    • Cuker, F.1    Smale, S.2
  • 42
    • 84925605946 scopus 로고    scopus 로고
    • The entire regularization path for the support vector machine
    • Dec.
    • 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, Dec. 2004.
    • (2004) J. Mach. Learn. Res. , vol.5 , pp. 1391-1415
    • Hastie, T.1    Rosset, S.2    Tibshirani, R.3    Zhu, J.4
  • 43
    • 34547980120 scopus 로고    scopus 로고
    • A kernel path algorithm for support vector machines
    • G. Wang, D. Y. Yeung, and F. H. Lochovsky, "A kernel path algorithm for support vector machines," in Proc. 24th ICML, 2007, pp. 951-958.
    • (2007) Proc. 24th ICML , pp. 951-958
    • Wang, G.1    Yeung, D.Y.2    Lochovsky, F.H.3
  • 44
    • 0012780893 scopus 로고    scopus 로고
    • Wavelet estimators in nonparametric regression: A comparative simulation study
    • Jun.
    • A. Antoniadis, J. Bigot, and T. Sapatinas, "Wavelet estimators in nonparametric regression: A comparative simulation study," J. Stat. Softw., vol.6, no.6, pp. 1-83, Jun. 2001.
    • (2001) J. Stat. Softw. , vol.6 , Issue.6 , pp. 1-83
    • Antoniadis, A.1    Bigot, J.2    Sapatinas, T.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.