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Volumn 7, Issue , 2006, Pages 817-854

Consistency and convergence rates of one-class SVMs and related algorithms

Author keywords

Convex loss functions; Gaussian kernel RKHS; Kernel density estimation; One class SVM; Regularization

Indexed keywords

ASYMPTOTIC STABILITY; BANDWIDTH; COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; OPTIMIZATION;

EID: 33646554819     PISSN: 15337928     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (139)

References (27)
  • 1
    • 5844297152 scopus 로고
    • Theory of reproducing kernels
    • N. Aronszajn. Theory of reproducing kernels. Trans. Am. Math. Soc., 68:337 - 404, 1950.
    • (1950) Trans. Am. Math. Soc. , vol.68 , pp. 337-404
    • Aronszajn, N.1
  • 3
    • 9444239294 scopus 로고    scopus 로고
    • Sparseness vs estimating conditional probabilities: Some asymptotic results
    • Springer
    • P. L. Bartlett and A, Tewari. Sparseness vs estimating conditional probabilities: Some asymptotic results. In Lecture Notes in Computer Science, volume 3120, pages 564-578. Springer, 2004.
    • (2004) Lecture Notes in Computer Science , vol.3120 , pp. 564-578
    • Bartlett, P.L.1    Tewari, A.2
  • 4
    • 26444592981 scopus 로고    scopus 로고
    • Local Rademacher complexities
    • P. L. Bartlett, O. Bousquet, and S. Mendelson. Local Rademacher complexities. Ann. Stat., 33(4): 1497-1537, 2005.
    • (2005) Ann. Stat. , vol.33 , Issue.4 , pp. 1497-1537
    • Bartlett, P.L.1    Bousquet, O.2    Mendelson, S.3
  • 6
    • 0004063876 scopus 로고
    • Springer Grundlehren der Mathematischen Wissenschaften. Springer Verlag
    • R. A. DeVore and G. G. Lorentz. Constructive Approximation. Springer Grundlehren der Mathematischen Wissenschaften. Springer Verlag, 1993.
    • (1993) Constructive Approximation
    • DeVore, R.A.1    Lorentz, G.G.2
  • 9
    • 0003906492 scopus 로고
    • Fourier analysis and its applications
    • Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA
    • G. B. Folland. Fourier analysis and its applications. The Wadsworth & Brooks/Cole Mathematics Series. Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1992.
    • (1992) The Wadsworth & Brooks/Cole Mathematics Series
    • Folland, G.B.1
  • 10
    • 0001341972 scopus 로고
    • Estimation of a convex density contour in two dimensions
    • J. A. Hartigan. Estimation of a convex density contour in two dimensions. J. Amer. Statist. Assoc., 82(397):267-270, 1987.
    • (1987) J. Amer. Statist. Assoc. , vol.82 , Issue.397 , pp. 267-270
    • Hartigan, J.A.1
  • 12
    • 9444269961 scopus 로고    scopus 로고
    • On the Bayes-risk consistency of regularized boosting methods
    • G. Lugosi and N. Vayatis. On the Bayes-risk consistency of regularized boosting methods. Ann. Stat., 32:30-55, 2004.
    • (2004) Ann. Stat. , vol.32 , pp. 30-55
    • Lugosi, G.1    Vayatis, N.2
  • 13
    • 0033234630 scopus 로고    scopus 로고
    • Smooth discrimination analysis
    • E. Mammen and A. Tsybakov. Smooth discrimination analysis. Ann. Stat., 27 (6): 1808-1829, 1999.
    • (1999) Ann. Stat. , vol.27 , Issue.6 , pp. 1808-1829
    • Mammen, E.1    Tsybakov, A.2
  • 14
    • 0000595627 scopus 로고    scopus 로고
    • Some applications of concentration inequalities to statistics
    • P. Massart. Some applications of concentration inequalities to statistics. Ann. Fac. Sc. Toulouse, IX (2):245-303, 2000.
    • (2000) Ann. Fac. Sc. Toulouse , vol.9 , Issue.2 , pp. 245-303
    • Massart, P.1
  • 15
    • 33646565189 scopus 로고    scopus 로고
    • Hilbert spaces induced by Toeplitz covariance kernels
    • Springer, Jan
    • M. T. Matache and V. Matache. Hilbert spaces induced by Toeplitz covariance kernels. In Lecture Notes in Control and Information Sciences, volume 280, pages 319-334. Springer, Jan 2002.
    • (2002) Lecture Notes in Control and Information Sciences , vol.280 , pp. 319-334
    • Matache, M.T.1    Matache, V.2
  • 17
    • 0000738873 scopus 로고
    • On the estimation of a probability density function by the maximum penalized likelihood method
    • B. W. Silverman. On the estimation of a probability density function by the maximum penalized likelihood method. Ann. Stat., 10:795-810, 1982.
    • (1982) Ann. Stat. , vol.10 , pp. 795-810
    • Silverman, B.W.1
  • 18
    • 0036749277 scopus 로고    scopus 로고
    • Support vector machines are universally consistent
    • I. Steinwart. Support vector machines are universally consistent. J. Complexity, 18:768-791, 2002.
    • (2002) J. Complexity , vol.18 , pp. 768-791
    • Steinwart, I.1
  • 19
    • 4644354708 scopus 로고    scopus 로고
    • Sparseness of support vector machines
    • I. Steinwart. Sparseness of support vector machines. J. Mach. Learn. Res., 4:1071-1105, 2003.
    • (2003) J. Mach. Learn. Res. , vol.4 , pp. 1071-1105
    • Steinwart, I.1
  • 20
    • 12444265838 scopus 로고    scopus 로고
    • Consistency of support vector machines and other regularized kernel classifiers
    • I. Steinwart. Consistency of support vector machines and other regularized kernel classifiers. IEEE Trans. Inform. Theory, 51(1):128-142, 2005a.
    • (2005) IEEE Trans. Inform. Theory , vol.51 , Issue.1 , pp. 128-142
    • Steinwart, I.1
  • 21
    • 33646586252 scopus 로고    scopus 로고
    • How to compare loss functions and their risks
    • Los Alamos National Laboratory
    • I. Steinwart. How to compare loss functions and their risks. Technical report, Los Alamos National Laboratory, 2005b.
    • (2005) Technical Report
    • Steinwart, I.1
  • 22
    • 33646422390 scopus 로고    scopus 로고
    • Fast rates for support vector machines using Gaussian kernels
    • Los Alamos National Laboratory
    • I. Steinwart and C. Scovel. Fast rates for support vector machines using Gaussian kernels. Technical Report LA-UR 04-8796, Los Alamos National Laboratory, 2004.
    • (2004) Technical Report , vol.LA-UR 04-8796
    • Steinwart, I.1    Scovel, C.2
  • 23
    • 33646584034 scopus 로고    scopus 로고
    • An explicit description of the reproducing kernel Hilbert spaces of Gaussian RBF kernels
    • Los Alamos National Laboratory
    • I. Steinwart, D. Hush, and C. Scovel. An explicit description of the reproducing kernel Hilbert spaces of Gaussian RBF kernels. Technical Report LA-UR 04-8274, Los Alamos National Laboratory, 2004.
    • (2004) Technical Report , vol.LA-UR 04-8274
    • Steinwart, I.1    Hush, D.2    Scovel, C.3
  • 24
    • 21844462364 scopus 로고    scopus 로고
    • A classification framework for anomaly detection
    • I. Steinwart, D. Hush, and Scovel C. A classification framework for anomaly detection. J. Mach. Learn. Res., 6:211-232, 2005.
    • (2005) J. Mach. Learn. Res. , vol.6 , pp. 211-232
    • Steinwart, I.1    Hush, D.2    Scovel, C.3
  • 26
    • 0031478562 scopus 로고    scopus 로고
    • On nonparametric estimation of density level sets
    • June
    • A. B. Tsybakov. On nonparametric estimation of density level sets. Ann. Stat., 25:948-969, June 1997.
    • (1997) Ann. Stat. , vol.25 , pp. 948-969
    • Tsybakov, A.B.1
  • 27
    • 4644257995 scopus 로고    scopus 로고
    • Statistical behavior and consistency of classification methods based on convex risk minimization
    • T. Zhang. Statistical behavior and consistency of classification methods based on convex risk minimization. Ann. Stat., 32:56-134, 2004.
    • (2004) Ann. Stat. , vol.32 , pp. 56-134
    • Zhang, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.