메뉴 건너뛰기




Volumn 51, Issue 7, 2005, Pages 2510-2522

On the eigenspectrum of the gram matrix and the generalization error of Kernel-PCA

Author keywords

Concentration bounds; Gram matrices; Kernel methods; Principal components analysis (PCA); Rademacher complexity; Spectra of random matrices; Statistical learning theory

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; POLYNOMIALS; PRINCIPAL COMPONENT ANALYSIS; STATISTICAL METHODS; THEOREM PROVING;

EID: 22844440983     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2005.850052     Document Type: Article
Times cited : (157)

References (29)
  • 4
    • 0032256758 scopus 로고    scopus 로고
    • "Authoritative sources in a hyperlinked environment"
    • San Francisco, CA, Jan.
    • J. Kleinberg, "Authoritative sources in a hyperlinked environment," in Proc. 9th ACM-SIAM Symp. Discrete Algorithms, San Francisco, CA, Jan. 1998.
    • (1998) Proc. 9th ACM-SIAM Symp. Discrete Algorithms
    • Kleinberg, J.1
  • 5
    • 0002505172 scopus 로고    scopus 로고
    • "The anatomy of a large-scale hypertextual (web) search engine"
    • Brisbane, Australia, Apr.
    • S. Brin and L. Page, "The anatomy of a large-scale hypertextual (web) search engine," in Proc. 7th Int. World Wide Web Conf., Brisbane, Australia, Apr. 1998.
    • (1998) Proc. 7th Int. World Wide Web Conf.
    • Brin, S.1    Page, L.2
  • 7
    • 0001226135 scopus 로고    scopus 로고
    • "Concentration of the spectral measure for large matrices"
    • A. Guionnet and O. Zeitouni, "Concentration of the spectral measure for large matrices," Electron. Commun. Prob., vol. 5, pp. 119-136, 2000.
    • (2000) Electron. Commun. Prob. , vol.5 , pp. 119-136
    • Guionnet, A.1    Zeitouni, O.2
  • 8
    • 0036459716 scopus 로고    scopus 로고
    • "On the concentration of eigenvalues of random symmetric matrices"
    • N. Alon, M. Krivelevich, and V. H. Vu, "On the concentration of eigenvalues of random symmetric matrices," Israel J. Math., vol. 131, pp. 259-267, 2002.
    • (2002) Israel J. Math. , vol.131 , pp. 259-267
    • Alon, N.1    Krivelevich, M.2    Vu, V.H.3
  • 9
    • 0039722607 scopus 로고    scopus 로고
    • "The effect of the input density distribution on kernel-based classifiers"
    • P. Langley, Ed. San Francisco, CA: Morgan Kaufmann
    • C. K. I. Williams and M. Seeger, "The effect of the input density distribution on kernel-based classifiers," in Proc. 17th Int. Conf. Machine Learning (ICML 2000), P. Langley, Ed. San Francisco, CA: Morgan Kaufmann, 2000.
    • (2000) Proc. 17th Int. Conf. Machine Learning (ICML 2000)
    • Williams, C.K.I.1    Seeger, M.2
  • 11
    • 0039813137 scopus 로고    scopus 로고
    • "Gaussian regression and optimal finite dimensional linear models"
    • C.M. Bishop, Ed. Berlin, Germany: Springer-Verlag
    • H. Zhu, C. K. I. Williams, R. J. Rohwer, and M. Morciniec, "Gaussian regression and optimal finite dimensional linear models," in Neural Networks and Machine Learning, C. M. Bishop, Ed. Berlin, Germany: Springer-Verlag, 1998.
    • (1998) Neural Networks and Machine Learning
    • Zhu, H.1    Williams, C.K.I.2    Rohwer, R.J.3    Morciniec, M.4
  • 12
    • 4344709031 scopus 로고    scopus 로고
    • "Random matrix approximation of spectra of integral operators"
    • V. Koltchinskii and E. Gine, "Random matrix approximation of spectra of integral operators," Bernoulli, vol. 6, no. 1, pp. 113-167, 2000.
    • (2000) Bernoulli , vol.6 , Issue.1 , pp. 113-167
    • Koltchinskii, V.1    Gine, E.2
  • 13
    • 0043152139 scopus 로고    scopus 로고
    • On the Distribution of the Largest Principal Component
    • Stanford Univ., Stanford, CA. [Online]. Available
    • I. Johnstone. (2000) On the Distribution of the Largest Principal Component. Stanford Univ., Stanford, CA. [Online]. Available: http://www-stat.stanford.edu/imj/Reports/index.html
    • (2000)
    • Johnstone, I.1
  • 14
    • 84898961678 scopus 로고    scopus 로고
    • "On the concentration of spectral properties"
    • T.G. Diettrich, S. Becker, and Z. Ghahramani, Eds. Cambridge, MA: MIT Press
    • J. Shawe-Taylor, N. Cristianini, and J. Kandola, "On the concentration of spectral properties," in Advances in Neural Information Processing Systems, T. G. Diettrich, S. Becker, and Z. Ghahramani, Eds. Cambridge, MA: MIT Press, 2002, vol. 14.
    • (2002) Advances in Neural Information Processing Systems , vol.14
    • Shawe-Taylor, J.1    Cristianini, N.2    Kandola, J.3
  • 16
    • 84947403595 scopus 로고
    • "Probability inequalities for sums of bounded random variables"
    • W. Hoeffding, "Probability inequalities for sums of bounded random variables," J. Amer. Stat. Assoc., vol. 58, pp. 13-30, 1963.
    • (1963) J. Amer. Stat. Assoc. , vol.58 , pp. 13-30
    • Hoeffding, W.1
  • 17
    • 84972574511 scopus 로고
    • "Weighted sums of certain dependent random variables"
    • K. Azuma, "Weighted sums of certain dependent random variables," Tohoku Math J., vol. 19, pp. 357-367, 1967.
    • (1967) Tohoku Math J. , vol.19 , pp. 357-367
    • Azuma, K.1
  • 18
    • 0001035413 scopus 로고
    • "On the method of bounded differences"
    • Cambridge, U.K.: Cambridge Univ. Press
    • C. McDiarmid, "On the method of bounded differences," in Surveys in Combinatorics 1989. Cambridge, U.K.: Cambridge Univ. Press, 1989, pp. 148-188.
    • (1989) Surveys in Combinatorics 1989 , pp. 148-188
    • McDiarmid, C.1
  • 20
    • 0030489977 scopus 로고    scopus 로고
    • "New concentration inequalities in product spaces"
    • M. Talagrand, "New concentration inequalities in product spaces," Invent. Math., vol. 126, pp. 505-563, 1996.
    • (1996) Invent. Math. , vol.126 , pp. 505-563
    • Talagrand, M.1
  • 21
    • 33645204160 scopus 로고    scopus 로고
    • "Variational characterization of eigenvalues of nonlinear eigen-problems"
    • Prague, Czech Republic, Jan.
    • H. Voss, "Variational characterization of eigenvalues of nonlinear eigen-problems," in Proc. Int. Conf. Mathematical and Computer Modeling in Science and Engineering, Prague, Czech Republic, Jan. 2003, pp. 379-383.
    • (2003) Proc. Int. Conf. Mathematical and Computer Modeling in Science and Engineering , pp. 379-383
    • Voss, H.1
  • 22
    • 0001381004 scopus 로고
    • "On Wielandt's inequality and its application to the asymptotic distribution of the eigenvalues of a random symmetric matrix"
    • M. L. Eaton and D. E. Tyler, "On Wielandt's inequality and its application to the asymptotic distribution of the eigenvalues of a random symmetric matrix," Ann. Statist., vol. 19, no. 1, pp. 260-271, 1991.
    • (1991) Ann. Statist. , vol.19 , Issue.1 , pp. 260-271
    • Eaton, M.L.1    Tyler, D.E.2
  • 23
    • 0001154834 scopus 로고
    • "The distribution of the latent roots of the covariance matrix"
    • A. T. James, "The distribution of the latent roots of the covariance matrix," Ann. Math. Statist., vol. 31, pp. 151-158, 1960.
    • (1960) Ann. Math. Statist. , vol.31 , pp. 151-158
    • James, A.T.1
  • 24
    • 0000815369 scopus 로고
    • "Tests of significance for the latent roots of covariance and correlation matrices"
    • D. N. Lawley, "Tests of significance for the latent roots of covariance and correlation matrices," Biometrika, vol. 43, no. 1/2, pp. 128-136, 1956.
    • (1956) Biometrika , vol.43 , Issue.1-2 , pp. 128-136
    • Lawley, D.N.1
  • 25
    • 0001699986 scopus 로고
    • "Asymptotic theory for principal component analysis"
    • T. W. Anderson, "Asymptotic theory for principal component analysis," Ann. Math. Statist., vol. 34, no. 1, pp. 122-148, 1963.
    • (1963) Ann. Math. Statist. , vol.34 , Issue.1 , pp. 122-148
    • Anderson, T.W.1
  • 26
    • 0017102226 scopus 로고
    • "Asymptotic distribution of the sample roots for a nonnormal population"
    • C. M. Waternaux, "Asymptotic distribution of the sample roots for a nonnormal population," Biometrika, vol. 63, no. 3, pp. 639-645, 1976.
    • (1976) Biometrika , vol.63 , Issue.3 , pp. 639-645
    • Waternaux, C.M.1
  • 28
    • 0038453192 scopus 로고    scopus 로고
    • "Rademacher and Gaussian complexities: Risk bounds and structural results"
    • P. L. Bartlett and S. Mendelson, "Rademacher and Gaussian complexities: Risk bounds and structural results," J. Mach. Learning Res., vol. 3, pp. 463-482, 2002.
    • (2002) J. Mach. Learning Res. , vol.3 , pp. 463-482
    • Bartlett, P.L.1    Mendelson, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.