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Volumn 38, Issue 1, 2010, Pages 1-50

The spectrum of kernel random matrices

Author keywords

Concentration of measure; Covariance matrices; Eigenvalues of covariance matrices; Hadamard matrix functions; High dimensional inference; Kernel matrices; Machine learning; Multivariate statistical analysis; Random matrix theory

Indexed keywords


EID: 73949087548     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOS648     Document Type: Article
Times cited : (237)

References (45)
  • 2
    • 0011812771 scopus 로고    scopus 로고
    • Kernel independent component analysis
    • MR1966051
    • BACH, F. R. and JORDAN, M. I. (2003). Kernel independent component analysis. J. Mach. Learn. Res. 3 1-48. MR1966051
    • (2003) J. Mach. Learn. Res. , vol.3 , pp. 1-48
    • Bach, F.R.1    Jordan, M.I.2
  • 3
    • 0347989448 scopus 로고    scopus 로고
    • Methodologies in spectral analysis of large-dimensional random matrices, a review
    • MR1711663
    • BAI, Z. D. (1999). Methodologies in spectral analysis of large-dimensional random matrices, a review. Statist. Sinica 9 611-677. MR1711663
    • (1999) Statist. Sinica , vol.9 , pp. 611-677
    • Bai, Z.D.1
  • 4
    • 51549106256 scopus 로고    scopus 로고
    • On asymptotics of eigenvectors of large sample covariance matrix
    • MR2330979
    • BAI, Z. D., MIAO, B. Q. and PAN, G. M. (2007). On asymptotics of eigenvectors of large sample covariance matrix. Ann. Probab. 35 1532-1572. MR2330979
    • (2007) Ann. Probab , vol.35 , pp. 1532-1572
    • Bai, Z.D.1    Miao, B.Q.2    Pan, G.M.3
  • 5
    • 22044453079 scopus 로고    scopus 로고
    • No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
    • MR1617051
    • BAI, Z. D. and SILVERSTEIN, J. W. (1998). No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices. Ann. Probab. 26 316-345. MR1617051
    • (1998) Ann. Probab , vol.26 , pp. 316-345
    • Bai, Z.D.1    Silverstein, J.W.2
  • 6
    • 0033164056 scopus 로고    scopus 로고
    • Exact separation of eigenvalues of largedimensional sample covariance matrices
    • MR1733159
    • BAI, Z. D. and SILVERSTEIN, J. W. (1999). Exact separation of eigenvalues of largedimensional sample covariance matrices. Ann. Probab. 27 1536-1555. MR1733159
    • (1999) Ann. Probab. , vol.27 , pp. 1536-1555
    • Bai, Z.D.1    Silverstein, J.W.2
  • 7
    • 27644476898 scopus 로고    scopus 로고
    • Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
    • MR2165575
    • BAIK, J., BEN AROUS, G. and PÉCHÉ, S. (2005). Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33 1643-1697. MR2165575
    • (2005) Ann. Probab. , vol.33 , pp. 1643-1697
    • Baik, J.1    Ben Arous, G.2    Péché, S.3
  • 8
    • 33646507506 scopus 로고    scopus 로고
    • Eigenvalues of large sample covariance matrices of spiked population models
    • MR2279680
    • BAIK, J. and SILVERSTEIN, J. (2006). Eigenvalues of large sample covariance matrices of spiked population models. J. Multivariate Anal. 97 1382-1408. MR2279680
    • (2006) J. Multivariate Anal. , vol.97 , pp. 1382-1408
    • Baik, J.1    Silverstein, J.2
  • 11
    • 0037471297 scopus 로고    scopus 로고
    • Spectral properties of distance matrices
    • MR1986436
    • BOGOMOLNY, E., BOHIGAS, O. and SCHMIT, C. (2003). Spectral properties of distance matrices. J. Phys. A 36 3595-3616. MR1986436
    • (2003) J. Phys.A , vol.36 , pp. 3595-3616
    • Bogomolny, E.1    Bohigas, O.2    Schmit, C.3
  • 12
    • 60349122379 scopus 로고    scopus 로고
    • Eigenvalues of euclidean random matrices
    • Available at. MR2462254
    • BORDENAVE, C. (2008). Eigenvalues of Euclidean random matrices. Random Structures Algorithms 33 515-532. Available at http://arxiv.org/abs/math/ 0606624. MR2462254
    • (2008) Random Structures Algorithms , vol.33 , pp. 515-532
    • Bordenave, C.1
  • 13
    • 0010015505 scopus 로고    scopus 로고
    • Limiting eigenvalue distribution of random matrices with correlated entries
    • MR1431189
    • BOUTET DE MONVEL, A., KHORUNZHY, A. and VASILCHUK, V. (1996). Limiting eigenvalue distribution of random matrices with correlated entries. Markov Process. Related Fields 2 607-636. MR1431189
    • (1996) Markov Process. Related Fields , vol.2 , pp. 607-636
    • Boutet De Monvel, A.1    Khorunzhy, A.2    Vasilchuk, V.3
  • 14
    • 41349122944 scopus 로고    scopus 로고
    • Spectral moments of correlated Wishart matrices
    • BURDA, Z., JURKIEWICZ, J. andWACłAW, B. (2005). Spectral moments of correlated Wishart matrices. Phys. Rev. E 71 026111.
    • (2005) Phys. Rev. e , vol.71 , pp. 026111
    • Burda, Z.1    Jurkiewicz, J.2    Wacław, B.3
  • 17
    • 46749089905 scopus 로고    scopus 로고
    • Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices
    • MR2308592
    • EL KAROUI, N. (2007). Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices. Ann. Probab. 35 663-714. MR2308592
    • (2007) Ann. Probab. , vol.35 , pp. 663-714
    • El Karoui, N.1
  • 18
    • 62349123505 scopus 로고    scopus 로고
    • Operator norm consistent estimation of large-dimensional sparse covariance matrices
    • MR2485011
    • EL KAROUI, N. (2008). Operator norm consistent estimation of large-dimensional sparse covariance matrices. Ann. Statist. 36 2717-2756. MR2485011
    • (2008) Ann. Statist. , vol.36 , pp. 2717-2756
    • El Karoui, N.1
  • 19
    • 73949116713 scopus 로고    scopus 로고
    • Concentration of measure and spectra of random matrices:With applications to correlation matrices, elliptical distributions and beyond
    • EL KAROUI, N. (2009). Concentration of measure and spectra of random matrices:With applications to correlation matrices, elliptical distributions and beyond. Ann. Appl. Probab. 19 2362-2405.
    • (2009) Ann. Appl. Probab. , vol.19 , pp. 2362-2405
    • El Karoui, N.1
  • 20
    • 0000609652 scopus 로고
    • The spectrum edge of random matrix ensembles
    • MR1236195
    • FORRESTER, P. J. (1993). The spectrum edge of random matrix ensembles. Nuclear Phys. B 402 709-728. MR1236195
    • (1993) Nuclear Phys. B , vol.402 , pp. 709-728
    • Forrester, P.J.1
  • 21
    • 0001436319 scopus 로고
    • A limit theorem for the norm of random matrices
    • MR0566592
    • GEMAN, S. (1980). A limit theorem for the norm of random matrices. Ann. Probab. 8 252-261. MR0566592
    • (1980) Ann. Probab. , vol.8 , pp. 252-261
    • Geman, S.1
  • 22
    • 0037356963 scopus 로고    scopus 로고
    • Necessary and sufficient condition that the limit of Stieltjes transforms is a Stieltjes transform
    • MR1962995
    • GERONIMO, J. S. and HILL, T. P. (2003). Necessary and sufficient condition that the limit of Stieltjes transforms is a Stieltjes transform. J. Approx. Theory 121 54-60. MR1962995
    • (2003) J. Approx. Theory , vol.121 , pp. 54-60
    • Geronimo, J.S.1    Hill, T.P.2
  • 24
    • 0004151494 scopus 로고
    • Cambridge Univ. Press, Cambridge. MR1084815
    • HORN, R. A. and JOHNSON, C. R. (1990). Matrix Analysis. Cambridge Univ. Press, Cambridge. MR1084815
    • (1990) Matrix Analysis
    • Horn, R.A.1    Johnson, C.R.2
  • 26
    • 0034340689 scopus 로고    scopus 로고
    • Shape fluctuations and random matrices
    • MR1737991
    • JOHANSSON, K. (2000). Shape fluctuations and random matrices. Comm. Math. Phys. 209 437-476. MR1737991
    • (2000) Comm. Math. Phys. , vol.209 , pp. 437-476
    • Johansson, K.1
  • 27
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal component analysis
    • MR1863961
    • JOHNSTONE, I. (2001). On the distribution of the largest eigenvalue in principal component analysis. Ann. Statist. 29 295-327. MR1863961
    • (2001) Ann. Statist. , vol.29 , pp. 295-327
    • Johnstone, I.1
  • 28
    • 4344709031 scopus 로고    scopus 로고
    • Random matrix approximation of spectra of integral operators
    • MR1781185
    • KOLTCHINSKII, V. and GINÉ, E. (2000). Random matrix approximation of spectra of integral operators. Bernoulli 6 113-167. MR1781185
    • (2000) Bernoulli , vol.6 , pp. 113-167
    • Koltchinskii, V.1    Giné, E.2
  • 30
    • 0000263239 scopus 로고
    • Distribution of eigenvalues in certain sets of random matrices
    • MR0208649
    • MARČENKO, V. A. and PASTUR, L. A. (1967). Distribution of eigenvalues in certain sets of random matrices. Mat. Sb. (N.S.) 72 507-536. MR0208649
    • (1967) Mat. Sb. (N.S.) , vol.72 , pp. 507-536
    • Marčenko, V.A.1    Pastur, L.A.2
  • 31
    • 38549175880 scopus 로고    scopus 로고
    • Asymptotics of sample eigenstructure for a large-dimensional spiked covariance model
    • MR2399865
    • PAUL, D. (2007). Asymptotics of sample eigenstructure for a large-dimensional spiked covariance model. Statist. Sinica 17 1617-1642. MR2399865
    • (2007) Statist. Sinica , vol.17 , pp. 1617-1642
    • Paul, D.1
  • 32
    • 55049106385 scopus 로고    scopus 로고
    • No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix
    • MR2460475
    • PAUL, D. and SILVERSTEIN, J. (2009). No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix. J. Multivariate Anal. 100 37-57. MR2460475
    • (2009) J. Multivariate Anal. , vol.100 , pp. 37-57
    • Paul, D.1    Silverstein, J.2
  • 34
    • 29144474701 scopus 로고    scopus 로고
    • n ball
    • Geometric Aspects of Functional Analysis, Springer, Berlin. MR1796723
    • SCHECHTMAN, G. and ZINN, J. (2000). Concentration on the lpn ball. In Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics 1745 245-256. Springer, Berlin. MR1796723
    • (2000) Lecture Notes in Mathematics , vol.1745 , pp. 245-256
    • Schechtman, G.1    Zinn, J.2
  • 37
    • 0002627253 scopus 로고
    • Strong convergence of the empirical distribution of eigenvalues of large-dimensional random matrices
    • MR1370408
    • SILVERSTEIN, J. W. (1995). Strong convergence of the empirical distribution of eigenvalues of large-dimensional random matrices. J. Multivariate Anal. 55 331-339. MR1370408
    • (1995) J. Multivariate Anal. , vol.55 , pp. 331-339
    • Silverstein, J.W.1
  • 38
    • 27644532196 scopus 로고
    • Level-spacing distribution and the Airy kernel
    • MR1257246
    • TRACY, C. and WIDOM, H. (1994). Level-spacing distribution and the Airy kernel. Comm. Math. Phys. 159 151-174. MR1257246
    • (1994) Comm. Math. Phys. , vol.159 , pp. 151-174
    • Tracy, C.1    Widom, H.2
  • 39
    • 0030545965 scopus 로고    scopus 로고
    • On orthogonal and symplectic matrix ensembles
    • MR1385083
    • TRACY, C. and WIDOM, H. (1996). On orthogonal and symplectic matrix ensembles. Comm. Math. Phys. 177 727-754. MR1385083
    • (1996) Comm. Math. Phys. , vol.177 , pp. 727-754
    • Tracy, C.1    Widom, H.2
  • 40
    • 0032163852 scopus 로고    scopus 로고
    • Correlation functions, cluster functions, and spacing distributions for random matrices
    • TRACY, C. andWIDOM, H. (1998). Correlation functions, cluster functions and spacing distributions for random matrices. J. Stat. Phys. 92 809-835. MR1657844 (Pubitemid 128361701)
    • (1998) Journal of Statistical Physics , vol.92 , Issue.5-6 , pp. 809-835
    • Tracy, C.A.1    Widom, H.2
  • 42
    • 0002247902 scopus 로고
    • The strong limits of random matrix spectra for sample matrices of independent elements
    • MR0467894
    • WACHTER, K. W. (1978). The strong limits of random matrix spectra for sample matrices of independent elements. Ann. Probab. 6 1-18. MR0467894
    • (1978) Ann. Probab. , vol.6 , pp. 1-18
    • Wachter, K.W.1
  • 43
    • 0000840166 scopus 로고
    • Characteristic vectors of bordered matrices with infinite dimensions
    • MR0077805
    • WIGNER, E. (1955). Characteristic vectors of bordered matrices with infinite dimensions. Ann. of Math. (2) 62 548-564. MR0077805
    • (1955) Ann. of Math. (2) , vol.62 , pp. 548-564
    • Wigner, E.1
  • 44
    • 0039722607 scopus 로고    scopus 로고
    • The effect of the input density distribution on kernelbased classifiers
    • WILLIAMS, C. and SEEGER, M. (2000). The effect of the input density distribution on kernelbased classifiers. International Conference on Machine Learning 17 1159-1166.
    • (2000) International Conference on Machine Learning , vol.17 , pp. 1159-1166
    • Williams, C.1    Seeger, M.2
  • 45
    • 0001136512 scopus 로고
    • On the limit of the largest eigenvalue of the large-dimensional sample covariance matrix
    • MR0950344
    • YIN, Y. Q., BAI, Z. D. and KRISHNAIAH, P. R. (1988). On the limit of the largest eigenvalue of the large-dimensional sample covariance matrix. Probab. Theory Related Fields 78 509-521. MR0950344
    • (1988) Probab. Theory Related Fields , vol.78 , pp. 509-521
    • Yin, Y.Q.1    Bai, Z.D.2    Krishnaiah, P.R.3


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