메뉴 건너뛰기




Volumn 12, Issue , 2011, Pages 3259-3281

The sample complexity of dictionary learning

Author keywords

Dictionary learning; Generalization bound; Sparse representation

Indexed keywords

COEFFICIENT VECTOR; DE-NOISING; DICTIONARY LEARNING; GENERALIZATION BOUND; HIGH DIMENSIONS; L1 NORM; LINEAR COMBINATIONS; NUMBER OF SAMPLES; ORTHOGONALITY; SAMPLE COMPLEXITY; SIGNAL PROCESSING APPLICATIONS; SIGNAL SEPARATION; SPARSE REPRESENTATION; STATISTICAL LEARNING THEORY;

EID: 84855384338     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (74)

References (30)
  • 1
    • 33750383209 scopus 로고    scopus 로고
    • K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation
    • DOI 10.1109/TSP.2006.881199
    • Michal Aharon, Michael Elad, and Alfred M. Bruckstein. K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing, 54 (11):4311-4322, 2006. (Pubitemid 44637761)
    • (2006) IEEE Transactions on Signal Processing , vol.54 , Issue.11 , pp. 4311-4322
    • Aharon, M.1    Elad, M.2    Bruckstein, A.3
  • 3
    • 0032167175 scopus 로고    scopus 로고
    • The minimax distortion redundancy in empirical quantizer design
    • PII S0018944898047877
    • Peter L. Bartlett, Tamás Linder, and Gábor Lugosi. The minimax distortion redundancy in empirical quantizer design. IEEE Transactions on Information Theory, 44(5):1802-1813, 1998. (Pubitemid 128738552)
    • (1998) IEEE Transactions on Information Theory , vol.44 , Issue.5 , pp. 1802-1813
    • Bartlett, P.L.1    Linder, T.2    Lugosi, G.3
  • 4
    • 26444592981 scopus 로고    scopus 로고
    • Local rademacher complexities
    • DOI 10.1214/009053605000000282
    • Peter L. Bartlett, Olivier Bousquet, and Shahar Mendelson. Local Rademacher complexities. Ann. Statist., 33:1497-1537, 2005. (Pubitemid 41423979)
    • (2005) Annals of Statistics , vol.33 , Issue.4 , pp. 1497-1537
    • Bartlett, P.L.1    Bousquet, O.2    Mendelson, S.3
  • 5
    • 39849091360 scopus 로고    scopus 로고
    • On the performance of clustering in Hilbert spaces
    • DOI 10.1109/TIT.2007.913516
    • Gérard Biau, Luc Devroye, and Gábor Lugosi. On the performance of clustering in Hilbert spaces. IEEE Transactions on Information Theory, 54(2):781-790, 2008. (Pubitemid 351314665)
    • (2008) IEEE Transactions on Information Theory , vol.54 , Issue.2 , pp. 781-790
    • Biau, G.1    Devroye, L.2    Lugosi, G.3
  • 6
    • 33847676413 scopus 로고    scopus 로고
    • Statistical properties of kernel principal component analysis
    • DOI 10.1007/s10994-006-6895-9, Special Issue on Learning Theory
    • Gilles Blanchard, Olivier Bousquet, and Laurent Zwald. Statistical properties of kernel principal component analysis. Machine Learning, 66(2):259-294, 2007. (Pubitemid 46360614)
    • (2007) Machine Learning , vol.66 , Issue.2-3 , pp. 259-294
    • Blanchard, G.1    Bousquet, O.2    Zwald, L.3
  • 7
    • 59749104367 scopus 로고    scopus 로고
    • From sparse solutions of systems of equations to sparse modeling of signals and images
    • Alfred M. Bruckstein, David L. Donoho, and Michael Elad. From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Review, 51(1):34-81, 2009.
    • (2009) SIAM Review , vol.51 , Issue.1 , pp. 34-81
    • Bruckstein, A.M.1    Donoho, D.L.2    Elad, M.3
  • 8
    • 33947416035 scopus 로고    scopus 로고
    • Near-optimal signal recovery from random projections: Universal encoding strategies?
    • DOI 10.1109/TIT.2006.885507
    • Emmanuel J. Candes and Terence Tao. Near-optimal signal recovery from random projections: Universal encoding strategies? IEEE Transactions on Information Theory, 52(12):5406-5425, 2006. (Pubitemid 46445381)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candes, E.J.1    Tao, T.2
  • 9
    • 0035273106 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • DOI 10.1137/S003614450037906X, PII S003614450037906X
    • Scott S. Chen, David L. Donoho, andMichael A. Saunders. Atomic decomposition by basis pursuit. SIAM Review, 43(1):129-159, 2001. (Pubitemid 32406896)
    • (2001) SIAM Review , vol.43 , Issue.1 , pp. 129-159
    • Chen, S.S.1    Donoho, D.L.2    Saunders, M.A.3
  • 10
    • 0024771664 scopus 로고
    • Orthogonal least squares methods and their application to non-linear system identification
    • Sheng Chen, Stephen A. Billings, and Wan Luo. Orthogonal least squares methods and their application to non-linear system identification. International Journal of Control, 50(5):1873-1896, 1989. (Pubitemid 20636409)
    • (1989) International Journal of Control , vol.50 , Issue.5 , pp. 1873-1896
    • Chen, S.1    Billings, S.A.2    Luo, W.3
  • 11
    • 0036071370 scopus 로고    scopus 로고
    • On the mathematical foundations of learning
    • Felipe Cucker and Stephen Smale. On the mathematical foundations of learning. Bull. Amer. Math. Soc, 39(1):1-50, 2002.
    • (2002) Bull. Amer. Math. Soc , vol.39 , Issue.1 , pp. 1-50
    • Cucker, F.1    Smale, S.2
  • 14
    • 84968468760 scopus 로고
    • A class of nonharmonic Fourier series
    • Richard J. Duffin and Albert C. Schaeer. A class of nonharmonic Fourier series. Trans. Amer. Math. Soc, 72:341-366, 1952.
    • (1952) Trans. Amer. Math. Soc , vol.72 , pp. 341-366
    • Duffin, R.J.1    Schaeer, A.C.2
  • 17
    • 0037313218 scopus 로고    scopus 로고
    • Dictionary learning algorithms for sparse representation
    • DOI 10.1162/089976603762552951
    • Kenneth Kreutz-Delgado, Joseph F. Murray, Bhaskar D. Rao, Kjersti Engan, Te-Won Lee, and Terrance J. Sejnowski. Dictionary learning algorithms for sparse representation. Neural Computation, 15(2):349-396, 2003. (Pubitemid 37049825)
    • (2003) Neural Computation , vol.15 , Issue.2 , pp. 349-396
    • Kreutz-Delgado, K.1    Murray, J.F.2    Rao, B.D.3    Engan, K.4    Lee, T.-W.5    Sejnowski, T.J.6
  • 22
    • 77958550281 scopus 로고    scopus 로고
    • K-dimensional coding schemes in hilbert spaces
    • November
    • Andreas Maurer and Massimiliano Pontil. K-dimensional coding schemes in hilbert spaces. IEEE Transactions on Information Theory, 56:5839-5846, November 2010.
    • (2010) IEEE Transactions on Information Theory , vol.56 , pp. 5839-5846
    • Maurer, A.1    Pontil, M.2
  • 24
    • 0030779611 scopus 로고    scopus 로고
    • Sparse coding with an overcomplete basis set: A strategy employed by V1?
    • DOI 10.1016/S0042-6989(97)00169-7, PII S0042698997001697
    • Bruno A. Olshausen and David J. Field. Sparse coding with an overcomplete basis set: A strategy employed by V1. Vision Research, 37:3311-3325, 1997. (Pubitemid 27493805)
    • (1997) Vision Research , vol.37 , Issue.23 , pp. 3311-3325
    • Olshausen, B.A.1    Field, D.J.2
  • 26
    • 42149186287 scopus 로고    scopus 로고
    • Sparse and redundant representations and motion-estimation-free algorithm for video denoising. Wavelets XII
    • Matan Protter and Michael Elad. Sparse and redundant representations and motion-estimation-free algorithm for video denoising. Wavelets XII. Proceedings of the SPIE, 6701:43, 2007.
    • (2007) Proceedings of the SPIE , vol.6701 , pp. 43
    • Protter, M.1    Elad, M.2
  • 28
    • 22844440983 scopus 로고    scopus 로고
    • On the eigenspectrum of the gram matrix and the generalization error of Kernel-PCA
    • DOI 10.1109/TIT.2005.850052
    • John Shawe-Taylor, Christopher K. I. Williams, Nello Cristianini, and Jaz Kandola. On the eigenspectrum of the Gram matrix and the generalization error of kernel-PCA. IEEE Transactions on Information Theory, 51(7):2510-2522, 2005. (Pubitemid 41136405)
    • (2005) IEEE Transactions on Information Theory , vol.51 , Issue.7 , pp. 2510-2522
    • Shawe-Taylor, J.1    Williams, C.K.I.2    Cristianini, N.3    Kandola, J.4
  • 29
    • 5444237123 scopus 로고    scopus 로고
    • Greed is good: Algorithmic results for sparse approximation
    • Joel A. Tropp. Greed is good: Algorithmic results for sparse approximation. IEEE Transactions on Information Theory, 50:2231-2242, 2004.
    • (2004) IEEE Transactions on Information Theory , vol.50 , pp. 2231-2242
    • Tropp, J.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.