메뉴 건너뛰기




Volumn 6, Issue 1, 2011, Pages 27-42

Tangent space learning and generalization

Author keywords

Machine learning; Manifold learning; Tangent space learning

Indexed keywords


EID: 79952316381     PISSN: 16733460     EISSN: 16733584     Source Type: Journal    
DOI: 10.1007/s11460-011-0124-4     Document Type: Article
Times cited : (11)

References (41)
  • 1
    • 0000325341 scopus 로고
    • On lines and planes of closest fit to systems of points in space
    • Pearson K. On lines and planes of closest fit to systems of points in space. Philosophical Magazine, 1901, 2(6): 559-572.
    • (1901) Philosophical Magazine , vol.2 , Issue.6 , pp. 559-572
    • Pearson, K.1
  • 2
    • 0347243182 scopus 로고    scopus 로고
    • Nonlinear component analysis as a kernel eigenvalue problem
    • Schölkopf B, Smola A, Müller K R. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 1998, 10(5): 1299-1319.
    • (1998) Neural Computation , vol.10 , Issue.5 , pp. 1299-1319
    • Schölkopf, B.1    Smola, A.2    Müller, K.R.3
  • 4
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • Tenenbaum J, de Silva V, Langford J. A global geometric framework for nonlinear dimensionality reduction. Science, 2000, 290(5500): 2319-2323.
    • (2000) Science , vol.290 , Issue.5500 , pp. 2319-2323
    • Tenenbaum, J.1    de Silva, V.2    Langford, J.3
  • 5
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • Roweis S, Saul L. Nonlinear dimensionality reduction by locally linear embedding. Science, 2000, 290(5500): 2323-2326.
    • (2000) Science , vol.290 , Issue.5500 , pp. 2323-2326
    • Roweis, S.1    Saul, L.2
  • 7
    • 4344605179 scopus 로고    scopus 로고
    • Global versus local methods in nonlinear dimensionality reduction
    • In: Becker S, Thrun S, Obermayer K, eds
    • de Silva V, Tenenbaum J B. Global versus local methods in nonlinear dimensionality reduction. In: Becker S, Thrun S, Obermayer K, eds. Proceedings of Advances in Neural Information Processing Systems. 2002, 15: 721-728.
    • (2002) Proceedings of Advances in Neural Information Processing Systems , vol.15 , pp. 721-728
    • de Silva, V.1    Tenenbaum, J.B.2
  • 8
    • 84864069440 scopus 로고    scopus 로고
    • MLLE: Modified locally linear embedding using multiple weights
    • In: Schölkopf B, Platt J, Hoffman T, eds
    • Zhang Z, Wang J. MLLE: Modified locally linear embedding using multiple weights. In: Schölkopf B, Platt J, Hoffman T, eds. Proceedings of Advances in Neural Information Processing Systems. 2007, 19: 1593-1600.
    • (2007) Proceedings of Advances in Neural Information Processing Systems , vol.19 , pp. 1593-1600
    • Zhang, Z.1    Wang, J.2
  • 11
    • 79952312105 scopus 로고    scopus 로고
    • Regional Conference Series in Mathematics, Providence: American Mathematical Society
    • Chung F R K. Spectral Graph Theory. Regional Conference Series in Mathematics Vol 92. Providence: American Mathematical Society, 1997.
    • (1997) Spectral Graph Theory , vol.92
    • Chung, F.R.K.1
  • 13
    • 84864042188 scopus 로고    scopus 로고
    • Convergence of Laplacian eigenmaps
    • B. Schöllkopf, J. Platt, and T. Hoffman (Eds.), Cambridge: MIT Press
    • Belkin M, Niyogi P. Convergence of Laplacian eigenmaps. In: Schöllkopf B, Platt J, Hoffman T, eds. Proceedings of Advances in Neural Information Processing Systems. Cambridge: MIT Press, 2007, 19: 129-136.
    • (2007) Proceedings of Advances in Neural Information Processing Systems , pp. 129-136
    • Belkin, M.1    Niyogi, P.2
  • 14
    • 33750729556 scopus 로고    scopus 로고
    • Manifold regularization: A geometric framework for learning from labeled and unlabeled examples
    • Belkin M, Niyogi P, Sindhwani V. Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. Journal of Machine Learning Research, 2006, 7: 2399-2434.
    • (2006) Journal of Machine Learning Research , vol.7 , pp. 2399-2434
    • Belkin, M.1    Niyogi, P.2    Sindhwani, V.3
  • 16
    • 72949097899 scopus 로고    scopus 로고
    • Laplacian regularized d-optimal design for active learning and its application to image retrieval
    • He X. Laplacian regularized d-optimal design for active learning and its application to image retrieval. IEEE Transactions on Image Processing, 2010, 19(1): 254-263.
    • (2010) IEEE Transactions on Image Processing , vol.19 , Issue.1 , pp. 254-263
    • He, X.1
  • 20
    • 0037948870 scopus 로고    scopus 로고
    • Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
    • Donoho D L, Grimes C. Hessian eigenmaps: locally linear embedding techniques for high-dimensional data. Proceedings of the National Academy of Sciences, 2003, 100(10): 5591-5596.
    • (2003) Proceedings of the National Academy of Sciences , vol.100 , Issue.10 , pp. 5591-5596
    • Donoho, D.L.1    Grimes, C.2
  • 21
    • 77955216309 scopus 로고    scopus 로고
    • Non-parametric regression between manifolds
    • In: Koller D, Schuurmans D, Bengio Y, Bottou L, eds
    • Steinke F, Hein M. Non-parametric regression between manifolds. In: Koller D, Schuurmans D, Bengio Y, Bottou L, eds. Proceedings of Advances in Neural Information Processing Systems. 2008, 21: 1561-1568.
    • (2008) Proceedings of Advances in Neural Information Processing Systems , vol.21 , pp. 1561-1568
    • Steinke, F.1    Hein, M.2
  • 22
    • 84860192651 scopus 로고    scopus 로고
    • Semi-supervised regression using hessian energy with an application to semi-supervised dimensionality reduction
    • In: Bengio Y, Schuurmans D, Lafferty J, Williams C K I, Culotta A, eds
    • Kim K I, Steinke F, Hein M. Semi-supervised regression using hessian energy with an application to semi-supervised dimensionality reduction. In: Bengio Y, Schuurmans D, Lafferty J, Williams C K I, Culotta A, eds. Advances in Neural Information Processing Systems. 2009, 22: 979-987.
    • (2009) Advances in Neural Information Processing Systems , vol.22 , pp. 979-987
    • Kim, K.I.1    Steinke, F.2    Hein, M.3
  • 23
    • 14544307975 scopus 로고    scopus 로고
    • Principal manifolds and nonlinear dimension reduction via local tangent space alignment
    • Zhang Z, Zha H. Principal manifolds and nonlinear dimension reduction via local tangent space alignment. SIAM Journal of Scientific Computing, 2004, 26(1): 313-338.
    • (2004) SIAM Journal of Scientific Computing , vol.26 , Issue.1 , pp. 313-338
    • Zhang, Z.1    Zha, H.2
  • 29
    • 40349102105 scopus 로고    scopus 로고
    • Finding the homology of submanifolds with high confidence from random samples
    • Niyogi P, Smale S, Weinberger S. Finding the homology of submanifolds with high confidence from random samples. Discrete and Computational Geometry, 2008, 39(1): 419-441.
    • (2008) Discrete and Computational Geometry , vol.39 , Issue.1 , pp. 419-441
    • Niyogi, P.1    Smale, S.2    Weinberger, S.3
  • 30
    • 79952314392 scopus 로고
    • CBMS Regional Conference Series in Mathematics, Providence: American Mathematical Society
    • Eells J, Lemaire L. Selected Topics in Harmonic Maps. CBMS Regional Conference Series in Mathematics, Vol 50. Providence: American Mathematical Society, 1983.
    • (1983) Selected Topics in Harmonic Maps , vol.50
    • Eells, J.1    Lemaire, L.2
  • 33
    • 77953610026 scopus 로고    scopus 로고
    • Approximately harmonic projection: Theoretical analysis and an algorithm
    • Lin B, He X, Zhou Y, Liu L, Lu K. Approximately harmonic projection: theoretical analysis and an algorithm. Pattern Recognition, 2010, 43(10): 3307-3313.
    • (2010) Pattern Recognition , vol.43 , Issue.10 , pp. 3307-3313
    • Lin, B.1    He, X.2    Zhou, Y.3    Liu, L.4    Lu, K.5
  • 40
    • 0036840404 scopus 로고    scopus 로고
    • Patrangenaru V. Nonparametic estimation of location and dispersion on riemannian manifolds
    • Bhattacharya R, Patrangenaru V. Nonparametic estimation of location and dispersion on riemannian manifolds. Journal of Statistical Planning and Inference, 2002, 108: 23-36.
    • (2002) Journal of Statistical Planning and Inference , vol.108 , pp. 23-36
    • Bhattacharya, R.1
  • 41
    • 0000802374 scopus 로고
    • The approximation of one matrix by another of lower rank
    • Eckart C, Young G. The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1(3): 211-218.
    • (1936) Psychometrika , vol.1 , Issue.3 , pp. 211-218
    • Eckart, C.1    Young, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.