메뉴 건너뛰기




Volumn 4, Issue 2, 2004, Pages 119-155

Think globally, fit locally: Unsupervised learning of low dimensional manifolds

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DATA PROCESSING; EIGENVALUES AND EIGENFUNCTIONS; INTERPOLATION; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; OPTIMIZATION; PROBABILITY; VISUALIZATION;

EID: 2342517502     PISSN: 15324435     EISSN: None     Source Type: Journal    
DOI: 10.1162/153244304322972667     Document Type: Article
Times cited : (1448)

References (79)
  • 1
    • 0033561886 scopus 로고    scopus 로고
    • Independent factor analysis
    • H. Attias. Independent factor analysis. Neural Computation, 11(4):803-851, 1999.
    • (1999) Neural Computation , vol.11 , Issue.4 , pp. 803-851
    • Attias, H.1
  • 3
    • 84880203756 scopus 로고    scopus 로고
    • Laplacian eigenmaps and spectral techniques for embedding and clustering
    • T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Cambridge, MA. MIT Press
    • M. Belkin and P. Niyogi. Laplacian eigenmaps and spectral techniques for embedding and clustering. In T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Advances in Neural Information Processing Systems 14, pages 585-591, Cambridge, MA, 2002. MIT Press.
    • (2002) Advances in Neural Information Processing Systems , vol.14 , pp. 585-591
    • Belkin, M.1    Niyogi, P.2
  • 4
    • 2342543476 scopus 로고    scopus 로고
    • Learning eigenfunctions of similarity: Linking spectral clustering and kernel PCA
    • Departement d'Informatique et Recherche Oprationnelle, Universite de Montreal
    • Y. Bengio, P. Vincent, and J.F. Paiement. Learning eigenfunctions of similarity: linking spectral clustering and kernel PCA. Technical Report 1232, Departement d'Informatique et Recherche Oprationnelle, Universite de Montreal, 2003.
    • (2003) Technical Report , vol.1232
    • Bengio, Y.1    Vincent, P.2    Paiement, J.F.3
  • 5
    • 0030056823 scopus 로고    scopus 로고
    • Image representation for visual learning
    • D. Beymer and T. Poggio. Image representation for visual learning. Science, 272:1905, 1996.
    • (1996) Science , vol.272 , pp. 1905
    • Beymer, D.1    Poggio, T.2
  • 8
    • 84898990205 scopus 로고    scopus 로고
    • Charting a manifold
    • S. Becker, S. Thrun, and K. Obermayer, editors, Cambridge, MA. MIT Press
    • M. Brand. Charting a manifold. In S. Becker, S. Thrun, and K. Obermayer, editors, Advances in Neural Information Processing Systems 15, Cambridge, MA, 2003. MIT Press.
    • (2003) Advances in Neural Information Processing Systems , vol.15
    • Brand, M.1
  • 10
    • 85153947273 scopus 로고
    • Nonlinear image interpolation using manifold learning
    • G. Tesauro, D. Touretzky, and T. Leen, editors, Cambridge, MA. MIT Press
    • C. Bregler and S. Omohundro. Nonlinear image interpolation using manifold learning. In G. Tesauro, D. Touretzky, and T. Leen, editors, Advances in Neural Information Processing Systems 7, pages 973-980, Cambridge, MA, 1995. MIT Press.
    • (1995) Advances in Neural Information Processing Systems , vol.7 , pp. 973-980
    • Bregler, C.1    Omohundro, S.2
  • 11
    • 84872004031 scopus 로고    scopus 로고
    • Sample-based synthesis of photo-realistic talking-heads
    • IEEE Computer Society
    • E. Cosatto and H. P. Graf. Sample-based synthesis of photo-realistic talking-heads. In Proceedings of Computer Animation, pages 103-110. IEEE Computer Society, 1998.
    • (1998) Proceedings of Computer Animation , pp. 103-110
    • Cosatto, E.1    Graf, H.P.2
  • 17
    • 0000362092 scopus 로고
    • Nonlinear dimensionality reduction
    • D. Hanson, J. Cowan, and L. Giles, editors, San Mateo, CA. Morgan Kaufmann
    • D. DeMers and G.W. Cottrell. Nonlinear dimensionality reduction. In D. Hanson, J. Cowan, and L. Giles, editors, Advances in Neural Information Processing Systems 5, pages 580-587, San Mateo, CA, 1993. Morgan Kaufmann.
    • (1993) Advances in Neural Information Processing Systems , vol.5 , pp. 580-587
    • DeMers, D.1    Cottrell, G.W.2
  • 19
    • 2342600478 scopus 로고    scopus 로고
    • When does Isomap recover the natural parameterization of families of articulated images?
    • Department of Statistics, Stanford University, August
    • D. L. Donoho and C. E. Grimes. When does Isomap recover the natural parameterization of families of articulated images? Technical Report 2002-27, Department of Statistics, Stanford University, August 2002.
    • (2002) Technical Report , vol.2002 , Issue.27
    • Donoho, D.L.1    Grimes, C.E.2
  • 21
    • 0023657610 scopus 로고
    • An analogue approach to the traveling salesman problem using an elastic net method
    • R. Durbin and D. Wilshaw. An analogue approach to the traveling salesman problem using an elastic net method. Nature, 326:689-691, 1987.
    • (1987) Nature , vol.326 , pp. 689-691
    • Durbin, R.1    Wilshaw, D.2
  • 24
    • 0015011520 scopus 로고
    • An algorithm for finding intrinsic dimensionality of data
    • K. Fukunaga and D. R. Olsen. An algorithm for finding intrinsic dimensionality of data. IEEE Transactions on Computers, 20(2):176-193, 1971.
    • (1971) IEEE Transactions on Computers , vol.20 , Issue.2 , pp. 176-193
    • Fukunaga, K.1    Olsen, D.R.2
  • 25
    • 0003744820 scopus 로고    scopus 로고
    • The EM algorithm for mixtures of factor analyzers
    • (revised February 1997), Department of Computer Science, University of Toronto, May
    • Z. Ghahramani and G. E. Hinton. The EM algorithm for mixtures of factor analyzers. Technical Report CRG-TR-96-1 (revised February 1997), Department of Computer Science, University of Toronto, May 1996.
    • (1996) Technical Report , vol.CRG-TR-96-1
    • Ghahramani, Z.1    Hinton, G.E.2
  • 26
    • 84899027721 scopus 로고    scopus 로고
    • N-Body problems in statistical learning
    • T. K. Leen, T. G. Dietterich, and V. Tresp, editors, Cambridge, MA. MIT Press
    • A. G. Gray and A. W. Moore. N-Body problems in statistical learning. In T. K. Leen, T. G. Dietterich, and V. Tresp, editors, Advances in Neural Information Processing Systems 13, pages 521-527, Cambridge, MA, 2001. MIT Press.
    • (2001) Advances in Neural Information Processing Systems , vol.13 , pp. 521-527
    • Gray, A.G.1    Moore, A.W.2
  • 34
    • 0344505705 scopus 로고    scopus 로고
    • Independent component analysis in the presence of gaussian noise by maximizing joint likelihood
    • A. Hyvärinen. Independent component analysis in the presence of gaussian noise by maximizing joint likelihood. Neurocomputing, 22:49-67, 1998.
    • (1998) Neurocomputing , vol.22 , pp. 49-67
    • Hyvärinen, A.1
  • 38
    • 0348139702 scopus 로고    scopus 로고
    • Dimension reduction by local principal component analysis
    • N. Kambhatla and T. K. Leen. Dimension reduction by local principal component analysis. Neural Computation, 9:1493-1516, 1997.
    • (1997) Neural Computation , vol.9 , pp. 1493-1516
    • Kambhatla, N.1    Leen, T.K.2
  • 40
    • 84898957854 scopus 로고    scopus 로고
    • Intrinsic dimension estimation using packing numbers
    • S. Becker, S. Thrun, and K. Obermayer, editors, Cambridge, MA. MIT Press
    • B. Kegl. Intrinsic dimension estimation using packing numbers. In S. Becker, S. Thrun, and K. Obermayer, editors, Advances in Neural Information Processing Systems 15, Cambridge, MA, 2003. MIT Press.
    • (2003) Advances in Neural Information Processing Systems , vol.15
    • Kegl, B.1
  • 41
    • 0033882729 scopus 로고    scopus 로고
    • Data visualization by multidimensional scaling: A deterministic annealing approach
    • H. Klock and J. Buhmann. Data visualization by multidimensional scaling: a deterministic annealing approach. Pattern Recognition, 33:651, 1999.
    • (1999) Pattern Recognition , vol.33 , pp. 651
    • Klock, H.1    Buhmann, J.2
  • 43
    • 0026113980 scopus 로고
    • Nonlinear principal component analysis using autoassociative neural networks
    • M. Kramer. Nonlinear principal component analysis using autoassociative neural networks. AIChE Journal, 37:233, 1991.
    • (1991) AIChE Journal , vol.37 , pp. 233
    • Kramer, M.1
  • 48
    • 0012287167 scopus 로고    scopus 로고
    • Learning segmentation by random walks
    • S. A. Solla, T. K. Leen, and K.-R. Müller, editors, Cambridge, MA. MIT Press
    • M. Meila and J. Shi. Learning segmentation by random walks. In S. A. Solla, T. K. Leen, and K.-R. Müller, editors, Advances in Neural Information Processing Systems 12, pages 873-879, Cambridge, MA, 2000. MIT Press.
    • (2000) Advances in Neural Information Processing Systems , vol.12 , pp. 873-879
    • Meila, M.1    Shi, J.2
  • 50
    • 84899013108 scopus 로고    scopus 로고
    • On spectral clustering: Analysis and an algorithm
    • T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Cambridge, MA. MIT Press
    • A. Y. Ng, M. Jordan, and Y. Weiss. On spectral clustering: analysis and an algorithm. In T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Advances in Neural Information Processing Systems 14, pages 849-856, Cambridge, MA, 2002. MIT Press.
    • (2002) Advances in Neural Information Processing Systems , vol.14 , pp. 849-856
    • Ng, A.Y.1    Jordan, M.2    Weiss, Y.3
  • 51
    • 0013111818 scopus 로고
    • Five balltree construction algorithms
    • International Computer Science Institute, December
    • S. Omohundro. Five balltree construction algorithms. Technical Report TR-89-063, International Computer Science Institute, December 1989.
    • (1989) Technical Report , vol.TR-89-063
    • Omohundro, S.1
  • 52
    • 0003241739 scopus 로고
    • Bumptrees for efficient function, constraint, and classification learning
    • R. Lippmann, J. Moody, and D. Touretzky, editors, San Mateo, CA. Morgan Kaufmann
    • S. Omohundro. Bumptrees for efficient function, constraint, and classification learning. In R. Lippmann, J. Moody, and D. Touretzky, editors, Advances in Neural Information Processing 3, pages 693-699, San Mateo, CA, 1991. Morgan Kaufmann.
    • (1991) Advances in Neural Information Processing , vol.3 , pp. 693-699
    • Omohundro, S.1
  • 53
    • 84898934594 scopus 로고    scopus 로고
    • Grouping and dimensionality reduction by locally linear embedding
    • T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Cambridge, MA. MIT Press
    • P. Perona and M. Polito. Grouping and dimensionality reduction by locally linear embedding. In T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Advances in Neural Information Processing Systems 14, pages 1255-1262, Cambridge, MA, 2002. MIT Press.
    • (2002) Advances in Neural Information Processing Systems , vol.14 , pp. 1255-1262
    • Perona, P.1    Polito, M.2
  • 55
    • 0344940087 scopus 로고    scopus 로고
    • Embedding images in non-flat spaces
    • Washington University, December
    • R. Pless and I. Simon. Embedding images in non-flat spaces. Technical Report WU-CS-01-43, Washington University, December 2001.
    • (2001) Technical Report WU-CS-01-43
    • Pless, R.1    Simon, I.2
  • 57
    • 84898929664 scopus 로고    scopus 로고
    • EM algorthms for PCA and SPCA
    • M. Kearns, M. Jordan, and S. Solla, editors, pages, Cambridge, MA. MIT Press
    • S. T. Roweis. EM algorthms for PCA and SPCA. In M. Kearns, M. Jordan, and S. Solla, editors, Advances in neural information processing systems 10, pages 626-632, Cambridge, MA, 1998. MIT Press.
    • (1998) Advances in Neural Information Processing Systems , vol.10 , pp. 626-632
    • Roweis, S.T.1
  • 58
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • S. T. Roweis and L. K. Saul. Nonlinear dimensionality reduction by locally linear embedding. Science, 290:2323-2326, 2000.
    • (2000) Science , vol.290 , pp. 2323-2326
    • Roweis, S.T.1    Saul, L.K.2
  • 59
    • 84898962959 scopus 로고    scopus 로고
    • Global coordination of locally linear models
    • T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Cambridge, MA. MIT Press
    • S. T. Roweis, L. K. Saul, and G. E. Hinton. Global coordination of locally linear models. In T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Advances in Neural Information Processing Systems 14, pages 889-896, Cambridge, MA, 2002. MIT Press.
    • (2002) Advances in Neural Information Processing Systems , vol.14 , pp. 889-896
    • Roweis, S.T.1    Saul, L.K.2    Hinton, G.E.3
  • 60
    • 34250232348 scopus 로고
    • EM algorithms for ML factor analysis
    • D. B. Rubin and D. T. Thayer. EM algorithms for ML factor analysis. Psychometrika, 47:69-76, 1982.
    • (1982) Psychometrika , vol.47 , pp. 69-76
    • Rubin, D.B.1    Thayer, D.T.2
  • 61
    • 84898995573 scopus 로고    scopus 로고
    • Periodic component analysis: An eigenvalue method for representing periodic structure in speech
    • T. K. Leen, T. G. Dietterich, and V. Tresp, editors, Cambridge, MA. MIT Press
    • L. K. Saul and J. B. Allen. Periodic component analysis: an eigenvalue method for representing periodic structure in speech. In T. K. Leen, T. G. Dietterich, and V. Tresp, editors, Advances in Neural Information Processing Systems 13, pages 807-813, Cambridge, MA, 2001. MIT Press.
    • (2001) Advances in Neural Information Processing Systems , vol.13 , pp. 807-813
    • Saul, L.K.1    Allen, J.B.2
  • 62
    • 0033884177 scopus 로고    scopus 로고
    • Maximum likelihood and minimum classification error factor analysis for automatic speech recognition
    • L. K. Saul and M. G. Rahim. Maximum likelihood and minimum classification error factor analysis for automatic speech recognition. IEEE Transactions on Speech and Audio Processing, 8(2): 115-125, 1999.
    • (1999) IEEE Transactions on Speech and Audio Processing , vol.8 , Issue.2 , pp. 115-125
    • Saul, L.K.1    Rahim, M.G.2
  • 64
    • 0347243182 scopus 로고    scopus 로고
    • Nonlinear component analysis as a kernel eigenvalue problem
    • B. Schölkopf, A. J. Smola, and K.-R. Müller. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10:1299-1319, 1998.
    • (1998) Neural Computation , vol.10 , pp. 1299-1319
    • Schölkopf, B.1    Smola, A.J.2    Müller, K.-R.3
  • 65
    • 0034704189 scopus 로고    scopus 로고
    • The manifold ways of perception
    • H. S. Seung and D. D. Lee. The manifold ways of perception. Science, 290:2268-2269, 2000.
    • (2000) Science , vol.290 , pp. 2268-2269
    • Seung, H.S.1    Lee, D.D.2
  • 67
    • 34250297158 scopus 로고
    • Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features
    • . Takane and F. W. Young. Nonmetric individual differences multidimensional scaling: an alternating least squares method with optimal scaling features. Psychometrika, 42:7, 1977.
    • (1977) Psychometrika , vol.42 , pp. 7
    • Takane, Y.1    Young, F.W.2
  • 68
    • 0001790593 scopus 로고
    • Depth-first search and linear graph algorithms
    • R. Tarjan. Depth-first search and linear graph algorithms. SIAM Journal on Computing, 1(2), 1972.
    • (1972) SIAM Journal on Computing , vol.1 , Issue.2
    • Tarjan, R.1
  • 69
    • 0003237296 scopus 로고
    • Data structures and network algorithms
    • Society for Industrial and Applied Mathematics
    • R. Tarjan. Data structures and network algorithms. In CBMS, volume 44. Society for Industrial and Applied Mathematics, 1983.
    • (1983) CBMS , vol.44
    • Tarjan, R.1
  • 70
    • 10944266507 scopus 로고    scopus 로고
    • Automatic alignment of hidden representations
    • S. Decker, S. Thrun, and K. Obermayer, editors, Cambridge, MA. MIT Press
    • Y. W. Teh and S. T. Roweis. Automatic alignment of hidden representations. In S. Decker, S. Thrun, and K. Obermayer, editors, Advances in Neural Information Processing Systems 15, Cambridge, MA, 2003. MIT Press.
    • (2003) Advances in Neural Information Processing Systems , vol.15
    • Teh, Y.W.1    Roweis, S.T.2
  • 71
    • 84898986732 scopus 로고    scopus 로고
    • Mapping a manifold of perceptual observations
    • M. I. Jordan, M. J. Kearns, and S. A. Solla, editors, Cambridge, MA. MIT Press
    • J. Tenenbaum. Mapping a manifold of perceptual observations. In M. I. Jordan, M. J. Kearns, and S. A. Solla, editors, Advances in Neural Information Processing Systems 10, pages 682-688, Cambridge, MA, 1998. MIT Press.
    • (1998) Advances in Neural Information Processing Systems , vol.10 , pp. 682-688
    • Tenenbaum, J.1
  • 72
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • J. B. Tenenbaum, V. de Silva, and J. C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science, 290:2319-2323, 2000.
    • (2000) Science , vol.290 , pp. 2319-2323
    • Tenenbaum, J.B.1    De Silva, V.2    Langford, J.C.3
  • 73
    • 0033556788 scopus 로고    scopus 로고
    • Mixtures of probabilistic principal component analysers
    • M. E. Tipping and C. M. Bishop. Mixtures of probabilistic principal component analysers. Neural Computation, 11(2):443-482, 1999.
    • (1999) Neural Computation , vol.11 , Issue.2 , pp. 443-482
    • Tipping, M.E.1    Bishop, C.M.2
  • 74
    • 0042663523 scopus 로고    scopus 로고
    • Coordinating mixtures of probabilistic principal component analyzers
    • Computer Science Institute, University of Amsterdam, The Netherlands, February
    • J. J. Verbeek, N. Vlassis, and B. Kröse. Coordinating mixtures of probabilistic principal component analyzers. Technical Report IAS-UVA-02-01, Computer Science Institute, University of Amsterdam, The Netherlands, February 2002a.
    • (2002) Technical Report , vol.IAS-UVA-02-01
    • Verbeek, J.J.1    Vlassis, N.2    Kröse, B.3
  • 75
    • 0036605005 scopus 로고    scopus 로고
    • A k-segments algorithm for finding principal curves
    • J.J. Verbeek, N. Vlassis, and B. Kröse. A k-segments algorithm for finding principal curves. Pattern Recognition Letters, 23(8):1009-1017, 2002b.
    • (2002) Pattern Recognition Letters , vol.23 , Issue.8 , pp. 1009-1017
    • Verbeek, J.J.1    Vlassis, N.2    Kröse, B.3
  • 76
    • 0001683280 scopus 로고    scopus 로고
    • Supervised dimension reduction of intrinsically low-dimensional data
    • N. Vlassis, Y. Motomura, and B. Kröse. Supervised dimension reduction of intrinsically low-dimensional data. Neural Computation, 14(1):191-215, 2002.
    • (2002) Neural Computation , vol.14 , Issue.1 , pp. 191-215
    • Vlassis, N.1    Motomura, Y.2    Kröse, B.3
  • 78
    • 84898939890 scopus 로고    scopus 로고
    • On a connection between kernel PCA and metric multidimensional scaling
    • T. K. Leen, T. G. Dietterich, and V. Tresp, editors,Cambridge, MA. MIT Press
    • C. K. I. Williams. On a connection between kernel PCA and metric multidimensional scaling. In T. K. Leen, T. G. Dietterich, and V. Tresp, editors, Advances in Neural Information Processing Systems 13, pages 675-681, Cambridge, MA, 2001. MIT Press.
    • (2001) Advances in Neural Information Processing Systems , vol.13 , pp. 675-681
    • Williams, C.K.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.