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Volumn 13, Issue , 2012, Pages 1609-1638

A unifying probabilistic perspective for spectral dimensionality reduction: Insights and new models

Author keywords

[No Author keywords available]

Indexed keywords

DIMENSIONALITY REDUCTION; GAUSSIAN MARKOV RANDOM FIELD; GAUSSIAN RANDOM FIELDS; HUMAN MOTION CAPTURE DATA; LAPLACIAN EIGENMAPS; LOCALLY LINEAR EMBEDDING; MAXIMUM ENTROPY; MAXIMUM ENTROPY PRINCIPLE; MAXIMUM VARIANCE; NEW MODEL; NONLINEAR GENERALIZATIONS; PARAMETER FITTING; ROBOT NAVIGATION;

EID: 84862001101     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (47)

References (31)
  • 1
    • 51849086132 scopus 로고    scopus 로고
    • Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data
    • Onureena Banerjee, Laurent El Ghaoui, and Alexandre d'Aspremont. Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data. Journal of Machine Learning Research, 2007.
    • (2007) Journal of Machine Learning Research
    • Banerjee, O.1    El Ghaoui, L.2    D'Aspremont, A.3
  • 2
    • 0042378381 scopus 로고    scopus 로고
    • Laplacian eigenmaps for dimensionality reduction and data representation
    • DOI 10.1162/089976603321780317
    • Mikhail Belkin and Partha Niyogi. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation, 15(6):1373-1396, 2003. doi: 10.1162/089976603321780317. (Pubitemid 37049796)
    • (2003) Neural Computation , vol.15 , Issue.6 , pp. 1373-1396
    • Belkin, M.1    Niyogi, P.2
  • 3
    • 4344599431 scopus 로고    scopus 로고
    • Learning eigenfunctions links spectral embedding and kernel PCA
    • DOI 10.1162/0899766041732396
    • Yoshua Bengio, Olivier Delalleau, Jean-Francois Palement, Nicolas Le Roux, Marie Ouimet, and Pascal Vincent. Learning eigenfunctions links spectral embedding and kernel PCA. Neural Computation, 16(10):2197-2219, 2004a. (Pubitemid 39137820)
    • (2004) Neural Computation , vol.16 , Issue.10 , pp. 2197-2219
    • Bengio, Y.1    Delalleau, O.2    Le Roux, N.3    Paiement, J.-F.4    Vincent, P.5    Ouimet, M.6
  • 4
    • 33947233031 scopus 로고    scopus 로고
    • Out-of-sample extensions for LLE, isomap, MDS, eigenmaps, and spectral clustering
    • Sebastian Thrun, Lawrence Saul, and Bernhard Schölkopf, editors, Cambridge, MA, MIT Press
    • Yoshua Bengio, Jean-Francois Paiement, Pascal Vincent, Olivier Delalleau, Nicolas Le Roux, and Marie Ouimet. Out-of-sample extensions for LLE, isomap, MDS, eigenmaps, and spectral clustering. In Sebastian Thrun, Lawrence Saul, and Bernhard Schölkopf, editors, Advances in Neural Information Processing Systems, volume 16, pages 177-184, Cambridge, MA, 2004b. MIT Press.
    • (2004) Advances in Neural Information Processing Systems , vol.16 , pp. 177-184
    • Bengio, Y.1    Paiement, J.-F.2    Vincent, P.3    Delalleau, O.4    Le Roux, N.5    Ouimet, M.6
  • 5
    • 0000582521 scopus 로고
    • Statistical analysis of non-lattice data
    • Julian Besag. Statistical analysis of non-lattice data. The Statistician, 24(3):179-195, 1975.
    • (1975) The Statistician , vol.24 , Issue.3 , pp. 179-195
    • Besag, J.1
  • 8
    • 85156256883 scopus 로고    scopus 로고
    • Does the wake-sleep algorithm learn good density estimators?
    • David Touretzky, Michael Mozer, and Mark Hasselmo, editors, Cambridge, MA, MIT Press
    • Brendan J. Frey, Geoffrey E. Hinton, and Peter Dayan. Does the wake-sleep algorithm learn good density estimators? In David Touretzky, Michael Mozer, and Mark Hasselmo, editors, Advances in Neural Information Processing Systems, volume 8, pages 661-670, Cambridge, MA, 1996. MIT Press.
    • (1996) Advances in Neural Information Processing Systems , vol.8 , pp. 661-670
    • Frey, B.J.1    Hinton, G.E.2    Dayan, P.3
  • 9
    • 45849134070 scopus 로고    scopus 로고
    • Sparse inverse covariance estimation with the graphical lasso
    • DOI 10.1093/biostatistics/kxm045
    • Jerome Friedman, Trevor Hastie, and Robert Tibshirani. Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3):432-441, Jul. 2008. doi: 10.1093/biostatistics/kxm045. (Pubitemid 351882084)
    • (2008) Biostatistics , vol.9 , Issue.3 , pp. 432-441
    • Friedman, J.1    Hastie, T.2    Tibshirani, R.3
  • 10
    • 11144299132 scopus 로고    scopus 로고
    • A kernel view of dimensionality reduction of manifolds
    • Russell Greiner and Dale Schuurmans, editors, Omnipress
    • Jihun Ham, Daniel D. Lee, Sebastian Mika, and Bernhard Schölkopf. A kernel view of dimensionality reduction of manifolds. In Russell Greiner and Dale Schuurmans, editors, Proceedings of the International Conference in Machine Learning, volume 21. Omnipress, 2004.
    • (2004) Proceedings of the International Conference in Machine Learning , vol.21
    • Ham, J.1    Lee, D.D.2    Mika, S.3    Schölkopf, B.4
  • 11
    • 0003678451 scopus 로고
    • Markov fields on finite graphs and lattices
    • John M. Hammersley and Peter Clifford. Markov fields on finite graphs and lattices. Technical report, 1971. URL http://www.statslab.cam.ac.uk/-grg/books/ hammfest/hamm-cliff.pdf.
    • (1971) Technical Report
    • Hammersley, J.M.1    Clifford, P.2
  • 12
    • 57849152974 scopus 로고    scopus 로고
    • Exploring model selection techniques for nonlinear dimensionality reduction
    • University of Edinburgh
    • Stefan Harmeling. Exploring model selection techniques for nonlinear dimensionality reduction. Technical Report EDI-INF-RR-0960, University of Edinburgh, 2007.
    • (2007) Technical Report EDI-INF-RR-0960
    • Harmeling, S.1
  • 14
    • 0002945580 scopus 로고
    • Bayesian methods: General background
    • J. H. Justice, editor, Cambridge University Press
    • Edwin T. Jaynes. Bayesian methods: General background. In J. H. Justice, editor, Maximum Entropy and Bayesian Methods in Applied Statistics, pages 1-25. Cambridge University Press, 1986.
    • (1986) Maximum Entropy and Bayesian Methods in Applied Statistics , pp. 1-25
    • Jaynes, E.T.1
  • 18
    • 84861999538 scopus 로고    scopus 로고
    • The neural autoregressive distribution estimator
    • Hugo Larochelle and Iain Murray. The neural autoregressive distribution estimator. JMLR: W&CP, 15:29-37, 2011.
    • (2011) JMLR: W&CP , vol.15 , pp. 29-37
    • Larochelle, H.1    Murray, I.2
  • 19
    • 84898980901 scopus 로고    scopus 로고
    • Gaussian process models for visualisation of high dimensional data
    • Sebastian Thrun, Lawrence Saul, and Bernhard Schölkopf, editors, Cambridge, MA, MIT Press
    • Neil D. Lawrence. Gaussian process models for visualisation of high dimensional data. In Sebastian Thrun, Lawrence Saul, and Bernhard Schölkopf, editors, Advances in Neural Information Processing Systems, volume 16, pages 329-336, Cambridge, MA, 2004. MIT Press.
    • (2004) Advances in Neural Information Processing Systems , vol.16 , pp. 329-336
    • Lawrence, N.D.1
  • 20
    • 27844605876 scopus 로고    scopus 로고
    • Probabilistic non-linear principal component analysis with Gaussian process latent variable models
    • Neil D. Lawrence. Probabilistic non-linear principal component analysis with Gaussian process latent variable models. Journal of Machine Learning Research, 6:1783-1816, 11 2005.
    • (2005) Journal of Machine Learning Research , vol.6 , Issue.11 , pp. 1783-1816
    • Lawrence, N.D.1
  • 21
    • 0347361674 scopus 로고    scopus 로고
    • Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data
    • Na Li and Matthew Stephens. Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data. Genetics, 165:2213-2233, 2003. URL http://www.genetics.org/cgi/content/abstract/ 165/4/2213. (Pubitemid 38040302)
    • (2003) Genetics , vol.165 , Issue.4 , pp. 2213-2233
    • Li, N.1    Stephens, M.2
  • 23
    • 44049116681 scopus 로고
    • Connectionist learning of belief networks
    • Radford M. Neal. Connectionist learning of belief networks. Artificial Intelligence, 56:71-113, 1992.
    • (1992) Artificial Intelligence , vol.56 , pp. 71-113
    • Neal, R.M.1
  • 24
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • DOI 10.1126/science.290.5500.2323
    • Sam T. Roweis and Lawrence K. Saul. Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500):2323-2326, 2000. doi: 10.1126/science.290.5500.2323. (Pubitemid 32041578)
    • (2000) Science , vol.290 , Issue.5500 , pp. 2323-2326
    • Roweis, S.T.1    Saul, L.K.2
  • 25
    • 0347243182 scopus 로고    scopus 로고
    • Nonlinear Component Analysis as a Kernel Eigenvalue Problem
    • Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10:1299-1319, 1998. doi: 10.1162/089976698300017467. (Pubitemid 128463674)
    • (1998) Neural Computation , vol.10 , Issue.5 , pp. 1299-1319
    • Scholkopf, B.1    Smola, A.2    Muller, K.-R.3
  • 26
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • DOI 10.1126/science.290.5500.2319
    • Joshua B. Tenenbaum, Virginia de Silva, and John C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500):2319-2323, 2000. doi: 10.1126/science.290.5500.2319. (Pubitemid 32041577)
    • (2000) Science , vol.290 , Issue.5500 , pp. 2319-2323
    • Tenenbaum, J.B.1    De Silva, V.2    Langford, J.C.3
  • 27
    • 0038959172 scopus 로고    scopus 로고
    • Probabilistic principal component analysis
    • doi: doi:10.1111/1467-9868.00196
    • Michael E. Tipping and Christopher M. Bishop. Probabilistic principal component analysis. Journal of the Royal Statistical Society, B, 6(3):611-622, 1999. doi: doi:10.1111/1467-9868.00196.
    • (1999) Journal of the Royal Statistical Society, B , vol.6 , Issue.3 , pp. 611-622
    • Tipping, M.E.1    Bishop, C.M.2
  • 28
    • 10644295905 scopus 로고    scopus 로고
    • Springer-Verlag, New York, ISBN 9780387402727
    • Larry A. Wasserman. All of Statistics. Springer-Verlag, New York, 2003. ISBN 9780387402727.
    • (2003) All of Statistics
    • Wasserman, L.A.1
  • 29
    • 14344251006 scopus 로고    scopus 로고
    • Learning a kernel matrix for nonlinear dimensionality reduction
    • Proceedings, Twenty-First International Conference on Machine Learning, ICML 2004
    • Kilian Q. Weinberger, Fei Sha, and Lawrence K. Saul. Learning a kernel matrix for nonlinear dimensionality reduction. In Russell Greiner and Dale Schuurmans, editors, Proceedings of the International Conference in Machine Learning, volume 21, pages 839-846. Omnipress, 2004. (Pubitemid 40290888)
    • (2004) Proceedings, Twenty-First International Conference on Machine Learning, ICML 2004 , pp. 839-846
    • Weinberger, K.Q.1    Sha, F.2    Saul, L.K.3
  • 30
    • 84898939890 scopus 로고    scopus 로고
    • On a connection between kernel PCA and metric multidimensional scaling
    • Todd K. Leen, Thomas G. Dietterich, and Volker Tresp, editors, Cambridge, MA, MIT Press
    • Christopher K. I. Williams. On a connection between kernel PCA and metric multidimensional scaling. In Todd K. Leen, Thomas G. Dietterich, and Volker Tresp, editors, Advances in Neural Information Processing Systems, volume 13, pages 675-681, Cambridge, MA, 2001. MIT Press.
    • (2001) Advances in Neural Information Processing Systems , vol.13 , pp. 675-681
    • Christopher, K.1    Williams, I.2
  • 31
    • 33749596705 scopus 로고    scopus 로고
    • Semi-supervised learning: From Gaussian fields to Gaussian processes
    • Carnegie Mellon University
    • Xiaojin Zhu, John Lafferty, and Zoubin Ghahramani. Semi-supervised learning: From Gaussian fields to Gaussian processes. Technical Report CMU-CS-03-175, Carnegie Mellon University, 2003.
    • (2003) Technical Report CMU-CS-03-175
    • Zhu, X.1    Lafferty, J.2    Ghahramani, Z.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.