메뉴 건너뛰기




Volumn 40, Issue 1, 2012, Pages 1-29

Nonlinear manifold representations for functional data

Author keywords

Dimension reduction; Functional data analysis; Functional manifold components; Modes of functional variation; Smoothing

Indexed keywords


EID: 84871206749     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AOS936     Document Type: Article
Times cited : (50)

References (34)
  • 2
    • 0042378381 scopus 로고    scopus 로고
    • Laplacian eigenmaps for dimensionality reduction and data representation
    • BELKIN, M. and NIYOGI, P. (2003). Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15 1373-1396.
    • (2003) Neural Comput. , vol.15 , pp. 1373-1396
    • Belkin, M.1    Niyogi, P.2
  • 4
    • 0022806525 scopus 로고
    • Principal modes of variation for processes with continuous sample curves
    • CASTRO, P. E., LAWTON, W. H. and SYLVESTRE, E. A. (1986). Principal modes of variation for processes with continuous sample curves. Technometrics 28 329-337.
    • (1986) Technometrics , vol.28 , pp. 329-337
    • Castro, P.E.1    Lawton, W.H.2    Sylvestre, E.A.3
  • 7
    • 84899009769 scopus 로고    scopus 로고
    • Global versus local methods in nonlinear dimensionality reduction
    • DE SILVA, V. and TENENBAUM, J. B. (2003). Global versus local methods in nonlinear dimensionality reduction. Adv. Neural Inf. Process. Syst. 15 721-728.
    • (2003) Adv. Neural Inf. Process. Syst. , vol.15 , pp. 721-728
    • De Silva, V.1    Tenenbaum, J.B.2
  • 9
    • 0037948870 scopus 로고    scopus 로고
    • Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
    • (electronic). MR19810199
    • DONOHO, D. L. and GRIMES, C. (2003). Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. Proc. Natl. Acad. Sci. USA 100 5591-5596 (electronic). MR19810199
    • (2003) Proc. Natl. Acad. Sci. USA , vol.100 , pp. 5591-5596
    • Donoho, D.L.1    Grimes, C.2
  • 10
    • 17444432924 scopus 로고    scopus 로고
    • Image manifolds which are isometric to Euclidean space
    • MR22089066
    • DONOHO, D. L. and GRIMES, C. (2005). Image manifolds which are isometric to Euclidean space. J. Math. Imaging Vision 23 5-24. MR22089066
    • (2005) J. Math. Imaging Vision , vol.23 , pp. 5-24
    • Donoho, D.L.1    Grimes, C.2
  • 13
    • 27944498298 scopus 로고    scopus 로고
    • Nonparametric maximum likelihood estimation of the structural mean of a sample of curves
    • MR22341877
    • GERVINI, D. and GASSER, T. (2005). Nonparametric maximum likelihood estimation of the structural mean of a sample of curves. Biometrika 92 801-820. MR22341877
    • (2005) Biometrika , vol.92 , pp. 801-820
    • Gervini, D.1    Gasser, T.2
  • 14
    • 0000360828 scopus 로고
    • Stochastic processes and statistical inference
    • MR00392022
    • GRENANDER, U. (1950). Stochastic processes and statistical inference. Ark. Mat. 1 195-277. MR00392022
    • (1950) Ark. Mat. , vol.1 , pp. 195-277
    • Grenander, U.1
  • 15
    • 35348874516 scopus 로고    scopus 로고
    • Methodology and convergence rates for functional linear regression
    • MR23322699
    • HALL, P. and HOROWITZ, J. L. (2007). Methodology and convergence rates for functional linear regression. Ann. Statist. 35 70-91. MR23322699
    • (2007) Ann. Statist. , vol.35 , pp. 70-91
    • Hall, P.1    Horowitz, J.L.2
  • 17
    • 80051862101 scopus 로고    scopus 로고
    • Inference on 3d Procrustes means: Tree bole growth, rank deficient diffusion tensors and perturbation models
    • HUCKEMANN, S. (2011). Inference on 3d Procrustes means: Tree bole growth, rank deficient diffusion tensors and perturbation models. Scand. J. Stat. 38 1467-9469.
    • (2011) Scand. J. Stat. , vol.38 , pp. 1467-9469
    • Huckemann, S.1
  • 18
    • 84858425542 scopus 로고    scopus 로고
    • Analysis of nonlinear modes of variation for functional data
    • MR23690299
    • IZEM, R. and MARRON, J. S. (2007). Analysis of nonlinear modes of variation for functional data. Electron. J. Stat. 1 641-676. MR23690299
    • (2007) Electron. J. Stat. , vol.1 , pp. 641-676
    • Izem, R.1    Marron, J.S.2
  • 19
    • 84887505391 scopus 로고
    • Displaying the important features of large collections of similar curves
    • JONES, M. C. and RICE, J. A. (1992). Displaying the important features of large collections of similar curves. Amer. Statist. 46 140-145.
    • (1992) Amer. Statist. , vol.46 , pp. 140-145
    • Jones, M.C.1    Rice, J.A.2
  • 22
    • 21144472058 scopus 로고
    • Statistical tools to analyze data representing a sample of curves
    • MR11862500
    • KNEIP, A. and GASSER, T. (1992). Statistical tools to analyze data representing a sample of curves. Ann. Statist. 20 1266-1305. MR11862500
    • (1992) Ann. Statist. , vol.20 , pp. 1266-1305
    • Kneip, A.1    Gasser, T.2
  • 23
    • 1542678851 scopus 로고    scopus 로고
    • Inference for density families using functional principal component analysis
    • KNEIP, A. and UTIKAL, K. J. (2001). Inference for density families using functional principal component analysis. J. Amer. Statist. Assoc. 96 519-531.
    • (2001) J. Amer. Statist. Assoc. , vol.96 , pp. 519-531
    • Kneip, A.1    Utikal, K.J.2
  • 24
    • 33749651702 scopus 로고    scopus 로고
    • Time ordering of gene co-expression
    • LENG, X. and MÜLLER, H. G. (2006). Time ordering of gene co-expression. Biostatistics 7 569-584.
    • (2006) Biostatistics , vol.7 , pp. 569-584
    • Leng, X.1    Müller, H.G.2
  • 26
    • 70349340213 scopus 로고    scopus 로고
    • Functional additive models
    • MR25042022
    • MÜLLER, H.-G. and YAO, F. (2008). Functional additive models. J. Amer. Statist. Assoc. 103 1534-1544. MR25042022
    • (2008) J. Amer. Statist. Assoc. , vol.103 , pp. 1534-1544
    • Müller, H.-G.1    Yao, F.2
  • 28
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • ROWEIS, S. T. and SAUL, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science 290 2323-2326.
    • (2000) Science , vol.290 , pp. 2323-2326
    • Roweis, S.T.1    Saul, L.K.2
  • 29
    • 0031742022 scopus 로고    scopus 로고
    • Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization
    • SPELLMAN, P. T., SHERLOCK, G. and ZHANG, M. Q. (1998). Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Mol. Biol. Cell 9 3273-3297.
    • (1998) Mol. Biol. Cell , vol.9 , pp. 3273-3297
    • Spellman, P.T.1    Sherlock, G.2    Zhang, M.Q.3
  • 30
    • 57749101466 scopus 로고    scopus 로고
    • Time-synchronized clustering of gene expression trajectories
    • TANG, R. and MÜLLER, H.-G. (2009). Time-synchronized clustering of gene expression trajectories. Biostatistics 10 32-45.
    • (2009) Biostatistics , vol.10 , pp. 32-45
    • Tang, R.1    Müller, H.-G.2
  • 31
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • TENENBAUM, J. B., DE SILVA, V. and LANGFORD, J. C. (2000). A global geometric framework for nonlinear dimensionality reduction. Science 290 2319-2323.
    • (2000) Science , vol.290 , pp. 2319-2323
    • Tenenbaum, J.B.1    De Silva, V.2    Langford, J.C.3
  • 33
    • 0033471035 scopus 로고    scopus 로고
    • Synchronizing sample curves nonparametrically
    • MR17147222
    • WANG, K. and GASSER, T. (1999). Synchronizing sample curves nonparametrically. Ann. Statist. 27 439-460. MR17147222
    • (1999) Ann. Statist. , vol.27 , pp. 439-460
    • Wang, K.1    Gasser, T.2
  • 34
    • 19744375466 scopus 로고    scopus 로고
    • Functional data analysis for sparse longitudinal data
    • MR21605611
    • YAO, F., MÜLLER, H.-G. and WANG, J.-L. (2005). Functional data analysis for sparse longitudinal data. J. Amer. Statist. Assoc. 100 577-590. MR21605611
    • (2005) J. Amer. Statist. Assoc. , vol.100 , pp. 577-590
    • Yao, F.1    Müller, H.-G.2    Wang, J.-L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.