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Volumn 60, Issue 6, 2000, Pages 2114-2142

New approach to dimensionality reduction: Theory and algorithms

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; OPTIMIZATION; THEOREM PROVING;

EID: 0034476075     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139998338583     Document Type: Article
Times cited : (51)

References (26)
  • 2
    • 0027599793 scopus 로고
    • Universal approximation bounds for superpositions of a sigmoidal function
    • A. R. BARRON, Universal approximation bounds for superpositions of a sigmoidal function, IEEE Trans. Neural Networks, 39 (1993), pp. 930-945.
    • (1993) IEEE Trans. Neural Networks , vol.39 , pp. 930-945
    • Barron, A.R.1
  • 3
    • 0001325515 scopus 로고
    • Approximation and estimation bounds for artificial neural networks
    • A. R. BARRON, Approximation and estimation bounds for artificial neural networks, Mach. Learning, 14 (1994), pp. 115-133.
    • (1994) Mach. Learning , vol.14 , pp. 115-133
    • Barron, A.R.1
  • 4
    • 0000572613 scopus 로고
    • Local adaptive Galerkin bases for large-dimensional dynamical systems
    • D. BROOMHEAD, R. INDIK, A. NEWELL, AND D. RAND, Local adaptive Galerkin bases for large-dimensional dynamical systems, Nonlinearity, 4 (1991), pp. 159-197.
    • (1991) Nonlinearity , vol.4 , pp. 159-197
    • Broomhead, D.1    Indik, R.2    Newell, A.3    Rand, D.4
  • 5
    • 0000621802 scopus 로고
    • Multivariable functional interpolation and adaptive networks
    • D. BROOMHEAD AND D. LOWE, Multivariable functional interpolation and adaptive networks, Complex Systems, 2 (1988), pp. 321-355.
    • (1988) Complex Systems , vol.2 , pp. 321-355
    • Broomhead, D.1    Lowe, D.2
  • 6
    • 0000416890 scopus 로고
    • Topological dimension and local coordinates from time series data
    • D. S. BROOMHEAD, R. JONES, AND G. P. KING, Topological dimension and local coordinates from time series data, J. Phys. A, 20 (1987), pp. L563-L569.
    • (1987) J. Phys. A , vol.20
    • Broomhead, D.S.1    Jones, R.2    King, G.P.3
  • 7
    • 0015011520 scopus 로고
    • An algorithm for finding intrinsic dimensionality of data
    • K. FUKUNAGA AND D. OLSEN, An algorithm for finding intrinsic dimensionality of data, IEEE Trans. Comput., C-20 (1971), pp. 176-183.
    • (1971) IEEE Trans. Comput. , vol.C-20 , pp. 176-183
    • Fukunaga, K.1    Olsen, D.2
  • 9
    • 0003275073 scopus 로고
    • Differential topology
    • Springer, New York
    • M. W. HIRSCH, Differential Topology, Grad. Texts in Math. 33, Springer, New York, 1976.
    • (1976) Grad. Texts in Math. , vol.33
    • Hirsch, M.W.1
  • 10
    • 0343313294 scopus 로고    scopus 로고
    • Empirical dynamical system reduction II: Neural charts
    • K. Coughlin, ed., CRM Proc. Lecture Notes 20, AMS, Providence, RI
    • D. HUNDLEY, M. KIRBY, AND R. MIRANDA, Empirical dynamical system reduction II: Neural charts, in Semi-Analytic Methods for the Navier-Stokes Equations, K. Coughlin, ed., CRM Proc. Lecture Notes 20, AMS, Providence, RI, 1999, pp. 65-83.
    • (1999) Semi-Analytic Methods for the Navier-Stokes Equations , pp. 65-83
    • Hundley, D.1    Kirby, M.2    Miranda, R.3
  • 11
    • 0000618153 scopus 로고
    • Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces
    • J. M. HYMAN, B. NICOLAENKO, AND S. ZALESKI, Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces, Phys. D, 23 (1986), pp. 265-292.
    • (1986) Phys. D , vol.23 , pp. 265-292
    • Hyman, J.M.1    Nicolaenko, B.2    Zaleski, S.3
  • 12
    • 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 Comput., 9 (1997), pp. 1493-1516.
    • (1997) Neural Comput. , vol.9 , pp. 1493-1516
    • Kambhatla, N.1    Leen, T.K.2
  • 13
    • 0025448183 scopus 로고
    • Back in the saddle again: A computer assisted study of the Kuramoto-Sivashinsky equation
    • I. G. KEVREKIDIS, B. NICOLAENKO, AND J. C. SCOVEL, Back in the saddle again: A computer assisted study of the Kuramoto-Sivashinsky equation, SIAM J. Appl. Math., 50 (1990), pp. 760-790.
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 760-790
    • Kevrekidis, I.G.1    Nicolaenko, B.2    Scovel, J.C.3
  • 14
    • 0001719783 scopus 로고
    • Global bifurcations in Rayleigh-Bénard convection. Experiments, empirical maps and numerical bifurcation analysis
    • I. KEVREKIDIS, R. RICO-MARTINEZ, R. ECKE, R. FARBER, AND A. LAPEDES, Global bifurcations in Rayleigh-Bénard convection. Experiments, empirical maps and numerical bifurcation analysis, Phys. D, 71 (1994), pp. 342-362.
    • (1994) Phys. D , vol.71 , pp. 342-362
    • Kevrekidis, I.1    Rico-Martinez, R.2    Ecke, R.3    Farber, R.4    Lapedes, A.5
  • 15
    • 0000926806 scopus 로고
    • Minimal dynamical systems from partial differential equations using Sobolev eigen-functions
    • M. KIRBY, Minimal dynamical systems from partial differential equations using Sobolev eigen-functions, Phys. D, 57 (1992), pp. 466-475.
    • (1992) Phys. D , vol.57 , pp. 466-475
    • Kirby, M.1
  • 16
    • 0342878282 scopus 로고    scopus 로고
    • Ill-conditioning and gradient based optimization of multi-layer perceptrons
    • Mathematics in Signal Processing IV, J. McWhirter and I. Proudler, eds., Oxford University Press, London
    • M. KIRBY, Ill-conditioning and gradient based optimization of multi-layer perceptrons, in Mathematics in Signal Processing IV, J. McWhirter and I. Proudler, eds., Inst. Math. Appl. Conf. Ser. 67, Oxford University Press, London, 1998, pp. 223-237.
    • (1998) Inst. Math. Appl. Conf. Ser. , vol.67 , pp. 223-237
    • Kirby, M.1
  • 17
    • 0000907576 scopus 로고
    • Reconstructing phase-space from PDE simulations
    • M. KIRBY AND D. ARMBRUSTER, Reconstructing phase-space from PDE simulations, Z. Angew. Math. Phys., 43 (1992), pp. 999-1022.
    • (1992) Z. Angew. Math. Phys. , vol.43 , pp. 999-1022
    • Kirby, M.1    Armbruster, D.2
  • 18
    • 0005906830 scopus 로고
    • Nonlinear reduction of high-dimensional dynamical systems via neural networks
    • M. KIRBY AND R. MIRANDA, Nonlinear reduction of high-dimensional dynamical systems via neural networks, Phys. Rev. Lett., 72 (1994), pp. 1822-1825.
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 1822-1825
    • Kirby, M.1    Miranda, R.2
  • 19
    • 0028756019 scopus 로고
    • The remodeling of chaotic dynamical systems
    • S. Dagli, B. Fernandez, J. Ghosh, and R. S. Kumara, eds., The American Society of Mechanical Engineers, New York
    • M. KIRBY AND R. MIRANDA, The remodeling of chaotic dynamical systems, in Intelligent Engineering Through Artificial Neural Networks 4, S. Dagli, B. Fernandez, J. Ghosh, and R. S. Kumara, eds., The American Society of Mechanical Engineers, New York, 1994, pp. 831-836.
    • (1994) Intelligent Engineering Through Artificial Neural Networks 4 , pp. 831-836
    • Kirby, M.1    Miranda, R.2
  • 20
    • 0005667945 scopus 로고    scopus 로고
    • Empirical dynamical system reduction I: Global nonlinear trans-formations
    • Semi-Analytic Methods for the Navier-Stokes Equations, K. Coughlin, ed., AMS, Providence, RI
    • M. KIRBY AND R. MIRANDA, Empirical dynamical system reduction I: Global nonlinear trans-formations, in Semi-Analytic Methods for the Navier-Stokes Equations, K. Coughlin, ed., CRM Proc. Lecture Notes 20, AMS, Providence, RI, 1999, pp. 41-64.
    • (1999) Crm Proc. Lecture Notes , vol.20 , pp. 41-64
    • Kirby, M.1    Miranda, R.2
  • 21
    • 0025236073 scopus 로고
    • Application of the Karhunen-Loève procedure for the characterization of human faces
    • M. KIRBY AND L. SIROVICH, Application of the Karhunen-Loève procedure for the characterization of human faces, IEEE Trans. PAMI, 12 (1990), pp. 103-108.
    • (1990) IEEE Trans. PAMI , vol.12 , pp. 103-108
    • Kirby, M.1    Sirovich, L.2
  • 22
    • 0026113980 scopus 로고
    • Nonlinear principal component analysis using autoassociative neural networks
    • M. A. KRAMER, Nonlinear principal component analysis using autoassociative neural networks, AIChE J., 37 (1991), pp. 233-243.
    • (1991) AIChE J. , vol.37 , pp. 233-243
    • Kramer, M.A.1
  • 24
    • 0000621817 scopus 로고
    • Data compression, feature extraction, and autoassociation in feedforward neural networks
    • T. Kohonen, K. Mäkisara, O. Simula, and J. Kangas, eds., Elsevier Science Publishers, New York
    • E. OJA, Data compression, feature extraction, and autoassociation in feedforward neural networks, in Artificial Neural Networks, T. Kohonen, K. Mäkisara, O. Simula, and J. Kangas, eds., Elsevier Science Publishers, New York, 1991, pp. 737-745.
    • (1991) Artificial Neural Networks , pp. 737-745
    • Oja, E.1
  • 26
    • 84975551912 scopus 로고
    • A low-dimensional procedure for the characterization of human faces
    • L. SIROVICH AND M. KIRBY, A low-dimensional procedure for the characterization of human faces., J. Opt. Soc. Amer. A, 4 (1987), pp. 519-524.
    • (1987) J. Opt. Soc. Amer. A , vol.4 , pp. 519-524
    • Sirovich, L.1    Kirby, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.