메뉴 건너뛰기




Volumn , Issue 9780817643768, 2006, Pages 231-252

Determining Intrinsic Dimension and Entropy of High-Dimensional Shape Spaces

Author keywords

entropy; geodesics; Intrinsic dimension; manifold learning; minimal spanning tree; nearest neighbor graph; Riemannian manifold

Indexed keywords


EID: 74949120047     PISSN: 21643679     EISSN: 21643725     Source Type: Book Series    
DOI: 10.1007/0-8176-4481-4_9     Document Type: Chapter
Times cited : (45)

References (23)
  • 1
    • 0042378381 scopus 로고    scopus 로고
    • Laplacian eigenmaps for dimensionality reduction and data representation
    • M. Belkin and P. Niyogi. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation, 15 (6): 1373-1396, June 2003.
    • (2003) Neural Computation , vol.15 , Issue.6 , pp. 1373-1396
    • Belkin, M.1    Niyogi, P.2
  • 6
    • 3543131272 scopus 로고    scopus 로고
    • Geodesic entropic graphs for dimension and entropy estimation in manifold learning
    • August
    • J. A. Costa and A. O. Hero. Geodesic entropic graphs for dimension and entropy estimation in manifold learning. IEEE Trans, on Signal Processing, 52 (8):2210-2221, August 2004.
    • (2004) IEEE Trans, on Signal Processing , vol.52 , Issue.8 , pp. 2210-2221
    • Costa, J.A.1    Hero, A.O.2
  • 7
    • 0037948870 scopus 로고    scopus 로고
    • Hessian eigenmaps: Locally linear embedding technique for high dimensional data
    • D. Donobo and C. Grimes. Hessian eigenmaps: locally linear embedding technique for high dimensional data. Proc. Nat. Acad. of Sci., 100 (10):5591-5596, 2003
    • (2003) Proc. Nat. Acad. of Sci. , vol.100 , Issue.10 , pp. 5591-5596
    • Donobo, D.1    Grimes, C.2
  • 8
    • 0002052671 scopus 로고    scopus 로고
    • On the definition and the construction of pockets on macromolecules
    • H. Edelsbrummer, M. Facello, and J. Liang. On the definition and the construction of pockets on macromolecules. Discrete Applied Math., 88:83-102. 1998.
    • (1998) Discrete Applied Math. , vol.88 , pp. 83-102
    • Edelsbrummer, H.1    Facello, M.2    Liang, J.3
  • 9
    • 85032752338 scopus 로고    scopus 로고
    • Applications of entropic spanning graphs
    • October
    • A. Hero. B. Ma, O. Michel, and J. Gorman. Applications of entropic spanning graphs. IEEE Signal Processing Magazine, 19 (5):85-95, October 2002.
    • (2002) IEEE Signal Processing Magazine , vol.19 , Issue.5 , pp. 85-95
    • Ma, A.H.1    Michel, O.2    Gorman, J.3
  • 11
    • 85156237082 scopus 로고    scopus 로고
    • Intrinsic dimension estimation using packing numbers
    • Vancouver, Canada. December
    • B. Kegl. Intrinsic dimension estimation using packing numbers. In Neural Information Processing Systems: NIPS, Vancouver, Canada. December 2002.
    • (2002) Neural Information Processing Systems: NIPS
    • Kegl, B.1
  • 13
    • 0032203257 scopus 로고    scopus 로고
    • Gradient-based learning applied to document recognition
    • Novermber
    • Y. LeCun, L. Bottou, Y. Bongio, and P. Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE. 86 (11):2278-2324. Novermber 1998.
    • (1998) Proceedings of the IEEE , vol.86 , Issue.11 , pp. 2278-2324
    • Lecun, Y.1    Bottou, L.2    Bongio, Y.3    Haffner, P.4
  • 14
    • 33745941948 scopus 로고    scopus 로고
    • Maximum likelihood estimation of intrinside dimension
    • Vancouver, Canada, December
    • E. Levina and P. Bickel. Maximum likelihood estimation of intrinside dimension. In Neural Information Processing Systems: NIPS. Vancouver, Canada, December 2004.
    • (2004) Neural Information Processing Systems: NIPS
    • Levina, E.1    Bickel, P.2
  • 16
    • 27544501369 scopus 로고    scopus 로고
    • Linage registration using entropy measures and entropic graphs. European Journal of Signal Processing
    • H. Neenuchwala. A. O. Hero, and P. Carson, linage registration using entropy measures and entropic graphs. European Journal of Signal Processing, Special Issue on Content-based Visual Information Retrieval. 85 (2):277-296, 2005.
    • (2005) Special Issue on Content-Based Visual Information Retrieval , vol.85 , Issue.2 , pp. 277-296
    • Neenuchwala, H.1    Hero, A.O.2    Carson, P.3
  • 17
    • 0039444596 scopus 로고    scopus 로고
    • A strong law for the largest nearest-neighbour link between random points
    • M. Penrose. A strong law for the largest nearest-neighbour link between random points. J. London Math. Soc., 60 (2) 951-960, 1999.
    • (1999) J. London Math. Soc. , vol.60 , Issue.2 , pp. 951-960
    • Penrose, M.1
  • 18
    • 0037274513 scopus 로고    scopus 로고
    • Weak laws of large numbers in geometric? Probability
    • M. Penrose and J. Yukich. Weak laws of large numbers in geometric? probability. Annals of Applied Probability, 13 (1):277-303, 2003.
    • (2003) Annals of Applied Probability , vol.13 , Issue.1 , pp. 277-303
    • Penrose, M.1    Yukich, J.2
  • 19
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • S. Rowels and L. Saul, Nonlinear dimensionality reduction by locally linear embedding. Science, 290 (1):2323-2326, 2000.
    • (2000) Science , vol.290 , Issue.1 , pp. 2323-2326
    • Rowels, S.1    Saul, L.2
  • 20
    • 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
  • 23
    • 14544307975 scopus 로고    scopus 로고
    • Principal manifolds and nonlinear dimension redaction via local tangent space alignment
    • Z. Zang and H. Zha. Principal manifolds and nonlinear dimension redaction via local tangent space alignment. SIAM Journal of Scientific Computing. 26 (1):313-338, 2001.
    • (2001) SIAM Journal of Scientific Computing , vol.26 , Issue.1 , pp. 313-338
    • Zang, Z.1    Zha, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.