[1] [1] Tenenbaum Joshua B,de Silva Vm,Langford John C.A Global Geometric Framework for Nonlinear Dimensionality Reduction[J].Science,2000,290(5500):2319-2323.

[2] [2] Roweis S T,Saul L K.Nonlinear Dimensionality Reduction by Locally Linear Embedding[J].Science,2000,290(5500):2323-2326.

[3] [3] Belkin M,Niyogi P.Laplacian Eigenmaps for Dimensionality Reduction and Data Representation[J].Neural Computations,2003,15(6):1373-1396.

[4] [4] Pettis K,Bailey T,Jain A K,et al.An Intrinsic Dimensionality Estimator from Near-neighbor Information[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1979,1(1):25-36.

[5] [5] Bruske J,Sommer G.Intrinsic Dimensionality Estimation with Optimally Topology Preserving Maps[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1998,20(5):572-575.

[6] [6] Mandekbrot B B.The Fractal Geometry of Nature[M].New York:W.H.Freeman and Company,1983.

[7] [7] Levina E,Bickel P.Maximum Likelihood Estimation of Intrinsic Dimension[M].Cambridge:MIT Press,2005.

[8] [8] Camastra F,Vinciarelli A.Estimating the Intrinsic Dimension of Data with a Fractal-based Method[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(10):1404-1407.

[9] [9] Kegl B.Intrinsic Dimension Estimation Using Packing Numbers[M].Cambridge:MIT Press,2003.

[10] [10] Costa J,Hero A O.Geodesic Entropic Graphs for Dimension and Entropy Estimation in Manifold Learning[J].IEEE Transactions on Signal Processing,2004,52(8):2210-2221.

[11] [11] Mordohai P,Medioni G.Unsupervised Dimensionality Estimation and Manifold Learning in High-dimensional Spaces by Tensor Voting[J].IEEE Transactions on Artificial Inteiligence,2005,24(6):798-803.

[12] [12] Costa J,Girotra A,Hero A O.Estimating Local Intrinsic Dimension with k-Nearest Neighbor Graphs[J].IEEE Transactions on Statistical Signal Processing,2005,30(23):1432-1436.

[14] [14] Armstrong M A.Basic Topology[M].New York:Springer-Verlag,1997.

[15] [15] Milnor J.Topology from the Differentiable Viewpoint[M].Princeton:Princeton University Press,1997.

[16] [16] Freedman D.Efficient Simplicial Reconstructions of Manifolds from their Samples[J].IEEE Transaction Pattern Analysis and Machine Intelligence,2002,24(10):1349-1357.