More topologically stable ISOMAP algorithm

Ruan Jian Xue Bao/Journal of Software

Volumn 18, Issue 4, 2007, Pages 869-877

  Shao, Chao ^a,b   Huang, Hou Kuan ^a   Zhao, Lian Wei ^a  

^a BEIJING JIAOTONG UNIVERSITY   (China)

^b HENAN UNIVERSITY OF ECONOMICS AND LAW   (China)

Author keywords

ISOMAP; Kernel density estimation; Local density; Neighborhood size; P ISOMAP (pruned ISOMAP); Residual variance; Topological stableness

Indexed keywords

MATLAB;

ISOMAP; KERNEL DENSITY ESTIMATION; LOCAL DENSITY; NEIGHBORHOOD SIZE; RESIDUAL VARIANCE; TOPOLOGICAL STABLENESS;

DATA VISUALIZATION;

EID: 34249692045     PISSN: 10009825     EISSN: None     Source Type: Journal    
DOI: 10.1360/jos180869     Document Type: Article

References (11)

1. Tenenbaum JB. Mapping a manifold of perceptual observations. In: Jordan MI, Kearns MJ, Solla SA, eds. Advances in Neural Information Processing Systems 10. Denver: MIT Press, 1997. 682-689.
2. Tenenbaum JB, de Silva V, Langford JC. A global geometric framework for nonlinear dimensionality reduction. Science, 2000, 290(22):2319-2323.
3. Roweis ST, Saul LK. Nonlinear dimensionality reduction by locally linear embedding. Science, 2000,290(22):2323-2326.
4. Balasubramanian M, Schwartz EL, Tenenbaum JB, de Silva V, Langford JC. The ISOMAP algorithm and topological stability. Science, 2002,295(5552):7. http://www.sciencemag.org/cgi/content/full/295/5552/7a
5. Kouropteva O, Okun O, Pietik-ainen M. Selection of the optimal parameter value for the locally linear embedding algorithm. In: Wang L, Halgamuge SK, Yao X, eds. Proc. of the 1st Int'l Conf. on Fuzzy Systems and Knowledge Discovery: Computational Intelligence for the E-Age. Singapore, 2002. 359-363. http://www.ee.oulu.fi/research/imag/document/publications/FSKD02.pdf
6. Shao C, Huang HK. Selection of the optimal parameter value for the isomap algorithm. In: Gelbukh A, de Albornoz A, Terashima H, eds. Proc. of the 4th Mexican Int'l Conf. on Artificial Intelligence. Monterrey: Springer-Verlag, 2005. 396-404.
7. Zhou ZH, Cao CG. Neural Networks and Its Applications. Beijing: Tsinghua University Press, 2004. 172-207 (in Chinese).
8. Bernstein M, de Silva V, Langford JC, Tenenbaum JB. Graph approximations to geodesics on embedded manifolds. Technical Report, Stanford University, 2000. http://isomap.stanford.edu/BdSLT.pdf
9. Lee JA, Lendasse A, Verleysen M. Nonlinear projection with curvilinear distances: ISOMAP versus curvilinear distance analysis. Neurocomputing, 2004,57(1):49-76.
10. Carreira-Perpiñán Má. A review of dimension reduction techniques. Technical Report, CS-96-09, Sheffield: University of Sheffield, 1996. 46-53.
11. Pelletier B. Kernel density estimation on riemannian manifolds. Statistics and Probability Letters, 2005,73(3):297-304.