Conical dimension as an intrisic dimension estimator and its applications

Proceedings of the 7th SIAM International Conference on Data Mining

Volumn , Issue , 2007, Pages 169-179

  Yang, Xin ^a   Michea, Sebastien ^a   Zha, Hongyuan ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b Georgia Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTERING ALGORITHMS;

APPLICATION AREA; CONFORMAL INVARIANCE; HIGH DIMENSIONAL DATA; INTRINSIC DIMENSIONS; ITS APPLICATIONS; MANIFOLD LEARNING; NUMERICAL ROBUSTNESS; SELF-INTERSECTIONS;

DATA MINING;

EID: 49749132118     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611972771.16     Document Type: Conference Paper

References (15)

1. Tenenbaum, J., De Silva, V. feLangford, J., A global geometric framework for nonlinear dimension reduction. Science,2 90:2319-2323, 2000.
2. Zhang, Z.&Zha, H. Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Al ignment. SIAM J. Scientific Computing,Vol. 26, No. 1, 313-338, 2004.Figure 21: Boundary detection of incomplete tire
3. Donoho, D., and Grimes, C, Hessian Eigenmaps new tools for nonlinear dimensionality reduction, Proceedings of National Academy of Science,5591-5596, 2003.
4. Sam T. Roweis and Lawrence K. Saul. Nonlinear Dimensionality Reduction by Locally Linear Embedding, Science,2 90:2323-2326, 2000.
5. Belkin, M. and Niyogi, P., Laplacian eigenmaps for dimensionality reduction and data compression, Advances in Neural Information Processing Systems,2002.
6. Kegl, B., Intrinsic dimension estimation using packing numbers. Advances in Neural Information Processing Systems,2003.
7. Levina, E. and Bickel, P., Maximum Likelihood Estimation of Intrinsic Dimension. Advances in Neural Information Processing Systems17 (NIPS2004). MIT Press, 2005.
8. Costa, J. and Hero, A. Geodesic entropic graphs for dimension and entropy estimation in manifold learning, IEEE Transactions on Signal Processing,52:2210-2221, 2004.
9. Raginsky, M., and Lazebnik, S., Estimation of intrinsic dimensionality using high-rate vector quantization, Advances in Neural Information Processing Systems,2005.
10. Fukunaga, K., and Olsen, D. R., An algorithm for finding intrinsic dimensionality of data, IEEE Transactions on Computers 20(2) (1976) 165-171.
11. Pettis, K., Bailey, T., Jain, T. and Dubes, R., An intrinsic dimensionality estimator from near-neighbor information, IEEE Transaction on Pattern Analysis and Machine Intelligence 1 (1) (1979) 25-37.
12. Trunk, G. V., Statistical estimation of the intrinsic dimensionality of a noisy signal collection, IEEE Transaction on Computers 25 (1976) 165-171.
13. Verveer, P. J., Duin, R., An evaluation of intrinsic dimensionality estimators, IEEE Transaction on Pattern Analysis and Machine Intelligence 17 (1) (1995) 81-86.
14. Camastra, F., and Vinciarelli, A., Estimating the intrinsic dimension of data with a fractal-based approach. IEEE Trans, on PAMI, 24(10): 1404-1407, 2002.
15. Yang, X., Pu,H., Zha, H. and Barlow, J., Semi-Supervised Nonlinear Dimensionality Reduction, Proceedings of the 23rd International Conference on Machine Learning, (ICML 2006).