Dimensionality Reduction by self organizing maps that preserve distances in output space

Proceedings of the International Joint Conference on Neural Networks

Volumn , Issue , 2009, Pages 432-438

  Campoy, Pascual ^a  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

DIMENSIONALITY REDUCTION; DOCUMENT INDEXING; FACE IMAGES; HIGH-DIMENSIONAL; INPUT DATAS; KEY FEATURE; KEY ISSUES; LEARNING PROCESS; NONLINEAR MANIFOLDS; SELF-ORGANIZATIONS;

DATA STRUCTURES; INFORMATION RETRIEVAL SYSTEMS; LEARNING ALGORITHMS; SELF ORGANIZING MAPS;

DATA REDUCTION;

EID: 70449434345     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/IJCNN.2009.5179009     Document Type: Conference Paper

References (23)

1. I. T. Jolliffe, Principal Component Analysis, Springer, New York, 1986.
2. C. Burges., Data Mining and Knowledge Discovery Handbook: A Complete Guide for Practitioners and Researchers, Academic Publishers, 2005.
3. E. P. L. J. P. Van der Maaten, H. van den Herik, Dimensionality reduction: A comparative review, Submitted to Neurocomputing.
4. I. Borg, P. Groenen, Modern multidimensional scaling, Springer-Verlag, New York, 1997, theory and applications.
5. J. B. Tenenbaum, V. de Silva, J. C. Langford, A global geometric framework for nonlinear dimensionality reduction, Science 290 (2000) 2319-2323. URL http://isomap. Stanford.edu/
6. K. Q. Weinberger, L. K. Saul, An introduction to nonlinear dimensionality reduction by maximum variance unfolding, in: AAAI, AAAI Press, 2006.
7. B. Schlkopf, A. Smola, K. Mller, Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation 10 (1998) 1299-1319.
8. J. S. Taylor, N. Cristianini, Kernel Methods for Pattern Analysis, Cambridge University Press, 2004. URL http://www.kernel-methods.net/
9. R. C. B. Nadler, S. Lafon, I. Kevrekidis, Diffusion maps, spectral clustering and the reaction coordinates of dynamical systems, Applied and Computational Harmonic Analysis: Special Issue on Diffusion Maps and Wavelets 21 (2006) 113-127.
10. S. Lafon, A. Lee, Diffusion maps and coarse-graining: A unified framework for dimensionality reduction, graph partitioning, and data set parameterization, IEEE Transactions on Pattern Analysis and Machine Intelligence 28 (9) (2006) 1393-1403.
11. M. A. Kramer, Nonlinear principal component analysis using autoassociative neural networks, AICHE Journal 37 (1991) 233-243.
12. D. DeMers, G. Cottrell, Non-linear dimensionality reduction, Advances in Neural Information Processing Systems 5 (1993) 580-587.
13. G. Hinton, R. Salakhutdinov, Reducing the dimensionality of data with neural networks, Science 313 (2006) 505-507.
14. S. T. Roweis, L. K. Saul, Nonlinear dimensionality reduction by locally linear embedding, Science 290 (2000) 2323-2326.
15. M. Belkin, P. Niyogi, Laplacian eigenmaps for dimensionality reduction and data representation, Neural Computation 15 (6) (2003) 1373-1396. URL http://neco.mitpress.org/cgi/content/abstract/15/6/1373
16. D. Donoho, C. Grimes, Hessian eigenmaps: New locally linear embedding techniques for high-dimensional data, in: Proceedings of the National Academy of Sciences, Vol. 102 (21), 2005, pp. 7426-7431.
17. Z. Zhang, H. Zha, Principal manifolds and nonlinear dimensionality reduction via local tangent space alignment, SIAM Journal of Scientific Computing 26 (1) (2004) 313-338.
18. X. F. W. C. L. Teng, H. Li, I. Shen., Dimension reduction of microarray data based on local tangent space alignment, in: Proceedings of the 4th IEEE International Conference on Cognitive Informatics, 2005, pp. 154-159.
19. M. Brand, Charting a manifold, Advances in Neural Information Processing Systems (2002) 985-992.
20. D. K. Agrafiotis, H. Xu, A self-organizing principle for learning nonlinear manifolds, PNAS 99 (25) (2002) 15869-15872. arXiv:http://www.pnas.org/ cgi/reprint/99/25/l5869.pdf, doi:10.1073/pnas.242424399. URL http://www.pnas.org/cgi/content/abstract/99/25/15869
21. T. Kohonen, Self-organized formation of topologically correct feature maps, Biological Cybernetics 43 (1982) 59-69.
22. D. Polani, Measures for the Organization of Self-Organizing Maps, Springer-Verlag, 2002.
23. L. Wiskott, T. Sejnowski, Objective functions for neural map formation, Lecture Notes in Computer Science 1327.