Dimensionality reduction mappings

IEEE SSCI 2011: Symposium Series on Computational Intelligence - CIDM 2011: 2011 IEEE Symposium on Computational Intelligence and Data Mining

Volumn , Issue , 2011, Pages 349-356

  Bunte, Kerstin ^a   Biehl, Michael ^a   Hammer, Barbara ^b  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

^b BIELEFELD UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DATA MANIFOLDS; DATA POINTS; DIMENSIONALITY REDUCTION; DIMENSIONALITY REDUCTION METHOD; EVALUATION SCHEME; FINITE SET; GENERALIZATION ABILITY; LINEAR MAPPING; LOCAL LINEAR MAPPING; OUT-OF-SAMPLE EXTENSION; QUANTITATIVE EVALUATION;

ARTIFICIAL INTELLIGENCE; COST FUNCTIONS; DATA MINING; DATA VISUALIZATION; MAPPING; VISUALIZATION;

DATA REDUCTION;

EID: 79961193893     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CIDM.2011.5949443     Document Type: Conference Paper

References (27)

1. J. Lee and M. Verleysen, Nonlinear dimensionality reduction, 1st ed. Springer, 2007.
2. L. J. P. van der Maaten, E. O. Postma, and H. J. van den Herik, "Dimensionality reduction: A comparative review," Tilburg University, Tech. Rep. TiCC-TR 2009-005, Oct 2009.
3. L. van der Maaten and G. Hinton, "Visualizing data using t-sne," Journal of Machine Learning Research, vol. 9, pp. 2579-2605, November 2008.
4. D. A. Keim, F. Mansmann, J. Schneidewind, J. Thomas, and H. Ziegler, "Visual analytics: Scope and challenges," in Visual Data Mining: Theory, Techniques and Tools for Visual Analytics, S. Simoff, M. H. Boehlen, and A. Mazeika, Eds. Springer, 2008, lecture Notes in Computer Science (LNCS).
5. J. Venna, J. Peltonen, K. Nybo, H. Aidos, and S. Kaski, "Information retrieval perspective to nonlinear dimensionality reduction for data visualization," J. Mach. Learn. Res., vol. 11, pp. 451-490, 2010.
6. S. T. Roweis and L. K. Saul, "Nonlinear Dimensionality Reduction by Locally Linear Embedding," Science, vol. 290, no. 5500, pp. 2323-2326, 2000. (Pubitemid 32041578)
7. J. B. Tenenbaum, V. d. Silva, and J. C. Langford, "A Global Geometric Framework for Nonlinear Dimensionality Reduction," Science, vol. 290, no. 5500, pp. 2319-2323, 2000. (Pubitemid 32041577)
8. M. Belkin and P. Niyogi., "Laplacian eigenmaps for dimensionality reduction and data representation," Neural Computation, vol. 15, pp. 1373-15 396, 2003.
9. K. Q. Weinberger and L. K. Saul, "An introduction to nonlinear dimensionality reduction by maximum variance unfolding," Proceedings of the 21st National Conference on Artificial Intelligence, 2006.
10. G. Hinton and S. Roweis, "Stochastic neighbor embedding," in Advances in Neural Information Processing Systems 15. MIT Press, 2003, pp. 833-840.
11. M. Á. Carreira-perpiñán, "The elastic embedding algorithm for dimensionality reduction," in 27th Int. Conf. Machine Learning (ICML 2010), 2010, pp. 167-174.
12. L. J. P. van der Maaten, "Learning a parametric embedding by preserving local structure," in Proceedings of the 12th International Conference on Artificial Intelligence and Statistics (AI-STATS), no. 5. JMLR W&CP, 2009, pp. 384-391.
13. W. Torgerson, "Multidimensional scaling, i: Theory and method," Psychometrika, vol. 17, pp. 401-419, 1952.
14. C. Bishop, Pattern Recognition and Machine Learning. Springer, 2007.
15. M. Brand, "Charting a manifold," Mitsubishi Electric Research Laboratories (MERL), Tech. Rep. 15, 2003.
16. Y. Teh and S. Roweis, "Automatic alignment of local representations," Advances in Neural Information Processing Systems, vol. 15, pp. 841-848, 2003.
17. C. M. Bishop and C. K. I. Williams, "Gtm: The generative topographic mapping," Neural Computation, vol. 10, pp. 215-234, 1998. (Pubitemid 128463659)
18. T. Kohonen, Self-organizing Maps. Springer, 1995.
19. Y. W. Teh and S. Roweis, "Automatic alignment of local representations," in In Advances in Neural Information Processing Systems 15. MIT Press, 2003, pp. 841-848.
20. J. A. K. Suykens, "Data visualization and dimensionality reduction using kernel maps with a reference point," Neural Networks, IEEE Transactions on, vol. 19, no. 9, pp. 1501 -1517, sept. 2008.
21. J. A. Lee and M. Verleysen, "Rank-based quality assessment of nonlinear dimensionality reduction," in 16th European Symposium on Artificial Neural Networks (ESANN), Bruges, Belgium, 2008, pp. 49-54.
22. -, "Quality assessment of dimensionality reduction: Rank-based criteria," Neurocomput., vol. 72, no. 7-9, pp. 1431-1443, 2009.
23. R. Möller and H. Hoffmann, "An extension of neural gas to local pca," Neurocomputing, vol. 62, no. 305-326, 2004.
24. P. Schneider, M. Biehl, and B. Hammer, "Adaptive relevance matrices in learning vector quantization," Neural Computation, vol. 21, no. 12, pp. 3532-3561, 2009.
25. M. Cottrell, B. Hammer, A. Hasenfuss, and T. Villmann, "Batch and median neural gas," Neural Networks, vol. 19, pp. 762-771, 2006. (Pubitemid 44148955)
26. "Limited rank matrix learning: Discriminative dimension reduction and visualization," submitted to Neural Networks.
27. P. L. Bartlett and S. Mendelson, "Rademacher and gaussian complexities: risk bounds and structural results," J. Mach. Learn. Res., vol. 3, pp. 463-482, 2003.