Magnification in divergence based neural maps

Proceedings of the International Joint Conference on Neural Networks

Volumn , Issue , 2011, Pages 437-441

  Villmann, T ^a   Haase, S ^a  

^a UNIVERSITY OF APPLIED SCIENCES MITTWEIDA   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DATA CODING; DISSIMILARITY MEASURES; EUCLIDEAN DISTANCE; PARAMETER SETTING;

OPTIMIZATION; VECTOR QUANTIZATION;

NEURAL NETWORKS;

EID: 80054724538     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/IJCNN.2011.6033254     Document Type: Conference Paper

References (48)

1. Simon Haykin, Neural Networks - A Comprehensive Foundation, IEEE Press, New York, 1994.
2. Y. Linde, A. Buzo, and R.M. Gray, "An algorithm for vector quantizer design", IEEE Transactions on Communications, vol. 28, pp. 84-95, 1980.
3. B.D. Ripley, Pattern Recognition and Neural Networks, Cambridge University Press, 1996.
4. Stanley C. Ahalt, Ashok K. Krishnamurty, Prakoon Chen, and Douglas E. Melton, "Competitive learning algorithms for vector quantization", Neural Networks, vol. 3, no. 3, pp. 277-290, 1990
5. Bernd Fritzke, "Vector quantization with a growing and splitting elastic net", in Proc. ICANN'93, International Conference on Artificial Neural Networks, Stan Gielen and Bert Kappen, Eds., London, UK, 1993, pp. 580-585, Springer.
6. R. Linsker, "How to generate maps by maximizing the mutual information between input and output signals", Neural Computation, vol. 1, pp. 402-411, 1989.
7. Teuvo Kohonen, Self-Organizing Maps, vol. 30 of Springer Series in Information Sciences, Springer, Berlin, Heidelberg, 1995, (Second Extended Edition 1997).
8. Thomas M. Martinetz, Stanislav G. Berkovich, and Klaus J. Schulten, "'Neural-gas' network for vector quantization and its application to time-series prediction", IEEE Trans. on Neural Networks, vol. 4, no. 4, pp. 558-569, 1993.
9. R. Durbin and D. Willshaw, "An analogue approach to the travelling salesman problem using an elastic net method", Nature, vol. 326, pp. 689-691, 1987.
10. D. J. Willshaw and C. Von der Malsburg, "How patterned neural connections can be set up by self-organization", Proceedings of the Royal Society of London, Series B, vol. 194, pp. 431-445, 1976.
11. Christopher M. Bishop, Markus Svensén, and Christopher K. I. Williams, "GTM: The generative topographic mapping", Neural Computation, vol. 10, pp. 215-234, 1998.
12. Hans-Ulrich Bauer and Klaus R. Pawelzik, "Quantifying the neighborhood preservation of Self-Organizing Feature Maps", IEEE Trans. on Neural Networks, vol. 3, no. 4, pp. 570-579, 1992.
13. H.-U. Bauer, M. Herrmann, and Th. Villmann, "Neural maps and topographic vector quantization", Neural Networks, vol. 12, no. 4-5, pp. 659-676, 1999.
14. T. Villmann and J.-C. Claussen, "Magnification control in self-organizing maps and neural gas", Neural Computation, vol. 18, no. 2, pp. 446-469, February 2006.
15. Yi Zheng and J. F. Greenleaf, "The effect of concave and convex weight adjustments on self-organizing maps", IEEE Transactions on Neural Networks, vol. 7, no. 1, pp. 87-96, 1996.
16. A. Banerjee, S. Merugu, I.S. Dhillon, and J. Ghosh, "Clustering with bregman divergences", Journal of Machine Learning Research, vol. 6, pp. 1705-1749, 2005.
17. E. Jang, C. Fyfe, and H. Ko, "Bregman divergences and the self organising map", in Intelligent Data Engineering and Automated Learning IDEAL 2008, C. Fyfe, D. Kim, S.-Y. Lee, and H. Yin, Eds., LNCS 5326, pp. 452-458. Springer, 2008.
18. T. Lehn-Schiler, A. Hegde, D. Erdogmus, and J.C. Principe, "Vector quantization using information theoretic concepts", Natural Computing, vol. 4, no. 1, pp. 39-51, 2005.
19. A. Hegde, D. Erdogmus, T. Lehn-Schioler, Y.N. Rao, and J.C. Principe, "Vector quantization by density matching in the minimum Kullback-Leibler-divergence sense", in Proc. of the International Joint Conference on Artificial Neural Networks (IJCNN) - Budapest, IEEE Press, 2004, pp. 105-109.
20. T. Villmann and S. Haase, "Divergence based vector quantization", Neural Computation, vol. 23, no. 5, pp. 1343-1392, 2011.
21. A. Cichocki, R. Zdunek, A.H. Phan, and S.-I. Amari, Nonnegative Matrix and Tensor Factorizations, Wiley, Chichester, 2009.
22. H. Fujisawa and S. Eguchi, "Robust parameter estimation with a small bias against heavy contamination", Journal of Multivariate Analysis, vol. 99, pp. 2053-2081, 2008.
23. P. L. Zador, "Asymptotic quantization error of continuous signals and the quantization dimension", IEEE Transaction on Information Theory, , no. 28, pp. 149-159, 1982.
24. T. Heskes, "Energy functions for self-organizing maps", in Kohonen Maps, E. Oja and S. Kaski, Eds., pp. 303-316. Elsevier, Amsterdam, 1999.
25. Ed Erwin, Klaus Obermayer, and Klaus Schulten, "Self-organizing maps: Ordering, convergence properties and energy functions", Biol. Cyb., vol. 67, no. 1, pp. 47-55, 1992.
26. P. Grassberger and I. Procaccia, "Measuring the strangeness of strange attractors", Physica, vol. 9D, pp. 189-208, 1983.
27. F. Takens, "On the numerical determination of the dimension of an attractor", in Dynamical Systems and Bifurcations, B. Braaksma, H. Broer, and F. Takens, Eds., Berlin, 1985, pp. 99-106, Lecture Notes in Mathematics, N0 1125, Springer-Verlag Berlin.
28. F. Camastra and A. Vinciarelli, "Intrinsic dimension estimation of data: an approach based Grassberger-Procaccia's algorithm", Neural Processing Letters, vol. 14, pp. 27-34, 2001.
29. J.P. Eckmann and D. Ruelle, "Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems", Physica, vol. D56, pp. 185-187, 1992.
30. W. Liebert, Chaos und Herzdynamik, Verlag Harri Deutsch, Frankfurt/M., Germany, 1991.
31. J. Theiler, "Satistical precision of dimension estimators", Physical Reviews A, vol. 41, pp. 3038-3051, 1990.
32. Thomas Villmann, Wieland Hermann, and Michael Geyer, "Variants of self-organizing maps for data mining and data visualization in medicine", Neural Network World, vol. 10, no. 4, pp. 751-762, 2000.
33. Th. Villmann, "Neural maps for faithful data modelling in medicine - state of the art and exemplary applications", Neurocomputing, vol. 48, no. 1-4, pp. 229-250, 2002.
34. Th. Villmann, E. Merényi, and B. Hammer, "Neural maps in remote sensing image analysis", Neural Networks, vol. 16, no. 3-4, pp. 389-403, 2003.
35. Dominik Dersch and Paul Tavan, "Asymptotic level density in topological feature maps", IEEE Trans. on Neural Networks, vol. 6, no. 1, pp. 230-236, January 1995.
36. H. Ritter and K. Schulten, "On the stationary state of Kohonen's self-organizing sensory mapping", Biol. Cyb., vol. 54, pp. 99-106, 1986.
37. Helge Ritter, Thomas Martinetz, and Klaus Schulten, Neural Computation and Self-Organizing Maps: An Introduction, Addison-Wesley, Reading, MA, 1992.
38. E. Merényi, A. Jain, and T. Villmann, "Explicit magnification control of self-organizing maps for "forbidden" data", IEEE Transactions on Neural Networks, vol. 18, no. 3, pp. 786-797, May 2007.
39. H.-U. Bauer, R. Der, and M. Herrmann, "Controlling the magnification factor of self-organizing feature maps", Neural Computation, vol. 8, no. 4, pp. 757-771, 1996.
40. Thomas Villmann, "Controlling strategies for the magnification factor in the neural gas network", Neural Network World, vol. 10, no. 4, pp. 739-750, 2000.
41. Jens Christian Claussen, "Generalized winner relaxing Kohonen feature maps", Neural Computation, vol. 17, no. 5, pp. 997-1009, 2005.
42. J.C. Claussen and Th. Villmann, "Magnification control in winner relaxing neural gas", Neurocomputing, vol. 63, no. 1, pp. 125-137, 2005.
43. Duane DeSieno, "Adding a conscience to competitive learning", in Proc. ICNN'88, International Conference on Neural Networks, Piscataway, NJ, 1988, pp. 117-124, IEEE Service Center.
44. Marc M. van Hulle, Faithful Representations and Topographic Maps From Distortion- to Information-based Self-organization, J. Wiley & Sons, Inc., 2000.
45. B. Hammer and A. Hasenfuss, "Topographic mapping of large dissimilarity data sets", Neural Computation, vol. 22, no. 9, pp. 2229-2284, 2010.
46. S. Kullback and R.A. Leibler, "On information and sufficiency", Annals of Mathematical Statistics, vol. 22, pp. 79-86, 1951.
47. J.N. Kapur, Measures of Information and their Application, Wiley, New Delhi, 1994.
48. A. Cichocki and S.-I. Amari, "Families of alpha- beta- and gamma-divergences: Flexible and robust measures of similarities", Entropy, vol. 12, pp. 1532-1568, 2010.