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Divergence Based Online Learning in Vector Quantization

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Artificial Intelligence and Soft Computing (ICAISC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6113))

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Abstract

We propose the utilization of divergences in gradient descent learning of supervised and unsupervised vector quantization as an alternative for the squared Euclidean distance. The approach is based on the determination of the Fréchet-derivatives for the divergences, wich can be immediately plugged into the online-learning rules.

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References

  1. Amari, S.-I.: Differential-Geometrical Methods in Statistics. Springer, Heidelberg (1985)

    MATH  Google Scholar 

  2. Banerjee, A., Merugu, S., Dhillon, I., Ghosh, J.: Clustering with bregman divergences. Journal of Machine Learning Research 6, 1705–1749 (2005)

    MathSciNet  Google Scholar 

  3. Bauer, H.-U., Pawelzik, K.R.: Quantifying the neighborhood preservation of Self-Organizing Feature Maps. IEEE Trans. on Neural Networks 3(4), 570–579 (1992)

    Article  Google Scholar 

  4. Campbell, J.: Introduction to Remote Sensing. The Guilford Press, U.S.A. (1996)

    Google Scholar 

  5. Cichocki, A., Zdunek, R., Phan, A., Amari, S.-I.: Nonnegative Matrix and Tensor Factorizations. Wiley, Chichester (2009)

    Book  Google Scholar 

  6. Clark, R.N.: Spectroscopy of rocks and minerals, and principles of spectroscopy. In: Rencz, A. (ed.) Manual of Remote Sensing. John Wiley and Sons, Inc., New York (1999)

    Google Scholar 

  7. Cottrell, M., Hammer, B., Hasenfu, A., Villmann, T.: Batch and median neural gas. Neural Networks 19, 762–771 (2006)

    Article  MATH  Google Scholar 

  8. Csiszr, I.: Information-type measures of differences of probability distributions and indirect observations. Studia Sci. Math. Hungaria 2, 299–318 (1967)

    Google Scholar 

  9. Frigyik, B.A., Srivastava, S., Gupta, M.: An introduction to functional derivatives. Technical Report UWEETR-2008-0001, Dept of Electrical Engineering, University of Washington (2008)

    Google Scholar 

  10. Fujisawa, H., Eguchi, S.: Robust parameter estimation with a small bias against heavy contamination. Journal of Multivariate Analysis 99, 2053–2081 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Heskes, T.: Energy functions for self-organizing maps. In: Oja, E., Kaski, S. (eds.) Kohonen Maps, pp. 303–316. Elsevier, Amsterdam (1999)

    Chapter  Google Scholar 

  12. Hulle, M.M.V.: Kernel-based topographic map formation achieved with an information theoretic approach. Neural Networks 15, 1029–1039 (2002)

    Article  Google Scholar 

  13. Jang, E., Fyfe, C., Ko, H.: Bregman divergences and the self organising map. In: Fyfe, C., Kim, D., Lee, S.-Y., Yin, H. (eds.) IDEAL 2008. LNCS, vol. 5326, pp. 452–458. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Kantorowitsch, I., Akilow, G.: Funktionalanalysis in normierten Rumen, 2nd edn. Akademie-Verlag, Berlin (1978) (revised edition)

    Google Scholar 

  15. Kohonen, T.: Self-Organizing Maps. Springer Series in Information Sciences, vol. 30. Springer, Heidelberg (1995) (Second Extended Edition 1997)

    Google Scholar 

  16. Kullback, S., Leibler, R.: On information and sufficiency. Annals of Mathematical Statistics 22, 79–86 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  17. Lee, J., Verleysen, M.: Generalization of the l p norm for time series and its application to self-organizing maps. In: Cottrell, M. (ed.) Proc. of Workshop on Self-Organizing Maps, WSOM 2005, Paris, Sorbonne, pp. 733–740 (2005)

    Google Scholar 

  18. Lehn-Schiler, T., Hegde, A., Erdogmus, D., Principe, J.: Vector quantization using information theoretic concepts. Natural Computing 4(1), 39–51 (2005)

    Article  MathSciNet  Google Scholar 

  19. Linde, Y., Buzo, A., Gray, R.: An algorithm for vector quantizer design. IEEE Transactions on Communications 28, 84–95 (1980)

    Article  Google Scholar 

  20. Martinetz, T.M., Berkovich, S.G., Schulten, K.J.: ‘Neural-gas’ network for vector quantization and its application to time-series prediction. IEEE Trans. on Neural Networks 4(4), 558–569 (1993)

    Article  Google Scholar 

  21. Principe, J.C., FisherIII, J.W., Xu, D.: Information theoretic learning. In: Haykin, S. (ed.) Unsupervised Adaptive Filtering, Wiley, New York (2000)

    Google Scholar 

  22. Qin, A., Suganthan, P.: A novel kernel prototype-based learning algorithm. In: Proc. of the 17th Internat. Conf. on Pattern Recognition, ICPR 2004, vol. 4, pp. 621–624 (2004)

    Google Scholar 

  23. Renyi, A.: On measures of entropy and information. In: Proc. of the 4th Berkeley Symp. on Mathematical Statistics and Probability. Univ. of California Press, Berkeley (1961)

    Google Scholar 

  24. Renyi, A.: Probability Theory. North-Holland Publish. Company, Amsterdam (1970)

    Google Scholar 

  25. Sato, A., Yamada, K.: Generalized learning vector quantization. In: Touretzky, D.S., Mozer, M.C., Hasselmo, M.E. (eds.) Proc. of the 1995 Conf. on Advances in Neural Information Processing Systems, vol. 8, pp. 423–429. MIT Press, Cambridge (1996)

    Google Scholar 

  26. Villmann, T., Claussen, J.-C.: Magnification control in self-organizing maps and neural gas. Neural Computation 18(2), 446–469 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  27. Villmann, T., Haase, S.: Mathematical aspects of divergence based vector quantization using frchet-derivatives - extended and revised version. Machine Learning Reports 4(MLR-01-2010), 1–35 (2010), ISSN:1865-3960, http://www.uni-leipzig.de/~compint/mlr/mlr_01_2010.pdf

    Google Scholar 

  28. Villmann, T., Merényi, E., Hammer, B.: Neural maps in remote sensing image analysis. Neural Networks 16(3-4), 389–403 (2003)

    Article  Google Scholar 

  29. Villmann, T., Schleif, F.-M.: Functional vector quantization by neural maps. In: Chanussot, J. (ed.) Proceedings of First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS 2009), pp. 1–4. IEEE Press, Los Alamitos (2009)

    Chapter  Google Scholar 

  30. Zador, P.L.: Asymptotic quantization error of continuous signals and the quantization dimension. IEEE Transaction on Information Theory (28), 149–159 (1982)

    Article  MathSciNet  Google Scholar 

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Villmann, T., Haase, S., Schleif, FM., Hammer, B. (2010). Divergence Based Online Learning in Vector Quantization. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2010. Lecture Notes in Computer Science(), vol 6113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13208-7_60

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  • DOI: https://doi.org/10.1007/978-3-642-13208-7_60

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13207-0

  • Online ISBN: 978-3-642-13208-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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