Funtional vector quantization by neural maps

WHISPERS '09 - 1st Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing

Volumn , Issue , 2009, Pages

  Villmann, Thomas ^a   Schleif, Frank Michael ^b  

^a UNIVERSITY OF APPLIED SCIENCES MITTWEIDA   (Germany)

^b UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

Classification; Sobolev norms; Vector quantization

Indexed keywords

ADAPTIVE VECTOR QUANTIZATION; CLASSIFICATION; FUNCTIONAL DATAS; MINKOWSKI; REMOTE SENSING DATA; SOBOLEV;

ADAPTIVE ALGORITHMS; REMOTE SENSING; SIGNAL PROCESSING; VECTORS;

VECTOR QUANTIZATION;

EID: 72049118459     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/WHISPERS.2009.5289064     Document Type: Conference Paper

References (16)

1. B. Hammer, M. Strickert, and T. Villmann. Relevance lvq versus svm. In L. Rutkowski, J. Siek-mann, R. Tadeusiewicz, and L. Zadeh, editors, Artificial Intelligence and Soft Computing (ICAISC 2004), LNAI 3070, pages 592-597. Springer Verlag, Berlin-Heidelberg, 2004.
2. B. Hammer, M. Strickert, and T. Villmann. On the generalization ability of GRLVQ networks. Neural Processing Letters, 21(2):109-120, 2005.
3. I. Kantorowitsch and G. Akilow. Funktionalanalysis in normierten Räumen. Akademie-Verlag, Berlin, 2nd, rev. ed., 1978.
4. T. Kohonen. Self-Organizing Maps, volume 30 of Springer Series in Information Sciences. Springer, Berlin, Heidelberg, 1995. (2nd ext. ed. 1997).
5. A. Kolmogorov and S. Fomin. Reelle Funktionen und Funktionalanalysis. VEB Deutscher Verlag der Wis-senschaften, Berlin, 1975.
6. D. Landgrebe. Signal Theory Methods in Multispectral Remote Sensing. Wiley, Hoboken, New Jersey, 2003.
7. p norm for time series and its application to self-organizing maps. In M. Cottrell, editor, Proc. of Workshop on Self-Organizing Maps (WSOM) 2005, pages 733-740, Paris, Sorbonne, 2005.
8. T. M. Martinetz, S. G. Berkovich, and K. J. Schulten. 'Neural-gas' network for vector quantization and its application to time-series prediction. IEEE Trans. on Neural Networks, 4(4):558-569, 1993.
9. J. Ramsay and B. Silverman. Functional Data Analysis. Springer Science+Media, New York, 2nd edition, 2006.
10. F. Rossi, B. Conan-Guez, and A. E. Golli. Clustering functional data with the SOM algorithm. In M.Verleysen, editor, Europ. Symp. on Artif Neur. Netw. 2004, pages 305-312. d-side publications, 2004.
11. A. Sato and K. Yamada. Generalized learning vector quantization. In D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo, editors, Advances in Neural Information Processing Systems 8. Proc. of the 1995 Conf., pages 423-9. MIT Press, Cambridge, MA, USA, 1996.
12. B. Silverman. Smoothed functional principal components analysis by the choice of norm. The Annals of Statistics, 24(1):1-24, 1996.
13. T. Villmann. Sobolev metrics for learning of functional data - mathematical and theoretical aspects. Machine Learning Reports, 1(MLR-03-2007): 1-15, 2007. ISSN: 1865-3960, http://www.uni-leipzig.de/~compint/ mlr/mlr-01-2007.pdf.
14. T. Villmann and B. Hammer. Functional principal component learning using ojaŠs method and sobolev norms. In J. Principe, editor, Proc. of the Workshop on Self-Oranizing Maps (WSOM), page in press. Springer, 2009.
15. T. Villmann, B. Hammer, F.-M. Schleif, T. Geweniger, and W. Herrmann. Fuzzy classification by fuzzy labeled neural gas. Neural Networks, 19:772-779, 2006.
16. T. Villmann, E. Merényi, and B. Hammer. Neural maps in remote sensing image analysis. Neural Networks, 16(3-4):389-403, 2003.