Functional principal component learning using oja's method and Sobolev norms

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5629 LNCS, Issue , 2009, Pages 325-333

  Villmann, Thomas ^a   Hammer, Barbara ^b  

^a UNIVERSITY OF APPLIED SCIENCES MITTWEIDA   (Germany)

^b CLAUSTHAL UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Functional PCA; Neural gas Sobolev norms

Indexed keywords

CONVERGENCE AND STABILITY; EUCLIDEAN; FUNCTIONAL DATAS; FUNCTIONAL PCA; FUNCTIONAL PRINCIPAL COMPONENT ANALYSIS; INNER PRODUCT; NEURAL GAS; NEURAL GAS SOBOLEV-NORMS; PRINCIPAL COMPONENTS; SOBOLEV; SOBOLEV NORMS; THEORETICAL FOUNDATIONS; VECTOR QUANTIZERS;

CONFORMAL MAPPING; CONVERGENCE OF NUMERICAL METHODS; FINANCIAL DATA PROCESSING; SELF ORGANIZING MAPS;

PRINCIPAL COMPONENT ANALYSIS;

EID: 69049086738     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-02397-2_37     Document Type: Conference Paper

References (16)

1. Kantorowitsch, I., Akilow, G.: Funktionalanalysis in normierten Räumen, 2nd revised edn. Akademie-Verlag, Berlin (1978)
2. Kolmogorov, A., Fomin, S.: Reelle Funktionen und Funktionalanalysis. VEB Deutscher Verlag der Wissenschaften, Berlin (1975)
3. Kushner, H., Clark, D.: Stochastic Appproximation Methods for Constrained and Unconstrained Systems. Springer, New York (1978)
4. Labusch, K., Barth, E., Martinetz, T.: Learning data representations with sparse coding neural gas. In: Verleysen, M. (ed.) Proceedings of the European Symposium on Artificial Neural Networks ESANN, pp. 233-238. D-Side Publications (2008)
5. Landgrebe, D.: Signal Theory Methods in Multispectral Remote Sensing. Wiley, Hoboken (2003)
6. Lee, J., Verleysen, M.: Generalization of the lp 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)
7. 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)
8. Oja, E.: Neural networks, principle components and suspaces. International Journal of Neural Systems 1, 61-68 (1989)
9. Oja, E.: Nonlinear pca: Algorithms and applications. In: Proc. of the World Congress on Neural Networks Portland, Portland, pp. 396-400 (1993)
10. Olshausen, B., Finch, D.: Emergnece of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381, 607-609 (1996)
11. Ramsay, J., Silverman, B.: Functional Data Analysis, 2nd edn. Springer Science+ Media, New York (2006)
12. Rossi, F., Delannay, N., Conan-Gueza, B., Verleysen, M.: Representation of functional data in neural networks. Neurocomputing 64, 183-210 (2005)
13. Sanger, T.: Optimal unsupervised learning in a single-layer linear feedforward neural network. Neural Networks 12, 459-473 (1989)
14. Triebel, H.: Analysis und mathematische Physik. BSB B.G., 3rd revised edn., Teubner Verlagsgesellschaft, Leipzig (1989)
15. Villmann, T.: 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
16. Villmann, T., Claussen, J.-C.: Magnification control in self-organizing maps and neural gas. Neural Computation 18(2), 446-469 (2006)