The Mathematics of Divergence Based Online Learning in Vector Quantization
Villmann T, Haase S, Schleif F-M, Hammer B, Biehl M (2010)
In: Artificial Neural Networks in Pattern Recognition. Schwenker F, El Gayar N (Eds); Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg: 108-119.
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| Veröffentlicht | Englisch
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Autor*in
Villmann, Thomas;
Haase, Sven;
Schleif, Frank-Michael;
Hammer, BarbaraUniBi 
;
Biehl, Michael
;
Biehl, MichaelHerausgeber*in
Schwenker, Friedhelm;
El Gayar, Neamat
Einrichtung
Abstract / Bemerkung
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. We provide the mathematical foundation of the respective framework. This framework includes usual gradient descent learning of prototypes as well as parameter optimization and relevance learning for improvement of the performance.
Erscheinungsjahr
2010
Buchtitel
Artificial Neural Networks in Pattern Recognition
Serientitel
Lecture Notes in Computer Science
Seite(n)
108-119
ISBN
978-3-642-12158-6
eISBN
978-3-642-12159-3
ISSN
0302-9743
eISSN
1611-3349
Page URI
https://pub.uni-bielefeld.de/record/2982116
Zitieren
Villmann T, Haase S, Schleif F-M, Hammer B, Biehl M. The Mathematics of Divergence Based Online Learning in Vector Quantization. In: Schwenker F, El Gayar N, eds. Artificial Neural Networks in Pattern Recognition. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg; 2010: 108-119.
Villmann, T., Haase, S., Schleif, F. - M., Hammer, B., & Biehl, M. (2010). The Mathematics of Divergence Based Online Learning in Vector Quantization. In F. Schwenker & N. El Gayar (Eds.), Lecture Notes in Computer Science. Artificial Neural Networks in Pattern Recognition (pp. 108-119). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-12159-3_10
Villmann, Thomas, Haase, Sven, Schleif, Frank-Michael, Hammer, Barbara, and Biehl, Michael. 2010. “The Mathematics of Divergence Based Online Learning in Vector Quantization”. In Artificial Neural Networks in Pattern Recognition, ed. Friedhelm Schwenker and Neamat El Gayar, 108-119. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg.
Villmann, T., Haase, S., Schleif, F. - M., Hammer, B., and Biehl, M. (2010). “The Mathematics of Divergence Based Online Learning in Vector Quantization” in Artificial Neural Networks in Pattern Recognition, Schwenker, F., and El Gayar, N. eds. Lecture Notes in Computer Science (Berlin, Heidelberg: Springer Berlin Heidelberg), 108-119.
Villmann, T., et al., 2010. The Mathematics of Divergence Based Online Learning in Vector Quantization. In F. Schwenker & N. El Gayar, eds. Artificial Neural Networks in Pattern Recognition. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 108-119.
T. Villmann, et al., “The Mathematics of Divergence Based Online Learning in Vector Quantization”, Artificial Neural Networks in Pattern Recognition, F. Schwenker and N. El Gayar, eds., Lecture Notes in Computer Science, Berlin, Heidelberg: Springer Berlin Heidelberg, 2010, pp.108-119.
Villmann, T., Haase, S., Schleif, F.-M., Hammer, B., Biehl, M.: The Mathematics of Divergence Based Online Learning in Vector Quantization. In: Schwenker, F. and El Gayar, N. (eds.) Artificial Neural Networks in Pattern Recognition. Lecture Notes in Computer Science. p. 108-119. Springer Berlin Heidelberg, Berlin, Heidelberg (2010).
Villmann, Thomas, Haase, Sven, Schleif, Frank-Michael, Hammer, Barbara, and Biehl, Michael. “The Mathematics of Divergence Based Online Learning in Vector Quantization”. Artificial Neural Networks in Pattern Recognition. Ed. Friedhelm Schwenker and Neamat El Gayar. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. Lecture Notes in Computer Science. 108-119.
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