Efficient Approximations of Kernel Robust Soft LVQ
Hofmann D, Gisbrecht A, Hammer B (2013)
In: Advances in Self-Organizing Maps. Estévez PA, Príncipe JC, Zegers P (Eds); Advances in Intelligent Systems and Computing. Berlin, Heidelberg: Springer Berlin Heidelberg: 183-192.
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| Veröffentlicht | Englisch
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Herausgeber*in
Estévez, Pablo A.;
Príncipe, José C.;
Zegers, Pablo
Abstract / Bemerkung
Robust soft learning vector quantization (RSLVQ) constitutes a probabilistic extension of learning vector quantization (LVQ) based on a labeled Gaussian mixture model of the data. Training optimizes the likelihood ratio of the model and recovers a variant similar to LVQ2.1 in the limit of small bandwidth. Recently, RSLVQ has been extended to a kernel version, thus opening the way towards more general data structures characterized in terms of a Gram matrix only. While leading to state of the art results, this extension has the drawback that models are no longer sparse, and quadratic training complexity is encountered. In this contribution, we investigate two approximation schemes which lead to sparse models: k-approximations of the prototypes and the Nyström approximation of the Gram matrix. We investigate the behavior of these approximations in a couple of benchmarks.
Erscheinungsjahr
2013
Buchtitel
Advances in Self-Organizing Maps
Serientitel
Advances in Intelligent Systems and Computing
Seite(n)
183-192
ISBN
978-3-642-35229-4
eISBN
978-3-642-35230-0
ISSN
2194-5357
eISSN
2194-5365
Page URI
https://pub.uni-bielefeld.de/record/2982102
Zitieren
Hofmann D, Gisbrecht A, Hammer B. Efficient Approximations of Kernel Robust Soft LVQ. In: Estévez PA, Príncipe JC, Zegers P, eds. Advances in Self-Organizing Maps. Advances in Intelligent Systems and Computing. Berlin, Heidelberg: Springer Berlin Heidelberg; 2013: 183-192.
Hofmann, D., Gisbrecht, A., & Hammer, B. (2013). Efficient Approximations of Kernel Robust Soft LVQ. In P. A. Estévez, J. C. Príncipe, & P. Zegers (Eds.), Advances in Intelligent Systems and Computing. Advances in Self-Organizing Maps (pp. 183-192). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-35230-0_19
Hofmann, Daniela, Gisbrecht, Andrej, and Hammer, Barbara. 2013. “Efficient Approximations of Kernel Robust Soft LVQ”. In Advances in Self-Organizing Maps, ed. Pablo A. Estévez, José C. Príncipe, and Pablo Zegers, 183-192. Advances in Intelligent Systems and Computing. Berlin, Heidelberg: Springer Berlin Heidelberg.
Hofmann, D., Gisbrecht, A., and Hammer, B. (2013). “Efficient Approximations of Kernel Robust Soft LVQ” in Advances in Self-Organizing Maps, Estévez, P. A., Príncipe, J. C., and Zegers, P. eds. Advances in Intelligent Systems and Computing (Berlin, Heidelberg: Springer Berlin Heidelberg), 183-192.
Hofmann, D., Gisbrecht, A., & Hammer, B., 2013. Efficient Approximations of Kernel Robust Soft LVQ. In P. A. Estévez, J. C. Príncipe, & P. Zegers, eds. Advances in Self-Organizing Maps. Advances in Intelligent Systems and Computing. Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 183-192.
D. Hofmann, A. Gisbrecht, and B. Hammer, “Efficient Approximations of Kernel Robust Soft LVQ”, Advances in Self-Organizing Maps, P.A. Estévez, J.C. Príncipe, and P. Zegers, eds., Advances in Intelligent Systems and Computing, Berlin, Heidelberg: Springer Berlin Heidelberg, 2013, pp.183-192.
Hofmann, D., Gisbrecht, A., Hammer, B.: Efficient Approximations of Kernel Robust Soft LVQ. In: Estévez, P.A., Príncipe, J.C., and Zegers, P. (eds.) Advances in Self-Organizing Maps. Advances in Intelligent Systems and Computing. p. 183-192. Springer Berlin Heidelberg, Berlin, Heidelberg (2013).
Hofmann, Daniela, Gisbrecht, Andrej, and Hammer, Barbara. “Efficient Approximations of Kernel Robust Soft LVQ”. Advances in Self-Organizing Maps. Ed. Pablo A. Estévez, José C. Príncipe, and Pablo Zegers. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. Advances in Intelligent Systems and Computing. 183-192.
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