Functional Principal Component Learning Using Oja’s Method and Sobolev Norms
Villmann T, Hammer B (2009)
In: Advances in Self-Organizing Maps. 7th International Workshop, WSOM 2009, St. Augustine, FL, USA, June 8-10, 2009. Proceedings. Príncipe JC, Miikkulainen R (Eds); Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg: 325-333.
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| Veröffentlicht | Englisch
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Autor*in
Villmann, Thomas;
Hammer, BarbaraUniBi 
Herausgeber*in
Príncipe, José C.;
Miikkulainen, Risto
Einrichtung
Abstract / Bemerkung
In this paper we present a method for functional principal component analysis based on the Oja-learning and neural gas vector quantizer. However, instead of the Euclidean inner product the Sobolev counterpart is applied, which takes the derivatives of the functional data into account and, therefore, uses information contained in the functional shape of the data into account. We investigate the theoretical foundations of the algorithm for convergence and stability and give exemplary applications.
Erscheinungsjahr
2009
Buchtitel
Advances in Self-Organizing Maps. 7th International Workshop, WSOM 2009, St. Augustine, FL, USA, June 8-10, 2009. Proceedings
Serientitel
Lecture Notes in Computer Science
Seite(n)
325-333
ISBN
978-3-642-02396-5
eISBN
978-3-642-02397-2
ISSN
0302-9743
eISSN
1611-3349
Page URI
https://pub.uni-bielefeld.de/record/2982118
Zitieren
Villmann T, Hammer B. Functional Principal Component Learning Using Oja’s Method and Sobolev Norms. In: Príncipe JC, Miikkulainen R, eds. Advances in Self-Organizing Maps. 7th International Workshop, WSOM 2009, St. Augustine, FL, USA, June 8-10, 2009. Proceedings. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg; 2009: 325-333.
Villmann, T., & Hammer, B. (2009). Functional Principal Component Learning Using Oja’s Method and Sobolev Norms. In J. C. Príncipe & R. Miikkulainen (Eds.), Lecture Notes in Computer Science. Advances in Self-Organizing Maps. 7th International Workshop, WSOM 2009, St. Augustine, FL, USA, June 8-10, 2009. Proceedings (pp. 325-333). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-02397-2_37
Villmann, Thomas, and Hammer, Barbara. 2009. “Functional Principal Component Learning Using Oja’s Method and Sobolev Norms”. In Advances in Self-Organizing Maps. 7th International Workshop, WSOM 2009, St. Augustine, FL, USA, June 8-10, 2009. Proceedings, ed. José C. Príncipe and Risto Miikkulainen, 325-333. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg.
Villmann, T., and Hammer, B. (2009). “Functional Principal Component Learning Using Oja’s Method and Sobolev Norms” in Advances in Self-Organizing Maps. 7th International Workshop, WSOM 2009, St. Augustine, FL, USA, June 8-10, 2009. Proceedings, Príncipe, J. C., and Miikkulainen, R. eds. Lecture Notes in Computer Science (Berlin, Heidelberg: Springer Berlin Heidelberg), 325-333.
Villmann, T., & Hammer, B., 2009. Functional Principal Component Learning Using Oja’s Method and Sobolev Norms. In J. C. Príncipe & R. Miikkulainen, eds. Advances in Self-Organizing Maps. 7th International Workshop, WSOM 2009, St. Augustine, FL, USA, June 8-10, 2009. Proceedings. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 325-333.
T. Villmann and B. Hammer, “Functional Principal Component Learning Using Oja’s Method and Sobolev Norms”, Advances in Self-Organizing Maps. 7th International Workshop, WSOM 2009, St. Augustine, FL, USA, June 8-10, 2009. Proceedings, J.C. Príncipe and R. Miikkulainen, eds., Lecture Notes in Computer Science, Berlin, Heidelberg: Springer Berlin Heidelberg, 2009, pp.325-333.
Villmann, T., Hammer, B.: Functional Principal Component Learning Using Oja’s Method and Sobolev Norms. In: Príncipe, J.C. and Miikkulainen, R. (eds.) Advances in Self-Organizing Maps. 7th International Workshop, WSOM 2009, St. Augustine, FL, USA, June 8-10, 2009. Proceedings. Lecture Notes in Computer Science. p. 325-333. Springer Berlin Heidelberg, Berlin, Heidelberg (2009).
Villmann, Thomas, and Hammer, Barbara. “Functional Principal Component Learning Using Oja’s Method and Sobolev Norms”. Advances in Self-Organizing Maps. 7th International Workshop, WSOM 2009, St. Augustine, FL, USA, June 8-10, 2009. Proceedings. Ed. José C. Príncipe and Risto Miikkulainen. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. Lecture Notes in Computer Science. 325-333.
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