Matrix Learning for Topographic Neural Maps
Arnonkijpanich B, Hammer B, Hasenfuss A, Lursinsap C (2008)
In: Artificial Neural Networks - ICANN 2008. Kůrková V, Neruda R, Koutník J (Eds); Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg: 572-582.
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| Veröffentlicht | Englisch
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Autor*in
Arnonkijpanich, Banchar;
Hammer, BarbaraUniBi
;
Hasenfuss, Alexander;
Lursinsap, Chidchanok
![](https://pub.uni-bielefeld.de/images/icon_orcid.png)
Herausgeber*in
Kůrková, Véra;
Neruda, Roman;
Koutník, Jan
Einrichtung
Abstract / Bemerkung
The self-organizing map (SOM) and neural gas (NG) constitute popular algorithms to represent data by means of prototypes arranged on a topographic map. Both methods rely on the Euclidean metric, hence clusters are isotropic. In this contribution, we extend prototype-based clustering algorithms such as NG and SOM towards a metric which is given by a full adaptive matrix such that ellipsoidal clusters are accounted for. We derive batch optimization learning rules for prototype and matrix adaptation based on a general cost function for NG and SOM and we show convergence of the algorithm. It can be seen that matrix learning implicitly performs minor local principal component analysis (PCA) and the local eigenvectors correspond to the main axes of the ellipsoidal clusters. We demonstrate the behavior in several examples.
Erscheinungsjahr
2008
Buchtitel
Artificial Neural Networks - ICANN 2008
Serientitel
Lecture Notes in Computer Science
Seite(n)
572-582
ISBN
978-3-540-87535-2
eISBN
978-3-540-87536-9
Page URI
https://pub.uni-bielefeld.de/record/2982119
Zitieren
Arnonkijpanich B, Hammer B, Hasenfuss A, Lursinsap C. Matrix Learning for Topographic Neural Maps. In: Kůrková V, Neruda R, Koutník J, eds. Artificial Neural Networks - ICANN 2008. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg; 2008: 572-582.
Arnonkijpanich, B., Hammer, B., Hasenfuss, A., & Lursinsap, C. (2008). Matrix Learning for Topographic Neural Maps. In V. Kůrková, R. Neruda, & J. Koutník (Eds.), Lecture Notes in Computer Science. Artificial Neural Networks - ICANN 2008 (pp. 572-582). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-87536-9_59
Arnonkijpanich, Banchar, Hammer, Barbara, Hasenfuss, Alexander, and Lursinsap, Chidchanok. 2008. “Matrix Learning for Topographic Neural Maps”. In Artificial Neural Networks - ICANN 2008, ed. Véra Kůrková, Roman Neruda, and Jan Koutník, 572-582. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg.
Arnonkijpanich, B., Hammer, B., Hasenfuss, A., and Lursinsap, C. (2008). “Matrix Learning for Topographic Neural Maps” in Artificial Neural Networks - ICANN 2008, Kůrková, V., Neruda, R., and Koutník, J. eds. Lecture Notes in Computer Science (Berlin, Heidelberg: Springer Berlin Heidelberg), 572-582.
Arnonkijpanich, B., et al., 2008. Matrix Learning for Topographic Neural Maps. In V. Kůrková, R. Neruda, & J. Koutník, eds. Artificial Neural Networks - ICANN 2008. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 572-582.
B. Arnonkijpanich, et al., “Matrix Learning for Topographic Neural Maps”, Artificial Neural Networks - ICANN 2008, V. Kůrková, R. Neruda, and J. Koutník, eds., Lecture Notes in Computer Science, Berlin, Heidelberg: Springer Berlin Heidelberg, 2008, pp.572-582.
Arnonkijpanich, B., Hammer, B., Hasenfuss, A., Lursinsap, C.: Matrix Learning for Topographic Neural Maps. In: Kůrková, V., Neruda, R., and Koutník, J. (eds.) Artificial Neural Networks - ICANN 2008. Lecture Notes in Computer Science. p. 572-582. Springer Berlin Heidelberg, Berlin, Heidelberg (2008).
Arnonkijpanich, Banchar, Hammer, Barbara, Hasenfuss, Alexander, and Lursinsap, Chidchanok. “Matrix Learning for Topographic Neural Maps”. Artificial Neural Networks - ICANN 2008. Ed. Véra Kůrková, Roman Neruda, and Jan Koutník. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. Lecture Notes in Computer Science. 572-582.