Abstract
In this paper we will give new aspects of the problem of finding relevant input arguments. This topic is of great interest in several scientific fields, such as complexity reduction or in applications in the areas of medicine, biology or technical fields.
Approximation theorists know well the problem of the curse of dimension, which causes problems for applications using approximation methods.
Here we give an approach which makes use of the scattered data interpolation abilities of Radial Basis Function Networks to handle this problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Caruana, R.A., Freitag, D. (1994): How useful is relevance? In: Working Notes of the AAAI Fall Symposium on Relevance, pp. 25–29, New Orleans, LA: AAAI Press.
Kiendl, H., Mache, D.H., Meyer, J., Schauten, D. (2003): Rekonstruktionsbasierte Selektion relevanter Einflussgrößen. In: Reihe Computational Intelligence des Son-derforschungsbereichs 531, Design und Management komplexer technischer Prozesse und Systeme mit Methoden der Computational Intelligence, Nr. CI-154/03.
Meyer, J. (2003): Multivariate Scattered Data Interpolation mit Radialen Basisfunktions Netzen als Ansatz zum Erkennen relevanter Eingabegrößen. Diploma thesis at the Institute for Applied Mathematics, Approximationstheorie at the University of Dortmund, supervised by Prof. Dr. D.H. Mache.
Micchelli, C.A. (1986): Interpolation of Scattered Data: Distances Matrices and Conditionally Positive Definite Functions. In: Constructive Approximation 2, pp. 11–22.
Wrobel, S., Morik, K., Joachims, T. (2000): Maschinelles Lernen and Data Mining. In: Görz, G., Rollinger, C.-R., Schneeberger, J. (Hrsg.) Handbuch der künstlichen Intelligenz. 3., vollständig überarbeitete Auflage. Oldenbourg-Verlag: München, Wien.
Pearson, K. (1901): On lines and places of closest fit to systems of points in space phil. Mag., 2: 559–572.
Pohlheim, H.: (2000): Evolutionäre Algorithmen. Springer-Verlag Berlin, Heidelberg, New York.
Shannon, C.E. (1948): A Mathematical Theory of Communication. In: The Bell System Technical Journal 27, 379–423 and 623–656.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Birkhäuser Verlag Basel/Switzerland
About this paper
Cite this paper
Mache, D.H., Meyer, J. (2005). Finding Relevant Input Arguments with Radial Basis Function Networks. In: Mache, D.H., Szabados, J., de Bruin, M.G. (eds) Trends and Applications in Constructive Approximation. ISNM International Series of Numerical Mathematics, vol 151. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7356-3_10
Download citation
DOI: https://doi.org/10.1007/3-7643-7356-3_10
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7124-1
Online ISBN: 978-3-7643-7356-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)