Abstract
We present a new interpolation technique allowing to build an approximation of a priori unknown principal manifolds of a data set which may be non-linear, non-connected and of various intrinsic dimension. This technique is based onto the Induced Delaunay Triangulation of the data built by a Topology Representing Network. It opens the way to a new field of research and applications in data analysis, data modeling and forecasting.
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
Hastie T, Stuetzle W. Principal curves. Journal of the American Statistical Association 1989, vol. 84, no. 406, pp. 502–516
Mulier F, Cherkassky V. Self-organization as an iterative kernel smoothing process. Neural Computation 1995, vol. 7, pp. 1165–1177
Ritter H. Parametrized self-organizing maps. In S. Gielen and B. Kappen Eds., Proc. of the Int. Conf. on Art. Neural Networks 1993, pp. 568–575, Springer Verlag, Berlin.
Walter J. Rapid learning in robotics. Cuvillier Verlag, Göttingen, Germany. Url:http://www.techfak.uni-bielefeld.de/~walter/
Göppert J, Rosenstiel W. Interpolation in SOM: Improved generalization by iterative methods. In EC2&Cie eds., Proc. of the Int. Conf. on Artificial Neural Networks 1995, vol. 10, Paris, France.
Aupetit M, Couturier P, Massotte P. Function approximation with continuous self-organizing maps using neighboring influence interpolation. Proc. of NC’2000, Berlin.
Martinetz T, Schulten K. Topology Representing Networks. Neural Networks 1994, vol. 7, no. 3, pp. 507–522, Elsevier Science.
Martinetz T, Berkovich S, Schulten K. “Neural-Gas” network for vector quantization and its application to time-series prediction. IEEE Trans, on Neural Networks 1993, vol. 4, no. 4, pp. 558–569
Moody J, Darken C. Fast learning in networks of locally-tuned processing units. Neural Computation 1989, vol. 1, pp. 281–294, MIT.
Bartels R, Beaty J, Barsky B. B-splines. Mathematiques et CAO, vol.4, Hermès 1988.
Sibson R. A brief description of natural neighbour interpolation. Interpreting Multivariate Data, pp. 21-36, V. Barnet eds., Wiley, Chichester 1981.
Aupetit M, Couturier P, Massotte P. Vector Quantization with γ-Observable Neighbors. Workshop on Self-Organizing Maps (WSOM01), Lincoln, UK, June 2001.
Marquardt D. J. Soc Appl. Math 1963, vol. 11, pp.431–441
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag London Limited
About this paper
Cite this paper
Aupetit, M., Couturier, P., Massotte, P. (2001). Induced Voronoï Kernels for Principal Manifolds Approximation. In: Advances in Self-Organising Maps. Springer, London. https://doi.org/10.1007/978-1-4471-0715-6_11
Download citation
DOI: https://doi.org/10.1007/978-1-4471-0715-6_11
Publisher Name: Springer, London
Print ISBN: 978-1-85233-511-3
Online ISBN: 978-1-4471-0715-6
eBook Packages: Springer Book Archive