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The Continuous Interpolating Self-organizing Map

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Abstract

The self-organizing map (SOM) [5] provides a general data approximation method which is suitable for several application domains. The topology preservation is an important feature in data-analysis and may also be advantageous for the evaluation of the data in a function approximation or regression task. For this reason the interpolated self-organizing map (I-SOM) adds an output layer to the SOM architecture which computes a real valued output vector. This paper presents an extension of I-SOM towards a continuous interpolation. It is compared to RBF and to the parametrized self-organizing map.

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References

  1. R. E. Barnhill, “Representation and approximation of surfaces”, in J.R. Rice, (ed.), Mathematical Software III, pp. 69–120, Academic Press, New York, 1977.

    Google Scholar 

  2. J. Göppert and W. Rosenstiel, “Interpolation in SOM: Improved generalization by iterative methods”, in Proc. of ICANN'95, pp. 425–434, Paris, France, 10 1995, EC2 & Cie.

    Google Scholar 

  3. J. Göppert and W. Rosenstiel, “Topological interpolation in SOM by affine transformations”, in Proc. of ESANN'95. D. facto, Vol. 4, 1995.

  4. Josef Göppert, “Die topologisch interpolierende selbstorganisierende Karte in den Funktionsapproximation (PhD Thesis)”, ISBN 3- 8265- 2401- 2, Shaker Verlag, Aachen, Germany, 1997.

    Google Scholar 

  5. T. Kohonen, “Self-organized formation of topology correct feature maps”, Biological Cybernetics, Vol. 43, pp. 59–69, 1982.

    Google Scholar 

  6. 6. T. Poggio and F. Girosi, “A theory of networks for approximation and learning”, AI memo 1140, MIT, 1989.

  7. H. Ritter, T. Martinez and K. Schulten, “Neuronale Netze: Eine Einführung in die Neuroinformatik Selbstorganisierender Netzwerke”, Addison Wesley, 1990.

  8. D. Shepard, “A two dimensional interpolation function for irregularly spaced data”, in Proc. 23rd Nat. Conf., pp. 517–523, ACM, 1968.

  9. J. Walter and H. Ritter, “Local PSOMs and Chebychev PSOMs improve the parameterized self-organizing maps”, in Proc. of ICANN'95, Vol. 1, pp. 95–102, Paris, France, 10 1995, EC2 & Cie.

    Google Scholar 

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Göppert, J., Rosentiel, W. The Continuous Interpolating Self-organizing Map. Neural Processing Letters 5, 185–192 (1997). https://doi.org/10.1023/A:1009694727439

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  • DOI: https://doi.org/10.1023/A:1009694727439

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