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Building Smooth Neighbourhood Kernels via Functional Data Analysis

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Artificial Neural Networks: Formal Models and Their Applications – ICANN 2005 (ICANN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3697))

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Abstract

In this paper we afford the problem of estimating high density regions from univariate or multivariate data samples. To be more precise, we propose a method based on the use of functional data analysis techniques for the construction of smooth kernel functions oriented to solve the One-Class problem. The proposed kernels increase the precision of One-Class estimation procedures. The advantages of this new point of view are shown using data sets drawn from representative density functions.

An erratum to this chapter can be found at http://dx.doi.org/10.1007/11550907_163 .

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References

  1. Moguerza, J.M., Muñoz, A.: Solving the One-Class Problem Using Neighbourhood Measures. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 680–688. Springer, Heidelberg (2004)

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  2. Ramsay, J.O., Silverman, B.W.: Functional Data Analysis. Springer, Heidelberg (1997)

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  3. Schölkopf, B., Platt, J.C., Shawe-Taylor, J., Smola, A.J., Williamson, R.C.: Estimating the Support of a High Dimensional Distribution. Neural Computation 13(7), 1443–1471 (2001)

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  4. Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, Boca Raton (1990)

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  5. Tikhonov, A.N., Arsenin, V.Y.: Solutions of ill-posed problems. John Wiley & Sons, New York (1977)

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Author information

Authors and Affiliations

  1. University Carlos III, c/ Madrid 126, 28903, Getafe, Spain

    Alberto Muñoz

  2. University Rey Juan Carlos, c/ Tulipán s/n, 28933, Móstoles, Spain

    Javier M. Moguerza

Authors
  1. Alberto Muñoz
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  2. Javier M. Moguerza
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Editor information

Editors and Affiliations

  1. Department of Informatics, Nicolaus Copernicus University, Toruń, Poland

    Włodzisław Duch

  2. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447, Warsaw, Poland

    Janusz Kacprzyk

  3. Adaptive Informatics Research Centre, Helsinki University of Technology, P.O. Box 5400, 02015, HUT, Finland

    Erkki Oja

  4. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Sławomir Zadrożny

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© 2005 Springer-Verlag Berlin Heidelberg

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Muñoz, A., Moguerza, J.M. (2005). Building Smooth Neighbourhood Kernels via Functional Data Analysis. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds) Artificial Neural Networks: Formal Models and Their Applications – ICANN 2005. ICANN 2005. Lecture Notes in Computer Science, vol 3697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11550907_100

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  • DOI: https://doi.org/10.1007/11550907_100

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28755-1

  • Online ISBN: 978-3-540-28756-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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