Gaussian Fitting Based FDA for Chemometrics

  • Tuomas Kärnä
  • Amaury Lendasse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4507)


In Functional Data Analysis (FDA) multivariate data are considered as sampled functions. We propose a non-supervised method for finding a good function basis that is built on the data set. The basis consists of a set of Gaussian kernels that are optimized for an accurate fitting. The proposed methodology is experimented with two spectrometric data sets. The obtained weights are further scaled using a Delta Test (DT) to improve the prediction performance. Least Squares Support Vector Machine (LS-SVM) model is used for estimation.


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  1. 1.
    Ramsay, J., Silverman, B.: Functional Data Analysis. Springer Series in Statistics. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  2. 2.
    Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming, Theory and Algorithms. John Wiley and Sons, New York (1993)zbMATHGoogle Scholar
  3. 3.
    Suykens, J., Van Gestel, T., De Brabanter, J., De Moor, B., Vandewalle, J.: Least Squares Support Vector Machines. World Scientific Publishing, Singapore (2002)zbMATHGoogle Scholar
  4. 4.
    Haykin, S.: Neural Networks: A Comprehensive Foundation, 2nd edn. Prentice Hall, New York (1999)zbMATHGoogle Scholar
  5. 5.
    Benoudjit, N., Cools, E., Meurens, M., Verleysen, M.: Chemometric calibration of infrared spectrometers: selection and validation of variables by non-linear models. Chemometrics and Intelligent Laboratory Systems 70, 47–53 (2004)CrossRefGoogle Scholar
  6. 6.
    Thodberg, H.: A Review of Bayesian Neural Networks with an Application to Near Infrared Spectroscopy. IEEE Transactions on Neural Networks 7, 56–72 (1996)CrossRefGoogle Scholar
  7. 7.
    Vila, J., Wagner, V., Neveu, P.: Pascal Neveu: Bayesian Nonlinear Model Selection and Neural Networks: A Conjugate Prior Approach. IEEE Transactions on Neural Networks 11, 265–278 (2000)CrossRefGoogle Scholar
  8. 8.
    Rossi, F., Lendasse, A., François, D., Wertz, V., Verleysen, M.: Mutual information for the selection of relevant variables in spectrometric nonlinear modelling. Chemometrics and Intelligent Laboratory Systems 80, 215–226 (2006)CrossRefGoogle Scholar
  9. 9.
    Aneiros-Pérez, G., Vieu, P.: Semi-functional partial linear regression. Statistics and Probability Letters 76, 1102–1110 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Ferré, L., Yao, A.: Smoothed Functional Inverse Regression. Statistica Sinica 15, 665–683 (2005)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Tuomas Kärnä
    • 1
  • Amaury Lendasse
    • 1
  1. 1.Helsinki University of Technology, Laboratory of Computer and Information Science, P.O. Box 5400 FI-02015Finland

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