Artificial Neural Networks for Nonlinear Projection and Exploratory Data Analysis

  • Denis Hamad
  • Mohamed Betrouni


Mapping scheme consists in projecting data samples represented as points in high-dimensional data space onto a subspace of few dimensions, generally two dimensions. Mapping methods are used in order to eliminate statistical redundancies in the original data set and to facilitate the visual inspection of the data by the analyst which discover clusters between the data samples. A feedforward neural network trained by means of an unsupervised backpropagation algorithm is used for the nonlinear mapping. The Sammon’s stress is used as an error function for the learning algorithm. The number of hidden units is related to the complexity of the nonlinear functions that can be generated by the network and is selected by means of an informational criterion. To provide some insight into the behavior of the interactive system, and to presents its main facilities, some results are reported.


Hide Layer Feedforward Neural Network Hide Unit Informational Criterion Nonlinear Principal Component Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Siedlecki W. Siedlecka K. and Sklansky J., “An Overview of Mapping Techniques for Exploratory Pattern Analysis,” Pattern Recognition, Vol. 21, No. 5, pp. 411–429, 1988.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Daoudi M., Hamad D. and Postaire J.-G., “A Display Oriented Technique for Interactive Pattern Recognition by Multilayer Neural Network”. In Proc. of IEEE ICNN, Vol. Ill, pp. 1633–1637, San Francisco, CA, March 1993.Google Scholar
  3. [3]
    Biswas G., Jain A. K. and Dubes R. C., “Evaluation of Projection Algorithms”. IEEE Trans. PAMI., Vol. 3, NO. 6, pp. 701–708, Nov. 1981.CrossRefGoogle Scholar
  4. [4]
    Sammon Jr., J. W., “A Non-linear Mapping for Data Structure Analysis,” IEEE Trans, on Computers, Vol. C- 18, pp. 401–409, May 1969.CrossRefGoogle Scholar
  5. [5]
    Kramer M.A., “Nonlinear Principal Component Analysis Using Autoassociative Neural Networks”, Aiche Journal, Vol. 37, N°. 2, pp. 233–243, February 1991.CrossRefGoogle Scholar
  6. [6]
    Jain A. K., and Mao J., “Artificial Neural Network for Non-linear Projection of Multivariate Data,” IJCNN, Vol. Ill, pp. 335-340, Baltimore, Maryland, June 7–11, 1992.Google Scholar
  7. [7]
    Akaike H., “A New Look at the Statistical Model Identification”, IEEE Trans. Appl. Comp. vol. AC-19, pp. 716–723, 1974.Google Scholar

Copyright information

© Springer-Verlag/Wien 1995

Authors and Affiliations

  • Denis Hamad
    • 1
  • Mohamed Betrouni
    • 1
  1. 1.Centre d’Automatique de LilleUSTLVilleneuve d’Ascq, CedexFrance

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