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Neural Networks. A General Framework for Non-Linear Function Approximation

Author

Listed:
  • Fischer, Manfred M.
Abstract
The focus of this paper is on the neural network modelling approach that has gained increasing recognition in GIScience in recent years. The novelty about neural networks lies in their ability to model non-linear processes with few, if any, a priori assumptions about the nature of the data-generating process. The paper discusses some important issues that are central for successful application development. The scope is limited to feedforward neural networks, the leading example of neural networks. It is argued that failures in applications can usually be attributed to inadequate learning and/or inadequate complexity of the network model. Parameter estimation and a suitably chosen number of hidden units are, thus, of crucial importance for the success of real world neural network applications. The paper views network learning as an optimization problem, reviews two alternative approaches to network learning, and provides insights into current best practice to optimize complexity so to perform well on generalization tasks.

Suggested Citation

  • Fischer, Manfred M., 2006. "Neural Networks. A General Framework for Non-Linear Function Approximation," MPRA Paper 77776, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:77776
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    File URL: https://mpra.ub.uni-muenchen.de/77776/1/MPRA_paper_77776.pdf
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    References listed on IDEAS

    as
    1. Manfred M. Fischer & Katerina Hlavácková-Schindler & Martin Reismann, 1999. "articles: A global search procedure for parameter estimation in neural spatial interaction modelling," Papers in Regional Science, Springer;Regional Science Association International, vol. 78(2), pages 119-134.
    2. Manfred M. Fischer, 2002. "Learning in neural spatial interaction models: A statistical perspective," Journal of Geographical Systems, Springer, vol. 4(3), pages 287-299, October.
    3. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318, January.
    4. Manfred M. Fischer & Yee Leung, 1998. "A genetic-algorithms based evolutionary computational neural network for modelling spatial interaction data," ERSA conference papers ersa98p478, European Regional Science Association.
    5. Aura Reggiani (ed.), 2000. "Spatial Economic Science," Advances in Spatial Science, Springer, number 978-3-642-59787-9.
    6. Fischer, Manfred M. & Reismann, Martin, 2002. "A Methodology for Neural Spatial Interaction Modeling," MPRA Paper 77794, University Library of Munich, Germany.
    7. Manfred M. Fischer, 2000. "Methodological Challenges in Neural Spatial Interaction Modelling: The Issue of Model Selection," Advances in Spatial Science, in: Aura Reggiani (ed.), Spatial Economic Science, chapter 6, pages 89-101, Springer.
    8. Fischer, Manfred M. & Gopal, Sucharita, 1994. "Artificial Neural Networks. A New Approach to Modelling Interregional Telecommunication Flows," MPRA Paper 77822, University Library of Munich, Germany.
    9. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905, January.
    10. Manfred M. Fischer & Arthur Getis (ed.), 1997. "Recent Developments in Spatial Analysis," Advances in Spatial Science, Springer, number 978-3-662-03499-6.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Julian Hagenauer, 2016. "Weighted merge context for clustering and quantizing spatial data with self-organizing neural networks," Journal of Geographical Systems, Springer, vol. 18(1), pages 1-15, January.
    2. Alan T. Murray, 2010. "Quantitative Geography," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 143-163, February.

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    Keywords

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    JEL classification:

    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics

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