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Birkhäuser

Computer Intensive Methods in Control and Signal Processing

The Curse of Dimensionality

  • Book
  • © 1997

Overview

Editors:
  1. Miroslav Kárný

    1. Institute of Information Theory and Automation, Academy of Sciences, Prague, Czech Republic

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    You can also search for this editor in PubMed   Google Scholar

  2. Kevin Warwick

    1. Department of Cybernetics, University of Reading Whiteknights, Reading, UK

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    You can also search for this editor in PubMed   Google Scholar

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Fighting Dimensionality with Linguistic Geometry: Serial and Concurrent Strategies

    • Boris Stilman
    Pages 1-47

  3. Statistical Physics and the Optimization of Autonomous Behaviour in Complex Virtual Worlds

    • Robert W. Penney
    Pages 49-61

  4. On Merging Gradient Estimation with Mean-Tracking Techniques for Cluster Identification

    • Paul D. Fox, Elmawati L. Sutanto, Kevin Warwick
    Pages 63-72

  5. Computational Aspects of Graph Theoretic Methods in Control

    • Katalin M. Hangos, Zsolt Tuza
    Pages 73-92

  6. Efficient Algorithms for Predictive Control of Systems with Bounded Inputs

    • Luigi Chisci, A. Marongiu, F. Schoen, G. Zappa
    Pages 93-104

  7. Applying New Numerical Algorithms to the Solution of Discrete-Time Optimal Control Problems

    • Rüdiger Franke, Eckhard Arnold
    Pages 105-117

  8. System Modeling using Composition Networks

    • Yves Moreau, Joos Vandewalle
    Pages 119-140

  9. Recursive Nonlinear Estimation of Non-linear/Non-Gaussian Dynamic Models

    • Rudolf Kulhavý
    Pages 141-167

  10. Monte Carlo Approach to Bayesian Regression Modeling

    • Jan Smid, Petr Volf, Gopal Rao
    Pages 169-180

  11. Identification of Reality in Bayesian Context

    • Luděk Berec, Miroslav Kárný
    Pages 181-193

  12. Nonlinear Nonnormal Dynamic Models: State Estimation and Software

    • Miroslav Šimandl, Miroslav Flidr
    Pages 195-207

  13. The EM Algorithm: A Guided Tour

    • Christophe Couvreur
    Pages 209-222

  14. Estimation of Quasipolynomials in Noise: Theoretical, Algorithmic and Implementation Aspects

    • Vytautas Slivinskas, Virginija Šimonytè
    Pages 223-235

  15. Iterative Reconstruction of Transmission Sinograms with Low Signal to Noise Ratio

    • Johan Nuyts, Patrick Dupont, Luc Mortelmans
    Pages 237-248

  16. Curse of Dimensionality: Classifying Large Multi-Dimensional Images with Neural Networks

    • Rudolf Hanka, Thomas P. Harte
    Pages 249-260

  17. Dimension-Independent Rates of Approximation by Neural Networks

    • Věra Kůrková
    Pages 261-270

  18. Estimation of Human Signal Detection Performance from Event-Related Potentials Using Feed-Forward Neural Network Model

    • Miloš Koska, Roman Rosipal, Artur König, Leonard J. Trejo
    Pages 271-281

  19. Utilizing Geometric Anomalies of High Dimension: When Complexity Makes Computation Easier

    • Paul C. Kainen
    Pages 283-294

  20. Approximation Using Cubic B-Splines with Improved Training Speed and Accuracy

    • Julian D. Mason, Kateřina Hlaváčková, Kevin Warwick
    Pages 295-303
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Keywords

About this book

Due to the rapid increase in readily available computing power, a corre­ sponding increase in the complexity of problems being tackled has occurred in the field of systems as a whole. A plethora of new methods which can be used on the problems has also arisen with a constant desire to deal with more and more difficult applications. Unfortunately by increasing the ac­ curacy in models employed along with the use of appropriate algorithms with related features, the resultant necessary computations can often be of very high dimension. This brings with it a whole new breed of problem which has come to be known as "The Curse of Dimensionality" . The expression "Curse of Dimensionality" can be in fact traced back to Richard Bellman in the 1960's. However, it is only in the last few years that it has taken on a widespread practical significance although the term di­ mensionality does not have a unique precise meaning and is being used in a slightly different way in the context of algorithmic and stochastic complex­ ity theory or in every day engineering. In principle the dimensionality of a problem depends on three factors: on the engineering system (subject), on the concrete task to be solved and on the available resources. A system is of high dimension if it contains a lot of elements/variables and/or the rela­ tionship/connection between the elements/variables is complicated.

Editors and Affiliations

  • Institute of Information Theory and Automation, Academy of Sciences, Prague, Czech Republic

    Miroslav Kárný

  • Department of Cybernetics, University of Reading Whiteknights, Reading, UK

    Kevin Warwick

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