Computer Intensive Methods in Control and Signal Processing: The Curse of Dimensionality

by Kevin Warwick, Miroslav Karny

Overview

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 dimensionality does not have a unique precise meaning and is being used in a slightly different way in the context of algorithmic and shastic complexity 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 relationship/connection between the elements/variables is complicated.

Product Details

ISBN-13:	9781461273738
Publisher:	Birkhäuser Boston
Publication date:	10/08/2012
Edition description:	Softcover reprint of the original 1st ed. 1997
Pages:	303
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1. Fighting Dimensionality with Linguistic Geometry.- 2. Statistical Physics and the Optimization of Autonomous Behaviour in Complex Virtual Worlds.- 3. On Merging Gradient Estimation with Mean-Tracking Techniques for Cluster Identification.- 4. Computational Aspects of Graph Theoretic Methods in Control.- 5. Efficient Algorithms for Predictive Control of Systems with Bounded Inputs.- 6. Applying New Numerical Algorithms to the Solution of Discrete-time Optimal Control Problems.- 7. System Identification using Composition Networks.- 8. Recursive Nonlinear Estimation of Non-linear/Non-Gaussian Dynamic Models.- 9. Monte Carlo Approach to Bayesian Regression Modelling.- 10. Identification of Reality in Bayesian Context.- 11. Nonlinear Nonnormal Dynamic Models: State Estimation and Software.- 12. The EM Algorithm: A Guided Tour.- 13. Estimation of Quasipolynomials in Noise: Theoretical, Algorithmic and Implementation Aspects.- 14. Iterative Reconstruction of Transmission Sinograms with Low Signal to Noise Ratio.- 15. Curse of Dimensionality: Classifying Large Multi-Dimensional Images with Neural Networks.- 16. Dimension-independent Rates of Approximation by Neural Networks.- 17. Estimation of Human Signal Detection Performance from Event-Related Potentials Using Feed-Forward Neural Network Model.- 18. Utilizing Geometric Anomalies of High Dimension: When Complexity Makes Computation Easier.- 19. Approximation Using Cubic B-Splines with Improved Training Speed and Accuracy.