Computer Intensive Methods in Control and Signal Processing
The Curse of Dimensionality
Published on 8. October 2012
Book
Paperback/Softback
XVI, 303 pages
978-1-4612-7373-8 (ISBN)
Description
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.
More details
Edition
Softcover reprint of the original 1st ed. 1997
Language
English
Place of publication
Boston
United States
Target group
Professional and scholarly
Research
Illustrations
XVI, 303 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 18 mm
Weight
493 gr
ISBN-13
978-1-4612-7373-8 (9781461273738)
DOI
10.1007/978-1-4612-1996-5
Schweitzer Classification
Other editions
Additional editions
Kevin Warwick | Miroslav Karny
Computer Intensive Methods in Control and Signal Processing
The Curse of Dimensionality
Book
03/1997
Birkhauser Boston Inc
€106.99
Shipment within 15-20 days
Content
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.