Communications and Control Engineering

Low Rank Approximation

Algorithms, Implementation, Applications

Authors: Markovsky, Ivan

  • Provides the reader with an analysis tool which is more generally applicable than the commonly-used total least squares
  • Shows the reader solutions to the problem of data modelling by linear systems from a sweeping field of applications
  • Supplementary electronic and class-based materials will aid tutors in presenting this material to their students
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  • ISBN 978-1-4471-2227-2
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Hardcover $129.00
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  • ISBN 978-1-4471-2226-5
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Softcover $129.00
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  • ISBN 978-1-4471-5836-3
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About this book

Data Approximation by Low-complexity Models details the theory, algorithms, and applications of structured low-rank approximation. Efficient local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. Much of the text is devoted to describing the applications of the theory including: system and control theory; signal processing; computer algebra for approximate factorization and common divisor computation; computer vision for image deblurring and segmentation; machine learning for information retrieval and clustering; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; and psychometrics for factor analysis.

Software implementation of the methods is given, making the theory directly applicable in practice. All numerical examples are included in demonstration files giving hands-on experience and exercises and MATLAB® examples assist in the assimilation of the theory.

About the authors

Dr. Ivan Markovsky completed his PhD in the Electrical Engineering Department of the Katholieke Universiteit Leuven, Belgium under the supervision of S. Van Huffel, B. De Moor, and J.C. Willems. He was a postdoctoral researcher at the same department, and since January 2007, he has been a lecturer at the School of Electronics and Computer Science of the University of Southampton. His research interests are in system identification in the behavioural setting, total least squares, errors-in-variables estimation, and data-driven control; topics on which he has published 23 journal papers and one monograph (with SIAM). Dr. Markovsky won Honorable Mention in the Alston Householder Prize for best dissertation in numerical linear algebra. He is a co-organiser of the Fourth International Workshop on Total Least Squares and Errors-in-Variables Modelling, a guest editor of Signal Processing for a special issue on total least squares, and an associate editor of the International Journal of Control.

Reviews

From the reviews:

“This is a carefully-elaborated monographic work on low rank approximation. It covers the state of the art in this field (key theoretical topics accompanied by the description of the associated algorithms) and discusses various classes of applications. The book provides a rigorous and self-contained material, including numerical examples implemented in MATLAB and a collection of relevant problems. The exposition corresponds to a postgraduate level.” (Octavian Pastravanu, Zentralblatt MATH, Vol. 1245, 2012)

“This book gently takes the reader from the basic ideas of LRA to the most critical concepts, with an adequate number of examples to explain things along the way. … Markovsky has presented LRA in a way that is unifying and cross-disciplinary. The pages abound with code, examples, applications, and problems, from which readers can pick according to their own interests and without the risk of losing the main thread of the book. … it is a good reference for students, practitioners, and researchers.” (Corrado Mencar, ACM Computing Reviews, December, 2012)


Table of contents (7 chapters)

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4471-2227-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-1-4471-2226-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-1-4471-5836-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Low Rank Approximation
Book Subtitle
Algorithms, Implementation, Applications
Authors
Series Title
Communications and Control Engineering
Copyright
2012
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-1-4471-2227-2
DOI
10.1007/978-1-4471-2227-2
Hardcover ISBN
978-1-4471-2226-5
Softcover ISBN
978-1-4471-5836-3
Series ISSN
0178-5354
Edition Number
1
Number of Pages
X, 258
Topics