Low Rank Approximation

Algorithms, Implementation, Applications
2012
ISBN: 978-1-4471-2226-5
Verlag: Springer

Buch, Englisch, 258 Seiten, Book, Format (B × H): 155 mm x 235 mm, Gewicht: 567 g

Reihe: Communications and Control Engineering

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.

Zielgruppe

Research

Autoren/Hrsg.

Markovsky, Ivan

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Computeralgebra
• Naturwissenschaften Biowissenschaften Angewandte Biologie Bioinformatik
• Naturwissenschaften Chemie Chemie Allgemein Chemometrik, Chemoinformatik
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Bioinformatik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Computer Vision
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Robotik

Inhaltsverzeichnis

Introduction.- From Data to Models.- Applications in System and Control Theory.- Applications in Signal Processing.- Applications in Computer Algebra.- Applications in Machine Learing.- Subspace-type Algorithms.- Algorithms Based on Local Optimization.- Data Smoothing and Filtering.- Recursive Algorithms.

Über Autor(innen)

Markovsky, Ivan
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.