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Low Rank Approximation

Algorithms, Implementation, Applications

By: Ivan Markovsky

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Paperback | 26 January 2014

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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 (R) examples assist in the assimilation of the theory.

Industry 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)

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