Randomized Algorithms for Matrices and Data

1. Auflage 2011
ISBN: 978-1-60198-506-4
Verlag: Now Publishers

Buch, Englisch, Band 9, 110 Seiten, Format (B × H): 156 mm x 234 mm

Reihe: Foundations and Trends® in Machine Learning

Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, largely since matrices are popular structures with which to model data drawn from a wide range of application domains, and the success of this line of work opens the possibility of performing matrix-based computations with truly massive data sets. Originating within theoretical computer science, this work was subsequently extended and applied in important ways by researchers from numerical linear algebra, statistics, applied mathematics, data analysis, and machine learning, as well as domain scientists. Randomized Algorithms for Matrices and Data provides a detailed overview, appropriate for both students and researchers from all of these areas, of recent work on the theory of randomized matrix algorithms as well as the application of those ideas to the solution of practical problems in large-scale data analysis. By focusing on ubiquitous and fundamental problems such as least-squares approximation and low-rank matrix approximation that have been at the center of recent developments, an emphasis is placed on a few simple core ideas that underlie not only recent theoretical advances but also the usefulness of these algorithmic tools in large-scale data applications.

Autoren/Hrsg.

Mahoney, Michael W.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

1: Introduction 2: Matrices in large-scale scientific data analysis 3: Randomization applied to matrix problems 4: Randomized algorithms for least-squares approximation 5: Randomized algorithms for low-rank matrix approximation 6: Empirical observations 7: A few general thoughts, and a few lessons learned 8: Conclusion. Acknowledgements. References