
Spectral Algorithms
now publishers Inc
1st Edition
Published on 6. October 2009
Book
Paperback/Softback
152 pages
978-1-60198-274-2 (ISBN)
Description
Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the y" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.
More details
Series
Language
English
Place of publication
Hanover
United States
Target group
Professional and scholarly
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 8 mm
Weight
224 gr
ISBN-13
978-1-60198-274-2 (9781601982742)
DOI
10.1561/0400000025
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Schweitzer Classification
Content
Part I Applications 1: The Best-Fit Subspace 2: Mixture Models 3: Probabilistic Spectral Clustering 4: Recursive Spectral Clustering 5: Optimization via Low-Rank Approximation Part II Algorithms 6: Matrix Approximation via Random Sampling 7: Adaptive Sampling Methods 8: Extensions of SVD. References.