The Random Projection Method by Santosh Vempala Review by Aravind Srinivasan7 Department of Computer Science and Institute for Advanced Computer Studies University of Maryland at College Park College Park, MD 20742, USA textttsrin@cs.umd.edu Introduction This book is an exposition of the Random Projection Method, wherein one projects a high-dimensional set of points or distribution to a random low-dimensional space using a careful choice of distribution. The book describes this method, which has seen active research recently, in the context of three major areas: combinatorial optimization (especially approximation algorithms), learning, and information retrieval. It is especially easy to imagine why dimension-reduction would help in these last two areas. Summary of Contents Chapter 1 starts with the fundamental observation of Johnson-Lindenstrauss and others that the pairwise Euclidean distances between n points in Euclidean space get distorted by at most (1 ± ) with high probability, when projected randomly to a space of dimension O((log n)/ 2 ). There are many natural choices for the random mapping here. Part 1 of the book deals with combinatorial optimization. Chapter 2 begins with the seminal work of Goemans & Williamson on MAX CUT, where the random projection is used in
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Review of The Random Projection Method by Santosh Vempala
Srinivasan, Aravind
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, Volume 37 (4)
Association for Computing Machinery – Dec 1, 2006
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