The random projection method
Author(s)
Bibliographic Information
The random projection method
（DIMACS series in discrete mathematics and theoretical computer science, v. 65）
American Mathematical Society, c2004
- : pbk
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Note
Includes bibliographical references (p. 97-100)
Description and Table of Contents
- Volume
-
ISBN 9780821820186
Description
Random projection is a simple geometric technique for reducing the dimensionality of a set of points in Euclidean space while preserving pairwise distances approximately. The technique plays a key role in several breakthrough developments in the field of algorithms. In other cases, it provides elegant alternative proofs. The book begins with an elementary description of the technique and its basic properties. Then it develops the method in the context of applications, which are divided into three groups. The first group consists of combinatorial optimization problems such as maxcut, graph coloring, minimum multicut, graph bandwidth and VLSI layout. Presented in this context is the theory of Euclidean embeddings of graphs. The next group is machine learning problems, specifically, learning intersections of halfspaces and learning large margin hypotheses. The projection method is further refined for the latter application. The last set consists of problems inspired by information retrieval, namely, nearest neighbor search, geometric clustering and efficient low-rank approximation.
Motivated by the first two applications, an extension of random projection to the hypercube is developed here. Throughout the book, random projection is used as a way to understand, simplify and connect progress on these important and seemin The book is suitable for graduate students and research mathematicians interested in computational geometry.
Table of Contents
- Random projection
- Embedding metrics in Euclidean space
- Euclidean embeddings: Beyond distance preservation
- Intersections of half-spaces
- Indexing and clustering
- Bibliography
- Appendix
- Volume
-
: pbk ISBN 9780821837931
Description
Random projection is a simple geometric technique for reducing the dimensionality of a set of points in Euclidean space while preserving pairwise distances approximately. The technique plays a key role in several breakthrough developments in the field of algorithms. In other cases, it provides elegant alternative proofs. The book begins with an elementary description of the technique and its basic properties. Then it develops the method in the context of applications, which are divided into three groups. The first group consists of combinatorial optimization problems such as maxcut, graph coloring, minimum multicut, graph bandwidth and VLSI layout.Presented in this context is the theory of Euclidean embeddings of graphs. The next group is machine learning problems, specifically, learning intersections of halfspaces and learning large margin hypotheses. The projection method is further refined for the latter application. The last set consists of problems inspired by information retrieval, namely, nearest neighbor search, geometric clustering and efficient low-rank approximation. Motivated by the first two applications, an extension of random projection to the hypercube is developed here. Throughout the book, random projection is used as a way to understand, simplify and connect progress on these important and seemingly unrelated problems. The book is suitable for graduate students and research mathematicians interested in computational geometry.
Table of Contents
Random projection Combinatorial optimization: Rounding via random projection Embedding metrics in Euclidean space Euclidean embeddings: Beyond distance preservation Learning theory: Robust concepts Intersections of half-spaces Information retrieval: Nearest neighbors Indexing and clustering Bibliography Appendix.
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