Sinossi
The classical nearest neighbors problem is formulated as follows: given a collection of N points in the Euclidean space R^d, for each point, find its k nearest neighbors (i.e. closest points). Obviously, for each point X, one can compute the distances from X to every other point, and then find k shortest distances in the resulting array. However, the computational cost of this naive approach is at least (d*N^2)/2 operations, which is prohibitively expensive in many applications. For example, "naively" solving the nearest neighbors problem with d=100, N=1,000,000 and k=30 on a modern laptop can take about as long as a day of CPU time. Fortunately, in such areas as data mining, image processing, machine learning etc., it often suffices to find "approximate" nearest neighbors instead of the "true" ones. In this work, a randomized approximate algorithm for the solution of the nearest neighbors problem is described. It has a considerably lower computational cost than the naive algorithm, and is fairly fast in practical applications. We provide a probabilistic analysis of this algorithm, and demonstrate its performance via several numerical experiments.
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L'autore
Dr. Andrei Osipov received his M.Sc. in mathematics fromthe Hebrew University of Jerusalem, Israel.He received his Ph.D. in applied mathematics from Yale University.Currently Dr. Osipov holds the position of Gibbs Assistant Professor at Yale.
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A Randomized Approximate Nearest Neighbors Algorithm
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LAP LAMBERT Academic Publishing Mai 2012, 2012
ISBN 10: 3659128384
ISBN 13: 9783659128387
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The classical nearest neighbors problem is formulated as follows: given a collection of N points in the Euclidean space R^d, for each point, find its k nearest neighbors (i.e. closest points). Obviously, for each point X, one can compute the distances from X to every other point, and then find k shortest distances in the resulting array. However, the computational cost of this naive approach is at least (d N^2)/2 operations, which is prohibitively expensive in many applications. For example, 'naively' solving the nearest neighbors problem with d=100, N=1,000,000 and k=30 on a modern laptop can take about as long as a day of CPU time. Fortunately, in such areas as data mining, image processing, machine learning etc., it often suffices to find 'approximate' nearest neighbors instead of the 'true' ones. In this work, a randomized approximate algorithm for the solution of the nearest neighbors problem is described. It has a considerably lower computational cost than the naive algorithm, and is fairly fast in practical applications. We provide a probabilistic analysis of this algorithm, and demonstrate its performance via several numerical experiments. 136 pp. Englisch. Codice articolo 9783659128387
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Autor/Autorin: Osipov AndreiDr. Andrei Osipov received his M.Sc. in mathematics fromthe Hebrew University of Jerusalem, Israel.He received his Ph.D. in applied mathematics from Yale University.Currently Dr. Osipov holds the position of Gibbs Assist. Codice articolo 5133436
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A Randomized Approximate Nearest Neighbors Algorithm
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LAP LAMBERT Academic Publishing Mai 2012, 2012
ISBN 10: 3659128384
ISBN 13: 9783659128387
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -The classical nearest neighbors problem is formulated as follows: given a collection of N points in the Euclidean space R^d, for each point, find its k nearest neighbors (i.e. closest points). Obviously, for each point X, one can compute the distances from X to every other point, and then find k shortest distances in the resulting array. However, the computational cost of this naive approach is at least (d\*N^2)/2 operations, which is prohibitively expensive in many applications. For example, 'naively' solving the nearest neighbors problem with d=100, N=1,000,000 and k=30 on a modern laptop can take about as long as a day of CPU time. Fortunately, in such areas as data mining, image processing, machine learning etc., it often suffices to find 'approximate' nearest neighbors instead of the 'true' ones. In this work, a randomized approximate algorithm for the solution of the nearest neighbors problem is described. It has a considerably lower computational cost than the naive algorithm, and is fairly fast in practical applications. We provide a probabilistic analysis of this algorithm, and demonstrate its performance via several numerical experiments.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 136 pp. Englisch. Codice articolo 9783659128387
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A Randomized Approximate Nearest Neighbors Algorithm : Theory and Applications
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LAP LAMBERT Academic Publishing, 2012
ISBN 10: 3659128384
ISBN 13: 9783659128387
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Taschenbuch. Condizione: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - The classical nearest neighbors problem is formulated as follows: given a collection of N points in the Euclidean space R^d, for each point, find its k nearest neighbors (i.e. closest points). Obviously, for each point X, one can compute the distances from X to every other point, and then find k shortest distances in the resulting array. However, the computational cost of this naive approach is at least (d N^2)/2 operations, which is prohibitively expensive in many applications. For example, 'naively' solving the nearest neighbors problem with d=100, N=1,000,000 and k=30 on a modern laptop can take about as long as a day of CPU time. Fortunately, in such areas as data mining, image processing, machine learning etc., it often suffices to find 'approximate' nearest neighbors instead of the 'true' ones. In this work, a randomized approximate algorithm for the solution of the nearest neighbors problem is described. It has a considerably lower computational cost than the naive algorithm, and is fairly fast in practical applications. We provide a probabilistic analysis of this algorithm, and demonstrate its performance via several numerical experiments. Codice articolo 9783659128387
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A Randomized Approximate Nearest Neighbors Algorithm | Theory and Applications
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Taschenbuch. Condizione: Neu. A Randomized Approximate Nearest Neighbors Algorithm | Theory and Applications | Andrei Osipov | Taschenbuch | 136 S. | Englisch | 2012 | LAP LAMBERT Academic Publishing | EAN 9783659128387 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu. Codice articolo 106437638
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A Randomized Approximate Nearest Neighbors Algorithm: Theory and Applications
Editore:
LAP LAMBERT Academic Publishing, 2012
ISBN 10: 3659128384
ISBN 13: 9783659128387
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