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A Note on the Nearest Neighbor in GrowthRestricted Metrics
 In 15th ACMSIAM Symp. on Discrete Algorithms (SODA
, 2004
"... In this paper, we give results relevant to sequential and distributed dynamic data structures for finding nearest neighbors in growthrestricted metrics. Our sequential data structure uses linear space, and requires O(log n) queries in expecation and O(log n) queries for lookups with high probabili ..."
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Cited by 19 (2 self)
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In this paper, we give results relevant to sequential and distributed dynamic data structures for finding nearest neighbors in growthrestricted metrics. Our sequential data structure uses linear space, and requires O(log n) queries in expecation and O(log n) queries for lookups with high
Finding Nearest Neighbors in Growthrestricted Metrics
 In 34th Annual ACM Symposium on the Theory of Computing
, 2002
"... Most research on nearest neighbor algorithms in the literature has been focused on the Euclidean case. In many practical search problems however, the underlying metric is nonEuclidean. Nearest neighbor algorithms for general metric spaces are quite weak, which motivates a search for other classes o ..."
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Cited by 174 (0 self)
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Most research on nearest neighbor algorithms in the literature has been focused on the Euclidean case. In many practical search problems however, the underlying metric is nonEuclidean. Nearest neighbor algorithms for general metric spaces are quite weak, which motivates a search for other classes
Finding Nearest Neighbors in Growthrestricted Metrics
"... Most research on nearest neighbor algorithms in the literature has been focused on the Euclidean case. In many practical search problems however, the underlying metric is nonEuclidean. Nearest neighbor algorithms for general metric spaces are quite weak, which motivates a search for other classes o ..."
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of metric spaces that can be tractably searched. In this paper, we develop an efficient dynamic data structure for nearest neighbor queries in growthconstrained metrics. These metrics satisfy the property that for any point q and distance d the number of points within distance 2d of q is at most a constant
Finding Nearest Neighbors in Growthrestricted Metrics
"... Most research on nearest neighbor algorithms in the literature has been focused on the Euclidean case. In many practical search problems however, the underlying metric is nonEuclidean. Nearest neighbor algorithms for general metric spaces are quite weak, which motivates a search for other classes o ..."
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of metric spaces that can be tractably searched. In this paper, we develop an efficient dynamic data structure for nearest neighbor queries in growthconstrained metrics. These metrics satisfy the property that for any point q and distance d the number of points within distance 2d of q is at most a constant
Finding Nearest Neighbors in Growthrestricted Metrics
"... Most research on nearest neighbor algorithms in the literature has been focused on the Euclidean case. In many practical search problems however, the underlying metric is nonEuclidean. Nearest neighbor algorithms for general metric spaces are quite weak, which motivates a search for other classes o ..."
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Most research on nearest neighbor algorithms in the literature has been focused on the Euclidean case. In many practical search problems however, the underlying metric is nonEuclidean. Nearest neighbor algorithms for general metric spaces are quite weak, which motivates a search for other classes
Nearest Neighbor Queries
, 1995
"... A frequently encountered type of query in Geographic Information Systems is to find the k nearest neighbor objects to a given point in space. Processing such queries requires substantially different search algorithms than those for location or range queries. In this paper we present an efficient bra ..."
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Cited by 594 (1 self)
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branchandbound Rtree traversal algorithm to find the nearest neighbor object to a point, and then generalize it to finding the k nearest neighbors. We also discuss metrics for an optimistic and a pessimistic search ordering strategy as well as for pruning. Finally, we present the results of several
Distance metric learning for large margin nearest neighbor classification
 In NIPS
, 2006
"... We show how to learn a Mahanalobis distance metric for knearest neighbor (kNN) classification by semidefinite programming. The metric is trained with the goal that the knearest neighbors always belong to the same class while examples from different classes are separated by a large margin. On seven ..."
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Cited by 685 (15 self)
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We show how to learn a Mahanalobis distance metric for knearest neighbor (kNN) classification by semidefinite programming. The metric is trained with the goal that the knearest neighbors always belong to the same class while examples from different classes are separated by a large margin
Approximate Nearest Neighbors: Towards Removing the Curse of Dimensionality
, 1998
"... The nearest neighbor problem is the following: Given a set of n points P = fp 1 ; : : : ; png in some metric space X, preprocess P so as to efficiently answer queries which require finding the point in P closest to a query point q 2 X. We focus on the particularly interesting case of the ddimens ..."
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Cited by 1017 (40 self)
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The nearest neighbor problem is the following: Given a set of n points P = fp 1 ; : : : ; png in some metric space X, preprocess P so as to efficiently answer queries which require finding the point in P closest to a query point q 2 X. We focus on the particularly interesting case of the d
Data Structures and Algorithms for Nearest Neighbor Search in General Metric Spaces
, 1993
"... We consider the computational problem of finding nearest neighbors in general metric spaces. Of particular interest are spaces that may not be conveniently embedded or approximated in Euclidian space, or where the dimensionality of a Euclidian representation is very high. Also relevant are highdim ..."
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Cited by 356 (5 self)
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We consider the computational problem of finding nearest neighbors in general metric spaces. Of particular interest are spaces that may not be conveniently embedded or approximated in Euclidian space, or where the dimensionality of a Euclidian representation is very high. Also relevant are high
An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions
 ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1994
"... Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any po ..."
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Cited by 983 (32 self)
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Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any
Results 1  10
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524,566