Data structures and algorithms for nearest neighbor search in general metric spaces
Peter N. Yianilos
- pp 311-321
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TLDR
The up-tree (vantage point tree) is introduced in several forms, together‘ with &&ciated algorithms, as an improved method for these difficult search problems in general metric spaces.Abstract:
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 1s very high. Also relevant are high-dimensional Euclidian settings in which the distribution of data is in some sense of lower dimension and embedded in the space. The up-tree (vantage point tree) is introduced in several forms, together‘ with &&ciated algorithms, as an improved method for these difficult search nroblems. Tree construcI tion executes in O(nlog(n i ) time, and search is under certain circumstances and in the imit, O(log(n)) expected time. The theoretical basis for this approach is developed and the results of several experiments are reported. In Euclidian cases, kd-tree performance is compared.read more
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References
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TL;DR: This completely revised second edition presents an introduction to statistical pattern recognition, which is appropriate as a text for introductory courses in pattern recognition and as a reference book for workers in the field.
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Voronoi diagrams—a survey of a fundamental geometric data structure
TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
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An Algorithm for Finding Best Matches in Logarithmic Expected Time
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A Branch and Bound Algorithm for Computing k-Nearest Neighbors
TL;DR: The method of branch and bound is implemented in the present algorithm to facilitate rapid calculation of the k-nearest neighbors, by eliminating the necesssity of calculating many distances.