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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Strategies for efficient incremental nearest neighbor search
TL;DR: It is shown that incremental search can be implemented as a sequence of invocations of a previously published non-incremental algorithm, and a new incremental search algorithm is presented which finds the next nearest neighbor more efficiently by eliminating redundant computations.
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A Technique to Identify Nearest Neighbors
TL;DR: It is shown that this procedure may be used to eliminate distance calculations when finding nearest neighbors according to any Minkowski p-metric.
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The nearest neighbor problem in an abstract metric space
TL;DR: A new method for achieving this goal in an abstract metric space by selecting those models that are closest to an unknown relational description in a database of relational models.
Journal ArticleDOI
Tree structures for high dimensionality nearest neighbor searching
TL;DR: A probabilistic version of the algorithm is presented which provides significantly faster searching with little degradation in retrieval quality and some savings over a sequential search can be achieved in this type of application.