S. Arya and D. Mount. Approximate nearest neighbor searching. In Proc. of 4th SODA, pp. 271--280, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... nearest neighbor search have been studied in computational geometry (e.g. see [14] Some interest problems solutions include: the nearest neighbor search: nding a point whose distance to the query point is at most 1 times the distance of the query point to the actual nearest neighbor [1, 2]; locality sensitive hashing techniques for nearest neighbors [10, 7] 3 The Approximate Nearest Neighbor Search Tree As stated previously, our goal is to develop an index structure that supports nearest neighbor queries with minimum node access and high accuracy. We begin this section by de ....

S. Arya and D. Mount. Approximate nearest neighbor searching. In Proc. of the Fourth Annual ACMSIAM Symposium on Discrete Algorithms, pages 271{ 280, 1993.

....any two side chains from coming closer than 3.8. We also take extra samples around the given folded state. Each milestone is then connected to at most k milestones among the nearest ones, where k is the number of dof in our protein s model. The nearest neighbors of a milestone are found using ANN [AM93], with the Euclidean distance over the conformational space, after normalizing each dof parameter to lie between 0 and 1. We also tried the RMSD metric, but it was slower and did not give significantly different results. To discretize a local path (and eventually decide if it is part of the PCR, ....

S. Arya and D.M. Mount. Approximate Nearest Neighbor Searching. Proc. 4th Ann. ACM-SIAM Symp. on Discrete Algorithms, 271-280, 1993.

....In this version of the problem, the search algorithm is required to find a database point whose distance to the query is within a factor of 1 of the distance to a nearest neighbor, where 0 is a predefined value. The best available (randomized) algorithm, following a long line of work [5, 13, 6, 26, 25, 27], uses (for an arbitrary constant , when stated in terms of the cell probe model) poly(n; d) cells of size O(d) each, and searches probing O(log log d) cells. This randomized upper bound nearly matches a recent deterministic lower bound of Omega Gamma 40 log d= log log log d) 11] which holds ....

S. Arya and D. Mount. Approximate nearest neighbor searching. In Proc. of 4th SODA, pp. 271--280, 1993.

....the answer may be any point further than the nearest neighbor by a factor as large as 2 #(log d) 1 # # , for any fixed # 0. 1 Introduction For a variety of practical reasons ranging from molecular biology to web searching, nearest neighbor searching has been a focus of attention lately [2] [9] 11] 21] 26] In the applications considered, the dimension of the ambient space is usually high, and predictably, classical lines of attack based on space partitioning fail. To overcome the wellknown curse of dimensionality, it is typical to relax the search by seeking only ....

....Hr in two stages: 1] For each k = 1, 2, h 1, choose d 5 nodes of Hr of depth k at random, uniformly without replacement among the nodes of depth k that are not descendants of chosen nodes of smaller depth. The (h 1)d 5 nodes chosen in this way are said to be picked by Sr . [2] For each node v picked by Sr , recursively choose a random Sr 1 within the corresponding tree Hr 1 (i.e. defined with respect to node v) Such a Sr 1 is called the canonical projection of Sr on v. The union of these (h 1)d 5 projections Sr 1 defines a random Sr within Hr . For r = ....

Arya, S., Mount, D.M. Approximate nearest neighbor searching, Proc. 4th Annu. ACM-SIAM Symp. Disc. Alg. (1993), 271--280.

....a factor of (1 ) of the distance to the closest database point. Usually, the parameter is fixed in the pre processing phase. To avoid confusion, we refer to the version of the problem requiring an exact answer as the exact NNS problem. For approximate NNS in Euclidean space, Arya and Mount [4] give O(1= d log n search time using O(1= d n storage. Clarkson [16] improves the dependence on to (1= d Gamma1) 2 . Arya, Mount, Netanyahu, Silverman, and Wu [5] give O( d= d log n) search time using O(n log n) storage (the preprocessing does not depend on ) In comparison ....

S. Arya and D. Mount. Approximate nearest neighbor searching. In Proc. of 4th SODA, pp. 271--280, 1993.

....O(log d n) query time. Arbitrary norm. The first result for approximate nearest neighbor in d was due to Bern [Bern93] His result (after recent improvement by Chan [Chan97] guarantees polynomial storage and query time polynomial in d and log n, but with c polynomial in d. Arya and Mount [AM93] gave an algorithm with query time O(1=ffl) d log 3 n and preprocessing O(1=ffl) d O(n) here and later we denote ffl = c Gamma 1) The dependence on ffl was later reduced by Clarkson [Cl94] and Chan [Chan97] to ffl Gamma(d Gamma1) 2 . Arya, Mount, Netanyahu, Silverman, and Wu ....

S. Arya and D. Mount. Approximate nearest neighbor searching. In: Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, 1993, pp. 271--280.

....aware of any analysis for high dimensional Euclidean spaces. In general, even the average case analysis of heuristics for points distributed over regions in d gives an exponential query time [7, 35, 59] The situation is only slightly better for approximate nearest neighbors. Arya and Mount [3] gave an algorithm with query time O(1=ffl) d O(log n) and preprocessing O(1=ffl) d O(n) The dependence on ffl was later reduced by Clarkson [17] and Chan [15] to ffl Gamma(d Gamma1) 2 . Arya, Mount, Netanyahu, Silverman, and Wu [5] obtained optimal O(n) preprocessing cost, but with query ....

S. Arya and D. Mount. Approximate nearest neighbor searching. In: Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, 1993, pp. 271--280.

....constructed by bisecting each pair of data points. point. Usually, the parameter is fixed in the preprocessing phase. To avoid confusion, we refer to the version of the problem requiring an exact answer as the exact NNS problem. For approximate NNS in Euclidean space, Arya and Mount [3] give O(1= d log n search time using O(1= d n storage. Clarkson [15] improves the dependence on to (1= d Gamma1) 2 . Arya, Mount, Netanyahu, Silverman, and Wu [4] give O( d= d log n) search time using O(n log n) storage (the pre processing does not depend on ) In comparison ....

S. Arya and D. Mount. Approximate nearest neighbor searching. In Proc. of 4th SODA, pp. 271--280, 1993.

No context found.

S. Arya and D. Mount. Approximate nearest neighbor searching. In Proc. of 4th SODA, pp. 271--280, 1993.

No context found.

S. Arya and D. M. Mount. Approximate nearest neighbor searching. In Proc. 4th Annu. ACM-SIAM Symp. Disc. Alg., pages 271--280, 1993.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC