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of 2 K offers a poor worst-case performance. ... However, we show that the backtracking search has a very high worst-case computational overhead and that this may be unacceptable in many practical applications such as realtime vector quantization encoding ... The analysis pertains to a search sequence where the current nearest-neighbor ball is also the actual nearest-neighbor ball. ...doi:10.1006/dspr.1997.0291 fatcat:fb7ah547vjbsdgcnxr5z4r5jhi
For the nearest neighbors problem, we propose a c-approximate solution for the restricted version of the decision problem with bounded radius which is then reduced to the nearest neighbors by a known reduction ... For range searching we propose a scheme that learns the parameters in a learning stage adopting them to the case of a set of points with low intrinsic dimension that are embedded in high dimensional space ... For each random translation/rotation, we use Worst case analysis We derive below the theoretical upper bound on the running time for the worst case scenario. ...doi:10.1109/iccv.2013.431 dblp:conf/iccv/AigerKR13 fatcat:civavvlcevhbpcxczg3iwdgpsa
Here, the emphasis is on the optimal design of the K-d tree for efficient nearest neighbor search in multidimensional space under a bucket-Voronoi intersection search framework. ... The proposed optimization criteria and bucket-Voronoi intersection search procedure are studied in the context of vector quantization encoding of speech waveform and are empirically observed to achieve ... The complexity of the nearest neighbor search can be reduced by using a partial distance search [ 161 within the bucket. ...doi:10.1109/78.120795 fatcat:ffdnuzowvzhydivj6ez3kxwlwe
We consider the task of nearest-neighbor search with the class of binary-spacepartitioning trees, which includes kd-trees, principal axis trees and random projection trees, and try to rigorously answer ... We also explore another factor affecting the search performancemargins of the partitions in these trees. ... Equipped with the bound on the candidate-neighbor distance, we bound the worst-case nearest-neighbor search errors as follows: Corollary 3.1. ...dblp:conf/nips/RamG13 fatcat:iuktlcunkjgr5nbnbaxhrifk7a
In this article, we propose a new fast nearest neighbor search algorithm, based on vector quantization. ... Unlike previously cited methods, this kind of partitions does not a priori allow to eliminate several brother nodes in the search tree with a single test. ... Let Proj Γ be a nearest neighbor projection on Γ. Γ is being partitioned into p subsets Γ 1 , · · · , Γ p with Γ i = Γ ∩ slab S (s i ), by their nearest neighbor projection on S. Consider q ∈ E. ...arXiv:1105.4953v1 fatcat:vfof4tlrdfdebbvsl3fots2ig4
This mapping guarantees, with high probability, that an approximate nearest neighbor lies among the k approximate nearest neighbors in the projected space. ... The approximate nearest neighbor problem ( -ANN) in Euclidean settings is a fundamental question, which has been addressed by two main approaches: Data-dependent space partitioning techniques perform well ... Results The "planted nearest neighbor model" datasets constitute a worst-case input for our approach since every query point has only one approximate nearest neighbor and has many points lying near the ...doi:10.4230/lipics.socg.2015.436 dblp:conf/compgeom/Anagnostopoulos15 fatcat:yjeymduq6vaerkycqwtcd3ej4e
Third, the proposed method improves accuracy of one of the popular distance-based classification algorithms: K-nearest neighbor classification, by taking into account the degree of distance distortion ... A quick examination shows that special types of noise such as Laplace noise provide worst case guarantee, while most existing methods such as adding normal or uniform noise, as well as random projection ... Typically, a K-nearest neighbor algorithm uses a small value of k to define the nearest neighbor search space. ...doi:10.1016/j.datak.2008.03.004 fatcat:atfcrk3vkfgrfbwg4iin5daije
We take a first step towards a rigorous asymptotic analysis of graph-based methods for finding (approximate) nearest neighbors in high-dimensional spaces, by analyzing the complexity of randomized greedy ... memory, and in this regime the asymptotic scaling of a greedy graph-based search matches optimal hash-based trade-offs of Andoni-Laarhoven-Razenshteyn-Waingarten . ... worst-case instances of (approximate) nearest neighbor searching. ...doi:10.4230/lipics.socg.2018.57 dblp:conf/compgeom/Laarhoven18 fatcat:ybdrcak45vbirce44fbnwu6hyq
In a d dimensional Euclidean space, for the former class of algorithms, the worst case query time are typically bounded by . ... From the perspective of computational complexity, there are two classes of nearest neighbor search algorithms for Euclidean space, one offers logarithmic or sub-linear worst case query bounds at the expense ... It is obvious that the worst case analysis is not applicable to most applications of the proposed MCP algorithm. ...doi:10.1137/120880331 fatcat:x26slgzhcreale3m5jzcg3lipy
Petunin (Kiev) Papadimitriou, Christos H.; Bentley, Jon Louis 81j:68110 A worst-case analysis of nearest neighbor searching by projection. Automata, languages and programming (Proc. Seventh Internat. ... Friedman, Baskett and Shustek described an algorithm for nearest neighbor searching based on projecting the points onto the various coordinate axes; their analysis of this method showed that a nearest ...
The use of this method can produce dimension reduction by as much as a factor of n, the number of data points in the database, over sequential search. ... There are several pieces of information that can be utilized in order to improve the efficiency of similarity searches on high-dimensional data. ... The time to perform a nearest neighbor search is reduced by a factor of five with no loss of accuracy, but can be improved up to a factor of ten at some loss of accuracy, as is shown in Figure 10 . ...doi:10.1109/sisap.2008.20 dblp:conf/sisap/TahmoushS08 fatcat:nqlypmg5jfaaxgqyldyoyh667y
The use of this method can produce dimension reduction by as much as a factor of n, the number of data points in the database, over sequential search. ... There are several pieces of information that can be utilized in order to improve the efficiency of similarity searches on high-dimensional data. ... The time to perform a nearest neighbor search is reduced by a factor of five with no loss of accuracy, but can be improved up to a factor of ten at some loss of accuracy, as is shown in Figure 10 . ...doi:10.1109/icdew.2008.4498342 dblp:conf/icde/TahmoushS08 fatcat:nkjset67kzdpzhjz4j3p5dtini
Lecture Notes in Computer Science
In this article, we present a highly scalable approach to compute the nearest neighbors of objects that instead focuses on preserving neighborhoods well using an ensemble of space-filling curves. ... indexed nearest neighbors. ... If k-nearest neighborhoods are needed, as it is the case for the most wellknown outlier detection methods, SFC is the method of choice. ...doi:10.1007/978-3-319-18123-3_2 fatcat:jbhn3t6vhrbqdcwwnjdzhaz3zu
In this paper, we provide an overview of fast nearest-neighbor search algorithms based on an &approxima-tion}elimination' framework under a class of elimination rules, namely, partial distance elimination ... Previous algorithms based on these elimination rules are reviewed in the context of approximation}elimination search. ... ers a much lower worst-case complexity; here this can be seen to be about a third of the complexity of¸ based search. ...doi:10.1016/s0031-3203(99)00134-x fatcat:262obja7szdqvkq7c5ooybz6yy
We also allow the user to specify an error bound e > 0, and consider the same problem in the context of approximate nearest neighbor searching. ... worst-case reporting time O(logn +k), where nm is the number of data points and k the number of points reported, and in d-space, with d even, using worst-case preprocessing time O(nlogn), storage O(n) ...
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