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On nearest-neighbor graphs
[chapter]

1992
*
Lecture Notes in Computer Science
*

We derive bounds

doi:10.1007/3-540-55719-9_93
fatcat:vcypqrabljg2pdynnmn5kn42ka
*on*the relationship between size and depth for the components of a*nearest*-*neighbor**graph*and prove some probabilistic properties of the k-*nearest*-*neighbors**graph*for a random set of points ... The "*nearest**neighbor*" relation, or more generally the "k*nearest**neighbors*" relation, defined for a set of points in a metric space, has found many uses in computational geometry and clustering analysis ... We can generalize NNG(V ) to k-NNG(V ), the k-*nearest*-*neighbors**graph*of V , by introducing k edges from a vertex to its k*nearest**neighbors*. ...##
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On Nearest-Neighbor Graphs

1997
*
Discrete & Computational Geometry
*

We derive bounds

doi:10.1007/pl00009293
fatcat:mz3eestmsrckzi3zmdrou3z6em
*on*the relationship between size and depth for the components of a*nearest*-*neighbor**graph*and prove some probabilistic properties of the k-*nearest*-*neighbors**graph*for a random set of points ... The "*nearest*-*neighbor*" relation, or more generally the "k-*nearest*-*neighbors*" relation, defined for a set of points in a metric space, has found many uses in computational geometry and clustering analysis ...*On**Nearest*-*Neighbor**Graphs*265 We can generalize NNG(V) to k-NNG(V), the k-*nearest*-*neighbors**graph*of V, by introducing k edges from a vertex to its k*nearest**neighbors*. ...##
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Scalable Nearest Neighbor Search based on kNN Graph
[article]

2017
*
arXiv
*
pre-print

In this paper, a scalable solution based

arXiv:1701.08475v2
fatcat:awotobncyfhizizl64niebs2lq
*on*hill-climbing strategy with the support of k-*nearest**neighbor**graph*(kNN) is presented. Two major issues have been considered in the paper. ... In addition, a comparative study*on*both the compressional and traditional*nearest**neighbor*search methods is presented. ... In*one*direction, the*nearest**neighbor*search is conducted based*on*k-*nearest**neighbor**graph*(kNN*graph*) [4] , [5] , [6] , in which the kNN*graph*is constructed offline. ...##
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Asynchronous opinion dynamics on the k-nearest-neighbors graph
[article]

2018
*
arXiv
*
pre-print

We assume that agents update their opinions asynchronously and that each agent's new opinion depends

arXiv:1803.07401v2
fatcat:4efbmya7t5cphd23fgr6nc6ilu
*on*the opinions of the k agents that are closest to it. ... The importance of this way of defining connectivity has been also captured by*graph*theorists, who have studied a the properties of what they call k-*nearest*-*neighbors**graph*. ... Conclusion In this paper we have introduced a new model of opinion dynamics with opiniondependent connectivity following the k-*nearest*-*neighbors**graph*. ...##
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Nearest-neighbor graphs on the cantor set

2009
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Advances in Applied Probability
*

We consider the asymptotics for the expected total edge length of the directed and undirected

doi:10.1017/s000186780000313x
fatcat:f5bashafgng5rougwllqzfasce
*nearest*-*neighbor**graph**on*We prove convergence to a constant of the rescaled expected total edge length of ... this random*graph*. ... Acknowledgements I would like to acknowledge the help of Joseph Yukich for proofreading and making suggestions*on*earlier drafts of this paper. He is an outstanding mentor and friend. ...##
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Nearest-neighbor graphs on the cantor set

2009
*
Advances in Applied Probability
*

We consider the asymptotics for the expected total edge length of the directed and undirected

doi:10.1239/aap/1240319576
fatcat:4suwo6bcp5alnmhxl3eucvys3e
*nearest*-*neighbor**graph**on*We prove convergence to a constant of the rescaled expected total edge length of ... this random*graph*. ... Acknowledgements I would like to acknowledge the help of Joseph Yukich for proofreading and making suggestions*on*earlier drafts of this paper. He is an outstanding mentor and friend. ...##
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EFANNA : An Extremely Fast Approximate Nearest Neighbor Search Algorithm Based on kNN Graph
[article]

2016
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arXiv
*
pre-print

To the best of our knowledge, EFANNA is the fastest algorithm so far both

arXiv:1609.07228v3
fatcat:2jwivsuv3fd5pc4watrvesjzda
*on*approximate*nearest**neighbor**graph*construction and approximate*nearest**neighbor*search. ... In this paper, we propose EFANNA, an extremely fast approximate*nearest**neighbor*search algorithm based*on*kNN*Graph*. ... EFANNA is an abbreviation for two algorithms: Extremely Fast Approximate k-*Nearest**Neighbor**graph*construction Algorithm and Extremely Fast Approximate*Nearest**Neighbor*search Algorithm based*on*kNN*graph*...##
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All nearest neighbor calculation based on Delaunay graphs
[article]

2018
*
arXiv
*
pre-print

In this paper, we introduce an algorithm for computing the all

arXiv:1802.09594v1
fatcat:n4ndyzouyberzajfici7jcmosu
*nearest*neighbour operator*on*spatial data sets based*on*their Delaunay*graphs*. ... In the Delaunay*graph*of a data set each point is linked to its*nearest*neighbours. ...*Nearest*neighbour algorithm For finding the*nearest*neighbour of a query point among the points of a dataset that there is a delaunay*graph**on*them, this*graph*is traversed with the help of an extension ...##
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Anomaly Detection with Score functions based on Nearest Neighbor Graphs
[article]

2009
*
arXiv
*
pre-print

We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based

arXiv:0910.5461v1
fatcat:4d7o7u34bbgbnpkhlnitg73mpa
*on*score functions derived from*nearest**neighbor**graphs**on*n-point nominal data. ... We demonstrate the algorithm*on*both artificial and real data sets in high dimensional feature spaces. ... Once a distance function is defined our next step is to form a K*nearest**neighbor**graph*(K-NNG) or alternatively an ǫ*neighbor**graph*(ǫ-NG). ...##
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Spectral Clustering Based on k-Nearest Neighbor Graph
[chapter]

2012
*
Lecture Notes in Computer Science
*

We present a novel spectral algorithm Speclus with a similarity measure based

doi:10.1007/978-3-642-33260-9_22
fatcat:7fcgwdxlwjfvrjsgtaz2czmyzi
*on*modified mutual*nearest**neighbor**graph*. The resulting affinity matrix reflex the true structure of data. ... The algorithm requires only*one*parameter -a number of*nearest**neighbors*, which can be quite easily established. ...*On*the other hand creating connections between*graph*vertices*on*the basis of mutual*nearest**neighbors*eliminates influence of any noises in the data. ...##
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Approximate Direct and Reverse Nearest Neighbor Queries, and the k-nearest Neighbor Graph

2009
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2009 Second International Workshop on Similarity Search and Applications
*

Then, we show how to use our approximate k-

doi:10.1109/sisap.2009.33
dblp:conf/sisap/FigueroaP09
fatcat:wieiyzyfdngdlarrn5rg2bjv6m
*nearest**neighbor*queries to construct (an approximation of) the k-*nearest**neighbor**graph*when we have a fixed dataset. ... Finally, combining both primitives we show how to dynamically maintain the approximate k-*nearest**neighbor**graph*of the objects currently stored within the metric dataset, that is, considering both object ... This algorithm needs |A| + C + C 2 distance computations. 3) k-*Nearest**neighbor**graph*: For each u ∈ U we solve a kNN query retrieving*neighbors*from U \ {u} using ApproxkNNU. ...##
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Estimation of Rényi Entropy and Mutual Information Based on Generalized Nearest-Neighbor Graphs
[article]

2010
*
arXiv
*
pre-print

The estimators are calculated as the sum of p-th powers of the Euclidean lengths of the edges of the 'generalized

arXiv:1003.1954v2
fatcat:id2rrrmmgvgy7fvvh6hnci6gvi
*nearest*-*neighbor*'*graph*of the sample and the empirical copula of the sample respectively ... We present simple and computationally efficient nonparametric estimators of Rényi entropy and mutual information based*on*an i.i.d. sample drawn from an unknown, absolutely continuous distribution over ... Szepesvári is*on*leave from SZTAKI, Hungary. ...##
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Graph based Nearest Neighbor Search: Promises and Failures
[article]

2019
*
arXiv
*
pre-print

Recently,

arXiv:1904.02077v5
fatcat:gdlf26kxpje55aul2hhx5qsy3u
*graph*based*nearest**neighbor*search gets more and more popular*on*large-scale retrieval tasks. ... The attractiveness of this type of approaches lies in its superior performance over most of the known*nearest**neighbor*search approaches as well as its genericness to various metrics. ... All the approaches in this category are built upon a k-*nearest**neighbor*(k-NN)*graph*or an approximate k-NN*graph*. ...##
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Fast Nearest Neighbor Search on Large Time-Evolving Graphs
[chapter]

2014
*
Lecture Notes in Computer Science
*

Finding the k

doi:10.1007/978-3-662-44848-9_2
fatcat:jcy2ee74yrdglkq57n5sehgp4q
*nearest**neighbors*(k-nns) of a given vertex in a*graph*has many applications such as link prediction, keyword search, and image tagging. ... We validate the effectiveness of our method*on*large real-world*graphs*from diverse domains. ... Note that direct*neighbors*, i.e. co-authors, are omitted from the top list as they constitute trivial*nearest**neighbors*. ...##
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Asynchronous opinion dynamics on the $k$-nearest-neighbors graph

2018
*
2018 IEEE Conference on Decision and Control (CDC)
*

We assume that agents update their opinions asynchronously and that each agent's new opinion depends

doi:10.1109/cdc.2018.8619285
dblp:conf/cdc/RossiF18
fatcat:fbjv7okxurhpvdqtszgcoknbu4
*on*the opinions of the k agents that are closest to it. ... The importance of this way of defining connectivity has been also captured by*graph*theorists, who have studied a the properties of what they call k-*nearest*-*neighbors**graph*. ... This feature makes control approaches based*on*leadership, like [19] , unsuitable to k-*nearest*-*neighbors*dynamics. ...
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