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On nearest-neighbor graphs [chapter]

Michael S. Paterson, F. Frances Yao
1992 Lecture Notes in Computer Science  
We derive bounds 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.  ... 
doi:10.1007/3-540-55719-9_93 fatcat:vcypqrabljg2pdynnmn5kn42ka

On Nearest-Neighbor Graphs

D. Eppstein, M. S. Paterson, F. F. Yao
1997 Discrete & Computational Geometry  
We derive bounds 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.  ... 
doi:10.1007/pl00009293 fatcat:mz3eestmsrckzi3zmdrou3z6em

Scalable Nearest Neighbor Search based on kNN Graph [article]

Wan-Lei Zhao, Jie Yang, Cheng-Hao Deng
2017 arXiv   pre-print
In this paper, a scalable solution based 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.  ... 
arXiv:1701.08475v2 fatcat:awotobncyfhizizl64niebs2lq

Asynchronous opinion dynamics on the k-nearest-neighbors graph [article]

Wilbert Samuel Rossi, Paolo Frasca
2018 arXiv   pre-print
We assume that agents update their opinions asynchronously and that each agent's new opinion depends 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.  ... 
arXiv:1803.07401v2 fatcat:4efbmya7t5cphd23fgr6nc6ilu

Nearest-neighbor graphs on the cantor set

Nathan Shank
2009 Advances in Applied Probability  
We consider the asymptotics for the expected total edge length of the directed and undirected 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.  ... 
doi:10.1017/s000186780000313x fatcat:f5bashafgng5rougwllqzfasce

Nearest-neighbor graphs on the cantor set

Nathan Shank
2009 Advances in Applied Probability  
We consider the asymptotics for the expected total edge length of the directed and undirected 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.  ... 
doi:10.1239/aap/1240319576 fatcat:4suwo6bcp5alnmhxl3eucvys3e

EFANNA : An Extremely Fast Approximate Nearest Neighbor Search Algorithm Based on kNN Graph [article]

Cong Fu, Deng Cai
2016 arXiv   pre-print
To the best of our knowledge, EFANNA is the fastest algorithm so far both 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  ... 
arXiv:1609.07228v3 fatcat:2jwivsuv3fd5pc4watrvesjzda

All nearest neighbor calculation based on Delaunay graphs [article]

Nasrin Mazaheri Soudani, Ali Karami
2018 arXiv   pre-print
In this paper, we introduce an algorithm for computing the all 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  ... 
arXiv:1802.09594v1 fatcat:n4ndyzouyberzajfici7jcmosu

Anomaly Detection with Score functions based on Nearest Neighbor Graphs [article]

Manqi Zhao, Venkatesh Saligrama
2009 arXiv   pre-print
We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based 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).  ... 
arXiv:0910.5461v1 fatcat:4d7o7u34bbgbnpkhlnitg73mpa

Spectral Clustering Based on k-Nearest Neighbor Graph [chapter]

Małgorzata Lucińska, Sławomir T. Wierzchoń
2012 Lecture Notes in Computer Science  
We present a novel spectral algorithm Speclus with a similarity measure based 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.  ... 
doi:10.1007/978-3-642-33260-9_22 fatcat:7fcgwdxlwjfvrjsgtaz2czmyzi

Approximate Direct and Reverse Nearest Neighbor Queries, and the k-nearest Neighbor Graph

Karina Figueroa, Rodrigo Paredes
2009 2009 Second International Workshop on Similarity Search and Applications  
Then, we show how to use our approximate k-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.  ... 
doi:10.1109/sisap.2009.33 dblp:conf/sisap/FigueroaP09 fatcat:wieiyzyfdngdlarrn5rg2bjv6m

Estimation of Rényi Entropy and Mutual Information Based on Generalized Nearest-Neighbor Graphs [article]

Dávid Pál, Barnabás Póczos, Csaba Szepesvári
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 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.  ... 
arXiv:1003.1954v2 fatcat:id2rrrmmgvgy7fvvh6hnci6gvi

Graph based Nearest Neighbor Search: Promises and Failures [article]

Peng-Cheng Lin, Wan-Lei Zhao
2019 arXiv   pre-print
Recently, 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.  ... 
arXiv:1904.02077v5 fatcat:gdlf26kxpje55aul2hhx5qsy3u

Fast Nearest Neighbor Search on Large Time-Evolving Graphs [chapter]

Leman Akoglu, Rohit Khandekar, Vibhore Kumar, Srinivasan Parthasarathy, Deepak Rajan, Kun-Lung Wu
2014 Lecture Notes in Computer Science  
Finding the k 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.  ... 
doi:10.1007/978-3-662-44848-9_2 fatcat:jcy2ee74yrdglkq57n5sehgp4q

Asynchronous opinion dynamics on the $k$-nearest-neighbors graph

Wilbert Samuel Rossi, Paolo Frasca
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 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.  ... 
doi:10.1109/cdc.2018.8619285 dblp:conf/cdc/RossiF18 fatcat:fbjv7okxurhpvdqtszgcoknbu4
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