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The Diameter of Nearest Neighbor Graphs
, 1992
"... Any connected plane nearest neighbor graph has diameter #(n 1/6 ). This bound generalizes to #(n 1/3d ) in any dimension d. For any set of n points in the plane, we define the nearest neighbor graph by selecting a unique nearest neighbor for each point, and adding an edge between each point an ..."
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Cited by 51 (0 self)
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Any connected plane nearest neighbor graph has diameter #(n 1/6 ). This bound generalizes to #(n 1/3d ) in any dimension d. For any set of n points in the plane, we define the nearest neighbor graph by selecting a unique nearest neighbor for each point, and adding an edge between each point
Cluster identification in nearestneighbor graphs
, 2007
"... Abstract. Assume we are given a sample of points from some underlying distribution which contains several distinct clusters. Our goal is to construct a neighborhood graph on the sample points such that clusters are “identified”: that is, the subgraph induced by points from the same cluster is connec ..."
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Cited by 2 (1 self)
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is connected, while subgraphs corresponding to different clusters are not connected to each other. We derive bounds on the probability that cluster identification is successful, and use them to predict “optimal ” values of k for the mutual and symmetric knearestneighbor graphs. We point out different
Separators for spherepackings and nearest neighbor graphs
 J. ACM
, 1997
"... Abstract. A collection of n balls in d dimensions forms a kply system if no point in the space is covered by more than k balls. We show that for every kply system �, there is a sphere S that intersects at most O(k 1/d n 1�1/d) balls of � and divides the remainder of � into two parts: those in the ..."
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Cited by 103 (8 self)
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that every knearest neighbor graphs of n points in d dimensions has a separator of size O(k 1/d n 1�1/d). In conjunction with a result of Koebe that every triangulated planar graph is isomorphic to the intersection graph of a diskpacking, our result not only gives a new geometric proof of the planar
Fast construction of kNearest Neighbor Graphs for Point Clouds
"... Abstract—We present a parallel algorithm for knearest neighbor graph construction that uses Morton ordering. Experiments show that our approach has the following advantages over existing methods: (1) Faster construction of knearest neighbor graphs in practice on multicore machines. (2) Less space ..."
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Cited by 28 (1 self)
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Abstract—We present a parallel algorithm for knearest neighbor graph construction that uses Morton ordering. Experiments show that our approach has the following advantages over existing methods: (1) Faster construction of knearest neighbor graphs in practice on multicore machines. (2) Less
Parallel Construction of kNearest Neighbor Graphs for Point Clouds
, 2008
"... We present a parallel algorithm for knearest neighbor graph construction that uses Morton ordering. Experiments show that our approach has the following advantages over existing methods: (1) Faster construction of knearest neighbor graphs in practice on multicore machines. (2) Less space usage. ( ..."
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Cited by 6 (1 self)
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We present a parallel algorithm for knearest neighbor graph construction that uses Morton ordering. Experiments show that our approach has the following advantages over existing methods: (1) Faster construction of knearest neighbor graphs in practice on multicore machines. (2) Less space usage
The size of components in continuum nearestneighbor graphs
 Ann. Probab
"... We study the size of connected components of random nearestneighbor graphs with vertex set the points of a homogeneous Poisson point process in R d. The connectivity function is shown to decay superexponentially, and we identify the exact exponent. From this we also obtain the decay rate of the maxi ..."
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Cited by 4 (0 self)
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” Poisson point located at the origin. Let ⃗Gd denote the directed graph whose vertices are the Poisson points and in which there is a directed edge from s ∈ X to s ′ ∈ X if s ′ is the nearest neighbor (NN) of s. Ignoring the directions of the edges leads to an undirected graph which we denote by just Gd
Estimation of Rényi entropy and mutual information based on generalized nearestneighbor graphs
, 2010
"... 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 R d. The estimators are calculated as the sum of pth powers of the Euclidean lengths of the edges ..."
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Cited by 31 (2 self)
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of the edges of the ‘generalized nearestneighbor ’ graph of the sample and the empirical copula of the sample respectively. For the first time, we prove the almost sure consistency of these estimators and upper bounds on their rates of convergence, the latter of which under the assumption that the density
Hubness: An Interesting Property of Nearest Neighbor Graphs and its Impact on Classication
"... Abstract: The presence of hubs, i.e., a few vertices that appear as neighbors of surprisingly many other vertices, is a recently explored property of nearest neighbor graphs. Several Authors argue that the presence of hubs should be taken into account for various data mining tasks, such as classicat ..."
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Abstract: The presence of hubs, i.e., a few vertices that appear as neighbors of surprisingly many other vertices, is a recently explored property of nearest neighbor graphs. Several Authors argue that the presence of hubs should be taken into account for various data mining tasks
Shortest path distance in random knearest neighbor graphs
 In ICML. icml.cc / Omnipress
, 2012
"... Consider a weighted or unweighted knearest neighbor graph that has been built on n data points drawn randomly according to some density p on Rd. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this ..."
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Cited by 4 (2 self)
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Consider a weighted or unweighted knearest neighbor graph that has been built on n data points drawn randomly according to some density p on Rd. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs
Results 1  10
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468,204