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Probabilistic Approximation of Metric Spaces and its Algorithmic Applications
 In 37th Annual Symposium on Foundations of Computer Science
, 1996
"... The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized ..."
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Cited by 351 (32 self)
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The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized
Geographical embedding of scalefree networks
 Physica A
, 2003
"... Abstract A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of scalefree networks embedded by the suggested algorithm are ..."
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Cited by 4 (0 self)
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Abstract A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of scalefree networks embedded by the suggested algorithm
Geographical Embedding of ScaleFree Networks
"... A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of scalefree networks embedded by the suggested algorithm are studied b ..."
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A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of scalefree networks embedded by the suggested algorithm are studied
OPTIMAL EMBEDDINGS OF DISTANCE TRANSITIVE GRAPHS INTO EUCLIDEAN SPACES
, 2005
"... In this paper we give an explicit formula for the least distortion embedding of a distance transitive graph into Euclidean space. We use this formula for finding least distortion embeddings for important examples: Hamming graphs, Johnson graphs, and Grassmann graphs. Our technique involves semidefi ..."
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Cited by 2 (1 self)
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In this paper we give an explicit formula for the least distortion embedding of a distance transitive graph into Euclidean space. We use this formula for finding least distortion embeddings for important examples: Hamming graphs, Johnson graphs, and Grassmann graphs. Our technique involves
EMBEDDING PRODUCTS OF GRAPHS INTO EUCLIDEAN SPACES Mikhail Skopenkov
, 808
"... Abstract. For any collection of graphs G1,..., GN we find the minimal dimension d such that the product G1 × · · · × GN is embeddable into R d. In particular, we prove that (K5) n and (K3,3) n are not embeddable into R 2n, where K5 and K3,3 are the Kuratowski graphs. This is a solution of a prob ..."
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Abstract. For any collection of graphs G1,..., GN we find the minimal dimension d such that the product G1 × · · · × GN is embeddable into R d. In particular, we prove that (K5) n and (K3,3) n are not embeddable into R 2n, where K5 and K3,3 are the Kuratowski graphs. This is a solution of a
Visualizing the embedding of objects in Euclidean space
 Proc. of the 24th Symp. on the Interface
, 1992
"... Matrices representing dissimilarities within a set of objects are familiar in mathematics, statistics and psychology. In this paper we describe XGvis, a software system which accepts diverse input data, such as graphs and multivariate data, develops a dissimilarity matrix from the data, and then ite ..."
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Cited by 9 (5 self)
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, and then iteratively and interactively embeds objects in a Euclidean space of arbitrary dimension. Using a technique called multidimensional scaling, objects are positioned so that their pairwise distances match the target dissimilarities as well as possible. Users can interact with XGobi, a software system
On the Embeddability of Weighted Graphs in Euclidean Spaces
, 1998
"... Given an incomplete edgeweighted graph, G = (V; E; !), G is said to be embeddable in ! r , or rembeddable, if the vertices of G can be mapped to points in ! r such that every two adjacent vertices v i , v j of G are mapped to points x i , x j 2 ! r whose Euclidean distance is equal to t ..."
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Cited by 12 (1 self)
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Given an incomplete edgeweighted graph, G = (V; E; !), G is said to be embeddable in ! r , or rembeddable, if the vertices of G can be mapped to points in ! r such that every two adjacent vertices v i , v j of G are mapped to points x i , x j 2 ! r whose Euclidean distance is equal
Structure Preserving Embedding
"... Structure Preserving Embedding (SPE) is an algorithm for embedding graphs in Euclidean space such that the embedding is lowdimensional and preserves the global topological properties of the input graph. Topology is preserved if a connectivity algorithm, such as knearest neighbors, can easily recove ..."
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Cited by 29 (6 self)
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Structure Preserving Embedding (SPE) is an algorithm for embedding graphs in Euclidean space such that the embedding is lowdimensional and preserves the global topological properties of the input graph. Topology is preserved if a connectivity algorithm, such as knearest neighbors, can easily
Unified graph matching in euclidean spaces
 In CVPR
, 2010
"... Graph matching is a classical problem in pattern recognition with many applications, particularly when the graphs are embedded in Euclidean spaces, as is often the case for computer vision. There are several variants of the matching problem, concerned with isometries, isomorphisms, homeomorphisms, a ..."
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Cited by 1 (1 self)
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Graph matching is a classical problem in pattern recognition with many applications, particularly when the graphs are embedded in Euclidean spaces, as is often the case for computer vision. There are several variants of the matching problem, concerned with isometries, isomorphisms, homeomorphisms
Diffusion kernels on graphs and other discrete input spaces
 in: Proceedings of the 19th International Conference on Machine Learning
, 2002
"... The application of kernelbased learning algorithms has, so far, largely been confined to realvalued data and a few special data types, such as strings. In this paper we propose a general method of constructing natural families of kernels over discrete structures, based on the matrix exponentiation ..."
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Cited by 223 (5 self)
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idea. In particular, we focus on generating kernels on graphs, for which we propose a special class of exponential kernels called diffusion kernels, which are based on the heat equation and can be regarded as the discretization of the familiar Gaussian kernel of Euclidean space.
Results 11  20
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2,236