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Advances in metric embedding theory
 IN STOC ’06: PROCEEDINGS OF THE THIRTYEIGHTH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 2006
"... Metric Embedding plays an important role in a vast range of application areas such as computer vision, computational biology, machine learning, networking, statistics, and mathematical psychology, to name a few. The theory of metric embedding received much attention in recent years by mathematicians ..."
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Cited by 36 (13 self)
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Metric Embedding plays an important role in a vast range of application areas such as computer vision, computational biology, machine learning, networking, statistics, and mathematical psychology, to name a few. The theory of metric embedding received much attention in recent years
CSC2414 Metric Embeddings
"... Lecture 7: Lower bounds on the embeddability in ¡£ ¢ via expander graphs and some algorithmic connections to ¡¥¤ Notes taken by Periklis Papakonstantinou revised by Hamed Hatami Summary: In view of Bourgain’s upper bound a central question in finite metric embeddings concerns explicit constructions ..."
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Lecture 7: Lower bounds on the embeddability in ¡£ ¢ via expander graphs and some algorithmic connections to ¡¥¤ Notes taken by Periklis Papakonstantinou revised by Hamed Hatami Summary: In view of Bourgain’s upper bound a central question in finite metric embeddings concerns explicit constructions
Metric embeddings with relaxed guarantees
 IN PROCEEDINGS OF THE 46TH IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 2005
"... We consider the problem of embedding finite metrics with slack: we seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community, whic ..."
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Cited by 25 (6 self)
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We consider the problem of embedding finite metrics with slack: we seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community
Metric Embeddings with Relaxed Guarantees
, 2005
"... We consider the problem of embedding finite metrics with slack: we seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community, w ..."
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Cited by 2 (1 self)
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We consider the problem of embedding finite metrics with slack: we seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community
Computational Metric Embeddings
, 2008
"... We study the problem of computing a lowdistortion embedding between two metric spaces. More precisely given an input metric space M we are interested in computing in polynomial time an embedding into a host space M ′ with minimum multiplicative distortion. This problem arises naturally in many appl ..."
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Cited by 2 (0 self)
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We study the problem of computing a lowdistortion embedding between two metric spaces. More precisely given an input metric space M we are interested in computing in polynomial time an embedding into a host space M ′ with minimum multiplicative distortion. This problem arises naturally in many
Metric Embeddings with Relaxed Guarantees
, 2008
"... We consider the problem of embedding finite metrics with slack: we seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community, whic ..."
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We consider the problem of embedding finite metrics with slack: we seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community
Approximation Algorithms for Metric Embedding Problems
, 2005
"... We initiate the study of metric embedding problems from an approximation point of view. Metric embedding is a map from a guest metric to a host metric. The quality of the embedding is defined in terms of distortion, the ratio by which pairwise distances get skewed in the host metric. While metric em ..."
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We initiate the study of metric embedding problems from an approximation point of view. Metric embedding is a map from a guest metric to a host metric. The quality of the embedding is defined in terms of distortion, the ratio by which pairwise distances get skewed in the host metric. While metric
Graph Augmentation via Metric Embedding
"... Abstract. Kleinberg [17] proposed in 2000 the first random graph model achieving to reproduce small world navigability, i.e. the ability to greedily discover polylogarithmic routes between any pair of nodes in a graph, with only a partial knowledge of distances. Following this seminal work, a major ..."
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Cited by 1 (0 self)
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challenge was to extend this model to larger classes of graphs than regular meshes, introducing the concept of augmented graphs navigability. In this paper, we propose an original method of augmentation, based on metrics embeddings. Precisely, we prove that, for any ε>0, any graph G such that its
Playlist prediction via metric embedding
 In Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
, 2012
"... Digital storage of personal music collections and cloudbased music services (e.g. Pandora, Spotify) have fundamentally changed how music is consumed. In particular, automatically generated playlists have become an important mode of accessing large music collections. The key goal of automated playl ..."
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Cited by 14 (4 self)
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playlist generation is to provide the user with a coherent listening experience. In this paper, we present Latent Markov Embedding (LME), a machine learning algorithm for generating such playlists. In analogy to matrix factorization methods for collaborative filtering, the algorithm does not require
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