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BiLipschitz embeddings into lowdimensional Euclidean spaces
, 1990
"... Let (X; d), (Y; ae) be metric spaces and f : X ! Y an injective mapping. ..."
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Cited by 30 (3 self)
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Let (X; d), (Y; ae) be metric spaces and f : X ! Y an injective mapping.
Embedding tree metrics into low dimensional Euclidean spaces
 Discrete Comput. Geom
, 2000
"... We consider the question of embedding metrics induced by trees into Euclidean spaces with a restricted number of dimensions. We show that any weighted tree T with n(T ) vertices and l(T ) leaves can be embedded into d dimensional Euclidean space with ~ O(l(T ) 1=(d\Gamma1) ) distortion. Further, ..."
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Cited by 29 (0 self)
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We consider the question of embedding metrics induced by trees into Euclidean spaces with a restricted number of dimensions. We show that any weighted tree T with n(T ) vertices and l(T ) leaves can be embedded into d dimensional Euclidean space with ~ O(l(T ) 1=(d\Gamma1) ) distortion. Further
Bypassing the embedding: Algorithms for lowdimensional metrics
 In Proceedings of the 36th ACM Symposium on the Theory of Computing (STOC
, 2004
"... The doubling dimension of a metric is the smallest k such that any ball of radius 2r can be covered using 2 k balls of radius r. This concept for abstract metrics has been proposed as a natural analog to the dimension of a Euclidean space. If we could embed metrics with low doubling dimension into l ..."
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Cited by 77 (3 self)
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into low dimensional Euclidean spaces, they would inherit several algorithmic and structural properties of the Euclidean spaces. Unfortunately however, such a restriction on dimension does not suffice to guarantee embeddibility in a normed space. In this paper we explore the option of bypassing
On the Decidability of Connectedness Constraints in 2D and 3D Euclidean Spaces
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... We investigate (quantifierfree) spatial constraint languages with equality, contact and connectedness predicates, as well as Boolean operations on regions, interpreted over lowdimensional Euclidean spaces. We show that the complexity of reasoning varies dramatically depending on the dimension of t ..."
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Cited by 6 (1 self)
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We investigate (quantifierfree) spatial constraint languages with equality, contact and connectedness predicates, as well as Boolean operations on regions, interpreted over lowdimensional Euclidean spaces. We show that the complexity of reasoning varies dramatically depending on the dimension
On Finding Good State Aggregation Functions
 Poster submission, ICML workshop on Hierarchy and Memory in Reinforcement Learning
, 2001
"... We describe a novel algorithm that learns to perform a Heuristic Embedding of Markov Processes (HEMP) into a low dimensional Euclidean space (Engel & Mannor, 2001) Learning is performed online by observing actual state transitions and gradually constructing a map of the Markov state space. ..."
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Cited by 1 (0 self)
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We describe a novel algorithm that learns to perform a Heuristic Embedding of Markov Processes (HEMP) into a low dimensional Euclidean space (Engel & Mannor, 2001) Learning is performed online by observing actual state transitions and gradually constructing a map of the Markov state space.
Actions as spacetime shapes
 IN ICCV
, 2005
"... Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as threedimensional shapes induced by the silhouettes in the spacetime volume. We adopt a recent approach [14] for analyzing 2D shapes and genera ..."
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Cited by 651 (4 self)
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Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as threedimensional shapes induced by the silhouettes in the spacetime volume. We adopt a recent approach [14] for analyzing 2D shapes
From Few to many: Illumination cone models for face recognition under variable lighting and pose
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... We present a generative appearancebased method for recognizing human faces under variation in lighting and viewpoint. Our method exploits the fact that the set of images of an object in fixed pose, but under all possible illumination conditions, is a convex cone in the space of images. Using a smal ..."
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Cited by 754 (12 self)
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conditions. The pose space is then sampled, and for each pose the corresponding illumination cone is approximated by a lowdimensional linear subspace whose basis vectors are estimated using the generative model. Our recognition algorithm assigns to a test image the identity of the closest approximated
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
, 2003
"... One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a lowdimensional manifold embedded in a highdimensional space. Drawing on the correspondenc ..."
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Cited by 1226 (15 self)
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One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a lowdimensional manifold embedded in a highdimensional space. Drawing
The geometry of graphs and some of its algorithmic applications
 COMBINATORICA
, 1995
"... In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that res ..."
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Cited by 524 (19 self)
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tensions. 0 For graphs embeddable in lowdimensional spaces with a small distortion, we can find lowdiameter decompositions (in the sense of [4] and [34]). The parameters of the decomposition depend only on the dimension and the distortion and not on the size of the graph. 0 In graphs embedded this way
Results 1  10
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