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Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear
ROCK: A Robust Clustering Algorithm for Categorical Attributes
 In Proc.ofthe15thInt.Conf.onDataEngineering
, 2000
"... Clustering, in data mining, is useful to discover distribution patterns in the underlying data. Clustering algorithms usually employ a distance metric based (e.g., euclidean) similarity measure in order to partition the database such that data points in the same partition are more similar than point ..."
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Cited by 446 (2 self)
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Clustering, in data mining, is useful to discover distribution patterns in the underlying data. Clustering algorithms usually employ a distance metric based (e.g., euclidean) similarity measure in order to partition the database such that data points in the same partition are more similar than
Ricci Flow with Surgery on ThreeManifolds
"... This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper, as the ..."
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Cited by 448 (2 self)
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was considered by Hamilton [H 5,§4,5]; unfortunately, his argument, as written, contains an unjustified statement (RMAX = Γ, on page 62, lines 710 from the bottom), which I was unable to fix. Our approach is somewhat different, and is aimed at eventually constructing a canonical Ricci flow, defined on a largest
Euclidean Distance Mapping
, 1980
"... Based on a twocomponent descriptor, a distance label for each point, it is shown that Euclidean distance maps can be generated by effective sequential algorithms. The map indicates, for each pixel in the objects (or the background) of the originally binary picture, the shortest distance to the near ..."
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Cited by 233 (0 self)
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picture itself. It is shown that skeletons can be produced by simple procedures and since these are based on Euclidean distances it is assumed that they are superior to skeletons based on d4, ds, and even octagonal metrics.
LogEuclidean metrics for fast and simple calculus on diffusion tensors
 Magnetic Resonance in Medicine
, 2006
"... Euclidean metrics on diffusion tensors. Total word count: 6400. ..."
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Cited by 217 (26 self)
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Euclidean metrics on diffusion tensors. Total word count: 6400.
The Canonical Metric For Vector Quantization
, 1995
"... . To measure the quality of a set of vector quantization points a means of measuring the distance between two points is required. Common metrics such as the Hamming and Euclidean metrics, while mathematically simple, are inappropriate for comparing speech signals or images. In this paper it is ar ..."
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Cited by 9 (0 self)
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. To measure the quality of a set of vector quantization points a means of measuring the distance between two points is required. Common metrics such as the Hamming and Euclidean metrics, while mathematically simple, are inappropriate for comparing speech signals or images. In this paper
Strong uniqueness of the Ricci flow
 arXiv:0706.3081. HUAIDONG CAO
"... In this paper, we derive some local a priori estimates for Ricci flow. This gives rise to some strong uniqueness theorems. As a corollary, let g(t) be a smooth complete solution to the Ricci flow onR 3, with the canonical Euclidean metric E as initial data, then g(t) is trivial, i.e. g(t)≡E. 1 ..."
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Cited by 92 (0 self)
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In this paper, we derive some local a priori estimates for Ricci flow. This gives rise to some strong uniqueness theorems. As a corollary, let g(t) be a smooth complete solution to the Ricci flow onR 3, with the canonical Euclidean metric E as initial data, then g(t) is trivial, i.e. g(t)≡E. 1
The Canonical Metric for Vector Quantization
, 1995
"... The Problem 1 Abstract To measure the quality of a set of vector quantization points a means of measuring the distance between two points is required. Common metrics such as the Hamming and Euclidean metrics, while mathematically simple, are inappropriate for comparing speech signals or images. In t ..."
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The Problem 1 Abstract To measure the quality of a set of vector quantization points a means of measuring the distance between two points is required. Common metrics such as the Hamming and Euclidean metrics, while mathematically simple, are inappropriate for comparing speech signals or images
Rigidity of quasiisometries for symmetric spaces and Euclidean buildings
 Inst. Hautes Études Sci. Publ. Math
, 1997
"... 1.1 Background and statement of results An (L, C) quasiisometry is a map Φ: X − → X ′ between metric spaces such that for all x1, x2 ∈ X ..."
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Cited by 189 (28 self)
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1.1 Background and statement of results An (L, C) quasiisometry is a map Φ: X − → X ′ between metric spaces such that for all x1, x2 ∈ X
Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors
, 2003
"... One of the challenges in 3D shape matching arises from the fact that in many applications, models should be considered to be the same if they differ by a rotation. Consequently, when comparing two models, a similarity metric implicitly provides the measure of similarity at the optimal alignment. E ..."
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Cited by 285 (11 self)
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One of the challenges in 3D shape matching arises from the fact that in many applications, models should be considered to be the same if they differ by a rotation. Consequently, when comparing two models, a similarity metric implicitly provides the measure of similarity at the optimal alignment
Results 1  10
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4,001