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878
Wavelet Synopsis for Data Streams: Minimizing NonEuclidean Error
, 2005
"... We consider the wavelet synopsis construction problem for data streams where given n numbers we wish to estimate the data by constructing a synopsis, whose size, say B is much smaller than n. The B numbers are chosen to minimize a suitable error between the original data and the estimate derived fro ..."
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Cited by 22 (3 self)
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) for minimizing a variety of nonEuclidean error measures including all weighted ℓp (including ℓ∞) and relative error ℓp metrics. In several previous works solutions (for weighted ℓ2, ℓ∞ and maximum relative error) where the B synopsis coefficients are restricted to be wavelet coefficients of the data were
ABSTRACT Wavelet Synopsis for Data Streams: Minimizing NonEuclidean Error
"... We consider the wavelet synopsis construction problem for data streams where given n numbers we wish to estimate the data by constructing a synopsis, whose size, say B is much smaller than n. The B numbers are chosen to minimize a suitable error between the original data and the estimate derived fro ..."
Abstract
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) for minimizing a variety of nonEuclidean error measures including all weighted ℓp (including ℓ∞) and relative error ℓp metrics. In several previous works solutions (for weighted ℓ2, ℓ∞ and maximum relative error) where the B synopsis coefficients are restricted to be wavelet coefficients of the data were
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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illumination cone (based on Euclidean distance within the image space). We test our face recognition method on 4050 images from the Yale Face Database B; these images contain 405 viewing conditions (9 poses ¢ 45 illumination conditions) for 10 individuals. The method performs almost without error, except
LucasKanade 20 Years On: A Unifying Framework: Part 3
 International Journal of Computer Vision
, 2002
"... Since the LucasKanade algorithm was proposed in 1981 image alignment has become one of the most widely used techniques in computer vision. Applications range from optical flow, tracking, and layered motion, to mosaic construction, medical image registration, and face coding. Numerous algorithms hav ..."
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Cited by 706 (30 self)
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first consider linear appearance variation when the error function is the Euclidean L2 norm. We describe three different algorithms, the simultaneous, project out, and normalization inverse compositional algorithms, and empirically compare them. Afterwards we consider the combination of linear
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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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
Face recognition using laplacianfaces
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Abstract—We propose an appearancebased face recognition method called the Laplacianface approach. By using Locality Preserving Projections (LPP), the face images are mapped into a face subspace for analysis. Different from Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) wh ..."
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Cited by 389 (38 self)
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) which effectively see only the Euclidean structure of face space, LPP finds an embedding that preserves local information, and obtains a face subspace that best detects the essential face manifold structure. The Laplacianfaces are the optimal linear approximations to the eigenfunctions of the Laplace
Locally Adaptive Dimensionality Reduction for Indexing Large Time Series Databases
 In proceedings of ACM SIGMOD Conference on Management of Data
, 2002
"... Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions' involve performing dimensionality reduction on the data, then indexing the reduced d ..."
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Cited by 316 (33 self)
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' of varying lengths' such that their individual reconstruction errors' are minimal. We show how APCA can be indexed using a multidimensional index structure. We propose two distance measures in the indexed space that exploit the high fidelity of APCA for fast searching: a lower bounding Euclidean
Error correction with euclidean qubits
 Quantum Computers & Computing
, 2001
"... In classical case there is simplest method of error correction with using three equal bits instead of one. In the paper is shown, how the scheme fails for quantum error correction with complex vector spaces of usual quantum mechanics, but works in real and quaternionic cases. It is discussed also, h ..."
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Cited by 2 (0 self)
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In classical case there is simplest method of error correction with using three equal bits instead of one. In the paper is shown, how the scheme fails for quantum error correction with complex vector spaces of usual quantum mechanics, but works in real and quaternionic cases. It is discussed also
BigBang Simulation for Embedding Network Distances in Euclidean Space
, 2004
"... Embedding of a graph metric in Euclidean space efficiently and accurately is an important problem in general with applications in topology aggregation, closest mirror selection, and application level routing. We propose a new graph embedding scheme called BigBang Simulation (BBS), which simulates a ..."
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Cited by 151 (4 self)
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Embedding of a graph metric in Euclidean space efficiently and accurately is an important problem in general with applications in topology aggregation, closest mirror selection, and application level routing. We propose a new graph embedding scheme called BigBang Simulation (BBS), which simulates
Principal manifolds and nonlinear dimensionality reduction via tangent space alignment
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 2004
"... Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and nonlinear dimension reduction. Based on a set of unorganized ..."
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Cited by 261 (15 self)
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to the underlying manifold by way of a partial eigendecomposition of the neighborhood connection matrix. We present a careful error analysis of our algorithm and show that the reconstruction errors are of secondorder accuracy. We illustrate our algorithm using curves and surfaces both in 2D/3D and higher
Results 1  10
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878