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SEQUENTIAL SUBSPACE FINDING: A NEW ALGORITHM FOR LEARNING LOWDIMENSIONAL LINEAR SUBSPACES
"... In this paper we propose a new algorithm for learning lowdimensional linear subspaces. Our proposed algorithm performs by sequentially finding some lowdimensional subspaces on which a set of training data lies. Each subspace is found in such a way that the number of signals lying on (or near to) it ..."
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In this paper we propose a new algorithm for learning lowdimensional linear subspaces. Our proposed algorithm performs by sequentially finding some lowdimensional subspaces on which a set of training data lies. Each subspace is found in such a way that the number of signals lying on (or near to
Lambertian Reflectance and Linear Subspaces
, 2000
"... We prove that the set of all reflectance functions (the mapping from surface normals to intensities) produced by Lambertian objects under distant, isotropic lighting lies close to a 9D linear subspace. This implies that, in general, the set of images of a convex Lambertian object obtained under a wi ..."
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Cited by 514 (20 self)
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wide variety of lighting conditions can be approximated accurately by a lowdimensional linear subspace, explaining prior empirical results. We also provide a simple analytic characterization of this linear space. We obtain these results by representing lighting using spherical harmonics and describing
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 747 (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
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
, 1997
"... We develop a face recognition algorithm which is insensitive to gross variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a highdimensional space. We take advantage of the observation that the images ..."
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Cited by 2263 (18 self)
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in a lowdimensional subspace even under severe variation in lighting and facial expressions. The Eigenface
Subspace Mappings for Image Sequences
 In: Proc. Workshop Statistical Methods in Video Processing
, 2002
"... We consider the use of lowdimensional linear subspace models to infer one highdimensional signal from another, for example, predicting an image sequence from a related image sequence. In the memoryless case the subspaces are found by rankconstrained division, and inference is an inexpensive seque ..."
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Cited by 9 (0 self)
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We consider the use of lowdimensional linear subspace models to infer one highdimensional signal from another, for example, predicting an image sequence from a related image sequence. In the memoryless case the subspaces are found by rankconstrained division, and inference is an inexpensive
The Extended Linear Complementarity Problem
, 1993
"... We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity of the biline ..."
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Cited by 776 (28 self)
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We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity
GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
 SIAM J. SCI. STAT. COMPUT
, 1986
"... We present an iterative method for solving linear systems, which has the property ofminimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an l2orthogonal basis of Krylov subspaces. It can be considered a ..."
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Cited by 2046 (40 self)
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We present an iterative method for solving linear systems, which has the property ofminimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an l2orthogonal basis of Krylov subspaces. It can be considered
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
, 2008
"... ..."
A Robust Subspace Approach to Layer Extraction
, 2002
"... Representing images with layers has many important applications, such as video compression, motion analysis, and 3D scene analysis. This paper presents a robust subspace approach to reliably extracting layers from images by taking advantages of the fact that homographies induced by planar patches in ..."
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Cited by 63 (6 self)
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in the scene form a low dimensional linear subspace. Such subspace provides not only a feature space where layers in the image domain are mapped onto denser and betterdefined clusters, but also a constraint for detecting outliers in the local measurements, thus making the algorithm robust to outliers
Results 1  10
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854,818