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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 526 (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 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
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 2310 (17 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 10 (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
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 2076 (41 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
Using Linear Algebra for Intelligent Information Retrieval
 SIAM REVIEW
, 1995
"... Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical ..."
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Cited by 676 (18 self)
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by 200300 of the largest singular vectors are then matched against user queries. We call this retrieval method Latent Semantic Indexing (LSI) because the subspace represents important associative relationships between terms and documents that are not evident in individual documents. LSI is a completely
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization,”
 SIAM Review,
, 2010
"... Abstract The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and col ..."
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Cited by 562 (20 self)
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Abstract The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding
Subspace methods for computational relighting
 in Proc. IS&T/SPIE Comput. Imaging XI
, 2013
"... We propose a vector space approach for relighting a Lambertian convex object with distant light source, whose crucial task is the decomposition of the reflectance function into albedos (or reflection coefficients) and lightings based on a set of images of the same object and its 3D model. Making us ..."
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Cited by 1 (1 self)
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use of the fact that reflectance functions are well approximated by a lowdimensional linear subspace spanned by the first few spherical harmonics, this inverse problem can be formulated as a matrix factorization, in which the basis of the subspace is encoded in the spherical harmonic matrix S. A
Efficient PointtoSubspace Query in `1: Theory and Applications in Computer Vision∗
"... Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of lowdimensional linear subspaces in a highdimensional ambient (image) space and a query point (image), efficiently determine the nearest subspace to the query in ..."
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Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of lowdimensional linear subspaces in a highdimensional ambient (image) space and a query point (image), efficiently determine the nearest subspace to the query
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