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Orthogonal Rank Decompositions for Tensors
 In preparation
, 1999
"... rder and all subdimensions are equal) then the inner product of A and B is defined as A \Delta B j m 1 X i 1 =1 m 2 X i 2 =1 \Delta \Delta \Delta mn X i n=1 A i 1 i 2 \Delta\Delta\Deltai n B i 1 i 2 \Delta\Delta\Deltai n : Correspondingly, the norm of A, kAk, is defined as kAk 2 j A \D ..."
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Cited by 3 (3 self)
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rder and all subdimensions are equal) then the inner product of A and B is defined as A \Delta B j m 1 X i 1 =1 m 2 X i 2 =1 \Delta \Delta \Delta mn X i n=1 A i 1 i 2 \Delta\Delta\Deltai n B i 1 i 2 \Delta\Delta\Deltai n : Correspondingly, the norm of A, kAk, is defined as kAk 2 j A \Delta A. A tensor A is a unit tensor if kAk = 1. A decomposed tensor is a tensor that can be written as x = x<F39
ORTHOGONAL RANKONE MATRIX PURSUIT FOR MATRIX COMPLETION
"... Abstract. In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rul ..."
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Abstract. In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating
Face recognition using discriminatively trained orthogonal rank one tensor projections
 In Proc. CVPR
, 2007
"... We propose a method for face recognition based on a discriminative linear projection. In this formulation images are treated as tensors, rather than the more conventional vector of pixels. Projections are pursued sequentially and take the form of a rank one tensor, i.e., a tensor which is the outer ..."
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Cited by 15 (2 self)
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product of a set of vectors. A novel and effective technique is proposed to ensure that the rank one tensor projections are orthogonal to one another. These constraints on the tensor projections provide a strong inductive bias and result in better generalization on small training sets. Our work is related
Face Recognition Based on LBP and Orthogonal RankOne Tensor Projections
"... In this paper, a novel framework for face recognition based on discriminatively trained orthogonal rankone tensor projections (ORO) and local binary pattern (LBP) is proposed. LBP is an efficient method for extracting shape and texture information and it is robustness to illumination and expression ..."
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In this paper, a novel framework for face recognition based on discriminatively trained orthogonal rankone tensor projections (ORO) and local binary pattern (LBP) is proposed. LBP is an efficient method for extracting shape and texture information and it is robustness to illumination
A Counterexample to the Possibility of an Extension of the EckartYoung LowRank approximation Theorem for the Orthogonal Rank Tensor Decomposition
 SIAM Journal on Matrix Analysis and Applications
, 2003
"... Abstract. Earlier work has shown that no extension of the Eckart–Young SVD approximation theorem can be made to the strong orthogonal rank tensor decomposition. Here, we present a counterexample to the extension of the Eckart–Young SVD approximation theorem to the orthogonal rank tensor decompositio ..."
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Cited by 20 (2 self)
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Abstract. Earlier work has shown that no extension of the Eckart–Young SVD approximation theorem can be made to the strong orthogonal rank tensor decomposition. Here, we present a counterexample to the extension of the Eckart–Young SVD approximation theorem to the orthogonal rank tensor
Face Recognition by Discriminative Orthogonal Rankone Tensor Decomposition
"... Discriminative subspace analysis has been a popular approach to face recognition. Most of the previous work such as Eigenfaces (Turk & Pentlend, 1991), LDA (Belhumeur et al., 1997), Laplacian faces (He et al., 2005a), as well as a variety of tensor based subspace ..."
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Discriminative subspace analysis has been a popular approach to face recognition. Most of the previous work such as Eigenfaces (Turk & Pentlend, 1991), LDA (Belhumeur et al., 1997), Laplacian faces (He et al., 2005a), as well as a variety of tensor based subspace
Reliable Communication in the Presence of Failures
 ACM Transactions on Computer Systems
, 1987
"... The design and correctness of a communication facility for a distributed computer system are reported on. The facility provides support for faulttolerant process groups in the form of a family of reliable multicast protocols that can be used in both local and widearea networks. These protocols at ..."
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Cited by 556 (20 self)
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properties like member rankings. A review of several uses for the protocols in the ISIS system, which supports faulttolerant resilient objects and bulletin boards, illustrates the significant simplification of higher level algorithms made possible by our approach.
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 672 (18 self)
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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 methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take advantage of the implicit higherorder structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented 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 automatic yet intelligent indexing method, widely applicable, and a promising way to improve users...
An introduction to variable and feature selection
 Journal of Machine Learning Research
, 2003
"... Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available. ..."
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Cited by 1283 (16 self)
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Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available.
Probabilistic Visual Learning for Object Representation
, 1996
"... We present an unsupervised technique for visual learning which is based on density estimation in highdimensional spaces using an eigenspace decomposition. Two types of density estimates are derived for modeling the training data: a multivariate Gaussian (for unimodal distributions) and a Mixtureof ..."
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Cited by 705 (15 self)
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We present an unsupervised technique for visual learning which is based on density estimation in highdimensional spaces using an eigenspace decomposition. Two types of density estimates are derived for modeling the training data: a multivariate Gaussian (for unimodal distributions) and a MixtureofGaussians model (for multimodal distributions). These probability densities are then used to formulate a maximumlikelihood estimation framework for visual search and target detection for automatic object recognition and coding. Our learning technique is applied to the probabilistic visual modeling, detection, recognition, and coding of human faces and nonrigid objects such as hands.
Results 1  10
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