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17,532
Robust principal component analysis?
 Journal of the ACM,
, 2011
"... Abstract This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a lowrank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the lowrank and the ..."
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Cited by 569 (26 self)
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rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the 1 norm. This suggests the possibility of a principled approach to robust principal component
Probabilistic Principal Component Analysis
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 1999
"... Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximumlikelihood estimation of paramet ..."
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Cited by 709 (5 self)
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Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximumlikelihood estimation
Mixtures of Probabilistic Principal Component Analysers
, 1998
"... Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a com ..."
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Cited by 532 (6 self)
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Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a
Sparse Principal Component Analysis
 Journal of Computational and Graphical Statistics
, 2004
"... Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA su#ers from the fact that each principal component is a linear combination of all the original variables, thus it is often di#cult to interpret the results. We introduce a new method ca ..."
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Cited by 279 (6 self)
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Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA su#ers from the fact that each principal component is a linear combination of all the original variables, thus it is often di#cult to interpret the results. We introduce a new method
Kernel principal component analysis
 ADVANCES IN KERNEL METHODS  SUPPORT VECTOR LEARNING
, 1999
"... A new method for performing a nonlinear form of Principal Component Analysis is proposed. By the use of integral operator kernel functions, one can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all ..."
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Cited by 274 (7 self)
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A new method for performing a nonlinear form of Principal Component Analysis is proposed. By the use of integral operator kernel functions, one can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space
On the distribution of the largest eigenvalue in principal components analysis
 ANN. STATIST
, 2001
"... Let x �1 � denote the square of the largest singular value of an n × p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x �1 � is the largest principal component variance of the covariance matrix X ′ X, or the largest eigenvalue of a pvariate Wishart distribu ..."
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Cited by 422 (4 self)
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Let x �1 � denote the square of the largest singular value of an n × p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x �1 � is the largest principal component variance of the covariance matrix X ′ X, or the largest eigenvalue of a pvariate Wishart
Principal Components
"... k for a linear function z 2 = ff 2 T x uncorrelated with ff 1 T x which has maximum variance subject to this condition, and so on, so that at the kth stage a linear function z k = ff k x is found which has maximum variance subject to being uncorrelated with ff 1 T x, ff 2 T x, : : : , ff k\Gamm ..."
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\Gamma1 T x. We refer to the kth derived variable ff k T x as the kth principal component. We stop after the mth stage when, in some sense, the majority of the variation has been accounted for. Before proceeding further, let us recall some results on means and variances of linear functions. Suppose
Principal Components
"... to this condition, and so on, so that at the kth stage a linear function z k = ff k x is found which has maximum variance subject to being uncorrelated with ff 1 x, ff 2 x, : : : , ff k\Gamma1 x. We refer to the kth derived variable ff k x as the kth principal component. We stop after the mt ..."
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to this condition, and so on, so that at the kth stage a linear function z k = ff k x is found which has maximum variance subject to being uncorrelated with ff 1 x, ff 2 x, : : : , ff k\Gamma1 x. We refer to the kth derived variable ff k x as the kth principal component. We stop after
Principal Component Analysis
 (IN PRESS, 2010). WILEY INTERDISCIPLINARY REVIEWS: COMPUTATIONAL STATISTICS, 2
, 2010
"... Principal component analysis (pca) is a multivariate technique that analyzes a data table in which observations are described by several intercorrelated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal var ..."
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Cited by 130 (7 self)
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Principal component analysis (pca) is a multivariate technique that analyzes a data table in which observations are described by several intercorrelated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal
Results 1  10
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17,532