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3,364,761
Maximum likelihood from incomplete data via the EM algorithm
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 1977
"... A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situat ..."
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Cited by 11807 (17 self)
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situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.
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 703 (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
Robust Principal Component Analysis?
, 2009
"... 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 sparse co ..."
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Cited by 553 (26 self)
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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 ℓ1 norm. This suggests the possibility of a principled approach to robust principal component analysis
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 270 (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 270 (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
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 125 (6 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
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 418 (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
WITH SPARSE PRINCIPAL COMPONENT ANALYSIS
"... The development of the technology makes it possible to measure large amount of genes expressions simultaneously. Since biological functions are mostly coordinated by multiple genes, called “gene pathway”, it is interesting to identify differential gene pathways which are associated with clinical phe ..."
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phenotype. Principal component analysis has been proposed to identify differential gene pathways in several literatures, while sparse principal component analysis (SPCA) has not drawn any attention. We proposed to use SPCA to identify differential gene pathways. The results show that, comparing to PCA, SPCA
Principal Component Analysis
, 2007
"... Principal component analysis (also known as principal components analysis) (PCA) is a technique from statistics for simplifying a data set. It was developed by Pearson (1901) and Hotelling (1933), whilst the best modern reference is Jolliffe (2002). The aim of the method is to reduce the dimensional ..."
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Principal component analysis (also known as principal components analysis) (PCA) is a technique from statistics for simplifying a data set. It was developed by Pearson (1901) and Hotelling (1933), whilst the best modern reference is Jolliffe (2002). The aim of the method is to reduce
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 1 (0 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
Results 1  10
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3,364,761