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10,065
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 low-rank 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 low-rank and the ..."
Abstract
-
Cited by 569 (26 self)
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Abstract This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank 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 low
Shape and motion from image streams under orthography: a factorization method
- INTERNATIONAL JOURNAL OF COMPUTER VISION
, 1992
"... Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orth ..."
Abstract
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Cited by 1094 (38 self)
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uses the singular-value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a
High dimensional graphs and variable selection with the Lasso
- ANNALS OF STATISTICS
, 2006
"... The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a ..."
Abstract
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Cited by 736 (22 self)
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The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso
Tensor Decompositions and Applications
- SIAM REVIEW
, 2009
"... This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N -way array. Decompositions of higher-order tensors (i.e., N -way arrays with N ⥠3) have applications in psychometrics, chemometrics, signal proce ..."
Abstract
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Cited by 723 (18 self)
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processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, etc. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decompo-
sition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum
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 p-variate Wishart distribu ..."
Abstract
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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 p-variate Wishart
Testing for Common Trends
- Journal of the American Statistical Association
, 1988
"... Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix ..."
Abstract
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Cited by 464 (7 self)
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matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are often modeled as having a unit root in their autoregressive representation, or (equivalently) as containing a stochastic
Matrix Polynomials
, 1982
"... Abstract. The pseudospectra of a matrix polynomial P (λ) are sets of complex numbers that are eigenvalues of matrix polynomials which are near to P (λ), i.e., their coefficients are within some fixed magnitude of the coefficients of P (λ). Pseudospectra provide important insights into the sensitivit ..."
Abstract
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Cited by 304 (9 self)
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into the sensitivity of eigenvalues under perturbations, and have several applications. First, qualitative properties concerning boundedness and connected components of pseudospectra are obtained. Then an accurate continuation algorithm for the numerical determination of the boundary of pseudospectra of matrix
The Determinants of Credit Spread Changes.
- Journal of Finance
, 2001
"... ABSTRACT Using dealer's quotes and transactions prices on straight industrial bonds, we investigate the determinants of credit spread changes. Variables that should in theory determine credit spread changes have rather limited explanatory power. Further, the residuals from this regression are ..."
Abstract
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Cited by 422 (2 self)
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are highly crosscorrelated, and principal components analysis implies they are mostly driven by a single common factor. Although we consider several macro-economic and financial variables as candidate proxies, we cannot explain this common systematic component. Our results suggest that monthly credit spread
Online learning for matrix factorization and sparse coding
, 2010
"... Sparse coding—that is, modelling data vectors as sparse linear combinations of basis elements—is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set in order to ad ..."
Abstract
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Cited by 330 (31 self)
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to adapt it to specific data. Variations of this problem include dictionary learning in signal processing, non-negative matrix factorization and sparse principal component analysis. In this paper, we propose to address these tasks with a new online optimization algorithm, based on stochastic approximations
Figure 2a. Rotated Component Matrix – CE 221 Figure 2b. Rotated Component Matrix – CE 221
"... Rotation converged in 5 iterations, and the component value is rejected below 0.30. Kaiser-Meyer Measure of Sampling Adequacy is 0.936, Bartlett’s Test of sphericity has approx. Chi square of 13047.557. The result of factor analysis for CE 221 by using SPSS is presented in Figures 2 (a, b). ..."
Abstract
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Rotation converged in 5 iterations, and the component value is rejected below 0.30. Kaiser-Meyer Measure of Sampling Adequacy is 0.936, Bartlett’s Test of sphericity has approx. Chi square of 13047.557. The result of factor analysis for CE 221 by using SPSS is presented in Figures 2 (a, b).
Results 1 - 10
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10,065
