A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis.

By Daniela M. Witten, Robert Tibshirani, Trevor J. Hastie. Biostatistics, 2009

1,644 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7953ea921cbd3c62cac3004dafcd630e31eae81d

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Citations in the corpus

Comprehensive integration of single-cell data (2018, background): “…these experiments is generally much larger than the total number of features shared between the datasets, we opt for a diagonalized CCA implementation that has shown promising performance in related high-dimensional applications [Witten et al., 2009; Dudoit et al., 2002; Tibshirani et al., 2003].”
Finding and Leveraging Structure in Learning Problems (2012, methodology): “This leads us to a strategy of biconvex optimization that mirrors the linear algorithm of [Witten et al., 2009]; specifically, initialize by solving the problem without the sparsity constraints, fix α and optimize for β and vice-versa until convergence.”
A Sparse Singular Value Decomposition Method for High-Dimensional Data (2014, methodology): “In the Appendix, Section B states the minimax result under normal assumptions and Section C shows simulation results to compare the performance of our method with that of Witten, Tibshirani, and Hastie (2009) and Lee et al. (2010).”
A Survey of Multi-View Representation Learning (2016, neutral): “Through fully investigating the characteristics of the existing successful multi-view representation learning techniques, we observe that there are several common underlying principles behind their success: correlation, consensus, and complementarity principles.”
Latent variable graphical model selection via convex optimization (2010, methodology): “, [38]) can be used to further factorize L̂, depending on the property that one desires in the factors (e.”
Bayesian group factor analysis with structured sparsity (2016, methodology): “Imposing element-wise sparsity in latent factor models has been studied through regularization via `1 type penalties (Zou et al., 2006; Witten et al., 2009; Salzmann et al., 2010).”
Random matrix theory in statistics: A review (2014, methodology): “…for the X and Y variables in the canonical correlation computation), are constrained to be sparse through imposition of sparse penalty, have also been proposed in the literature, notably by Hardoon and Shawe-Taylor (2009), Lee et al. (2009), Parkhomenko et al. (2009) and Witten et al. (2009).”
A feasible method for optimization with orthogonality constraints (2012, methodology): “Sparse principal component analysis (PCA) PCA methods such as [15,58] are widely used is data analysis and dimension reduction.”
Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics (2016, methodology): “In this section, we consider an application of the perturbation bounds given in Theorem 1 to the canonical correlation analysis (CCA), which is one of the most important tools in multivariate analysis in exploring the relationship between two sets of variables (Hotelling, 1936; Anderson, 2003; Witte”
Proximal Algorithms in Statistics and Machine Learning (2015, background): “…practice and it arises, for example, in sparse regression [Tibshirani, 1996], spatial smoothing [Tibshirani et al., 2005], covariance estimation [Witten et al., 2009], image processing [Geman and Reynolds, 1992, Geman and Yang, 1995, Rudin et al., 1992], nonlinear curve ﬁtting [Tibshirani,…”
Sparse PLS discriminant analysis: biologically relevant feature selection and graphical displays for multiclass problems (2011, methodology): “These penalties ( l 1 and/or l 2 ) were applied to the variable weight vectors in order to select the relevant variables in PCA [20,21] and more recently in Canonical Correlation Analysis [22-24] and in PLS [25-27].”
Robust Computation of Linear Models by Convex Relaxation (2012, result): “], and it has been explored by many other authors [1,18,43,49,75].”
Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning (2017, background): “It attracts a lot of attention in applications such as bioinformatics, big data analysis, and machine learning, where a parsimonious interpretation of the data set is desired, see references [37], [125]–[127] for examples.”
Large Covariance Estimation by Thresholding Principal Orthogonal Complements (2011, positive): “…components, which has been widely used to enhance the convergence of the principal components in high-dimensional space. d’Aspremont, Bach and El Ghaoui (2008), Shen and Huang (2008), Witten, Tibshirani, and Hastie (2009) and Ma (2011) proposed and studied various algorithms for computations.”