Sparse principal component analysis via regularized low rank matrix approximation

By Haipeng Shen, Jianhua Z. Huang. 2008

733 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Signal Processing

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Citations in the corpus

MINIMAX SPARSE PRINCIPAL SUBSPACE ESTIMATION IN HIGH DIMENSIONS (2012, methodology): “When q = 1 this is equivalent to a penalized form of the sparse PCA estimator considered in Jolliﬀe, Trendaﬁlov and Uddin (2003) and it also bears similarity to the estimator considered by Shen and Huang (2008).”
Finding and Leveraging Structure in Learning Problems (2012, background): “A lot of recent work has dealt with estimation of sparse eigenvectors of A′A, see for example the papers [6, 103, 169, 204, 212].”
Penalized classification using Fisher’s linear discriminant (2011, background): “The criterion (12) and Algorithm 1 for optimizing it are closely related to the penalized principal components algorithms considered by a number of authors (see e.g. Zou et al., 2006; Shen and Huang, 2008; Witten et al., 2009).”
Sparse Principal Component Analysis and Iterative Thresholding (2011, methodology): “…addition the leading eigenvector has exactly k non-zero loadings, Amini and Wainwright [1] studied conditions for recovering the non-zero locations using the methods in [14] and [3], and Shen, et al [28] established conditions for consistency of a sparse PCA method in [29] when p → ∞ and n is ﬁxed.”
Joint variable and rank selection for parsimonious estimation of high-dimensional matrices (2011, background): “ious attempts to achieve a similar goal belong mainly to the class of sparse PCA algorithms, see, e.g., SCotLass (Jolliﬀe, Trendaﬁlov, and Uddin, 2003), sparse PCA (Zou, Hastie, and Tibshirani, 2006; Shen and Huang, 2008), and the penalized matrix decomposition (PMD) (Witten, Tibshirani, and Hastie,”
Generalized Power Method for Sparse Principal Component Analysis (2008, methodology): “[24]) and the sPCA-rSVD algorithm (Shen and Huang [18]).”
Truncated power method for sparse eigenvalue problems (2011, methodology): “Here we do not directly compare to two representative sparse PCA algorithms sPCA-rSVD (Shen and Huang, 2008) and DSPCA (d’Aspremont et al.”
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.”
A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. (2009, methodology): “The PMD is similar to a method of Shen & Huang (2008) for identifying sparse principal compo-”
Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, background): “Shen and Huang (2008) applied a regularized low-rank approach with its consistency established in Shen et al. (2013).”
JOINT AND INDIVIDUAL VARIATION EXPLAINED (JIVE) FOR INTEGRATED ANALYSIS OF MULTIPLE DATA TYPES (2011, methodology): “Sparse versions of exploratory methods such as PCA [Shen and Huang, 2008], PLS [Le Cao et al., 2008] and CCA [Parkhomenko et al., 2009] already exist.”
Generalized Low Rank Models (2014, background): “Many variants on this basic idea have been proposed, together with a wide variety of algorithms [33, 161, 128, 94, 155, 122, 152].”
Recommender Systems (2016, neutral): “Regularized singular value decomposition methods for complete matrices are discussed in [541].”
Principal Component Analysis on Spatial Data: An Overview (2013, neutral): “D'Aspremont et al. 2007; Shen and Huang 2008).”
A Sparse Singular Value Decomposition Method for High-Dimensional Data (2014, background): “…data has been the focus of a considerable literature; a representative but incomplete list of references is Lu (2002), Zou, Hastie, and Tibshirani (2006), Paul (2007), Paul and Johnstone (2007), Shen and Huang (2008), Johnstone and Lu (2009), Shen, Shen, and Marron (2013), and Ma (2013).”