A Modified Principal Component Technique Based on the LASSO

By Ian T. Jolliffe, Nickolay T. Trendafilov, Mudassir Uddin. 2003

949 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Statistics and Probability

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Citations in the corpus

In search of simple structures in climate: simplifying EOFs (2006, methodology): “…to the constraints aTk al = δkl (16) as with EOFs; but to achieve simplicity, the LASSO technique requires an extra constraint to be satisfied (Jolliffe et al., 2003): ‖ak‖1 = p∑ j=1 |akj | = aTk sign(ak) ≤ τ (17) where τ is a tunable parameter and sign(ak) = (sign(ak1), . . . , sign(akp))T…”
Empirical orthogonal functions and related techniques in atmospheric science: A review (2007, methodology): “A particularly interesting one, simplified EOFs, is a method based on the least absolute shrinkage and selection operator (LASSO) approach introduced in the context of regression by Tibshirani (1996) and adapted to EOFs by Jolliffe et al. (2003).”
The spectral norm of random inner-product kernel matrices (2015, methodology): “Computationally-efficient procedures for estimating sparse principal components include diagonal thresholding [31, 32, 9], `1- and model-selection-penalization approaches [33, 62, 21, 49, 60, 12], iterative thresholding via the QR method [40], approximate message passing [22], and covariance thresho”
Sparse Principal Component Analysis and Iterative Thresholding (2011, neutral): “See, for example, [15, 37, 3, 29, 32, 36].”
Least angle and ℓ1 penalized regression: A review (2008, methodology): “Principal Component and Discriminant Analysis Jolliffe et al. (2003) and Zou et al. (2006) apply l1 penalties to get sparse loadings in principal components. Trendafilov and Joilliffe (2007) discuss l1 penalties in linear discriminant analysis.”
Sparse Principal Component Analysis (2006, methodology): “ Jollifie & Uddin (2003) used their SCoTLASS to flnd the modifled”
Sparse canonical methods for biological data integration: application to a cross-platform study (2009, neutral): “This valuable orthogonal property between loading vectors is kept in the sparse methods (sPLS, CCA-EN), which is not often the case, for example with the sparse PCA approaches [8,23,32].”
Supervised probabilistic principal component analysis (2006, methodology): “Inspired by these sparsification techniques, SCoTLASS (Jolliffe, 2003) combines the maximum variance PCA objective with an L1 penalty (similar to LASSO), and sparse PCA (SPCA) (Zou et al.”
A Direct Formulation for Sparse PCA Using Semidefinite Programming (2004, positive): “[4] applied SCoTLASS to this problem and [5] used their SPCA approach, both with the goal of obtaining sparse principal c omponents that can better be interpreted than those of PCA.”
Infinite latent feature models and the Indian buffet process (2005, neutral): “F can be expressed as the elementwise (Hadamard) product of Z and V, F = Z V, as illustrated in Figure 3. In many latent feature models, such as PCA and CVQ, objects have non-zero values on every feature, and every entry of Z is 1. In sparse latent feature models (e.g., sparse PCA; d’Aspremont, Ghao”