Simple Principal Components

Vines, S. K.

doi:10.1111/1467-9876.00204

Cited by 84 publications

(65 citation statements)

References 10 publications

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“…The only complication is how best to combine several pairwise rotations into a single step. This is discussed further in Vines (2000).…”

Section: Discussionmentioning

confidence: 91%

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Simplified EOFs-three alternatives to rotation

Jolliffe

Uddin²,

Vines³

2002

Clim. Res.

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Principal component analysis (PCA) is widely used in atmospheric science, and the resulting empirical orthogonal functions (EOFs) are often rotated to aid interpretation. In this paper 3 methods are described which provide alternatives to the standard 2-stage procedure of PCA followed by rotation. The techniques are illustrated on a small example involving sea-surface temperatures in the Mediterranean. Each method is shown to give different simplified interpretations for the major sources of variation in the data set. All 3 techniques have advantages over standard rotation.

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“…The only complication is how best to combine several pairwise rotations into a single step. This is discussed further in Vines (2000).…”

Section: Discussionmentioning

confidence: 91%

“…Further details and discussion can be found in Jolliffe & Uddin (2000), Vines (2000) and Joliffe et al (unpubl. ) which also include a number of examples from outside atmospheric science.…”

Section: Discussionmentioning

confidence: 99%

Simplified EOFs-three alternatives to rotation

Jolliffe

Uddin²,

Vines³

2002

Clim. Res.

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“…Jolliffe (1972Jolliffe ( , 1973 examined methods that discard irrelevant variables based on threshold values using multiple correlations, PCA itself, and clustering.These methods are very simple; however, this might be misleading as pointed out by Cadima and Jolliffe (1995). Other methods that aid in the interpretation of principal components include orthogonal rotation, similar to those used in factor analysis (Jolliffe, 1989(Jolliffe, , 1995, that restrict the coefficients of the components to a small set of possible values such as −1, 0, 1 (Hausman, 1982;Vines, 2000) and to introduce penalty functions to force the coefficients of irrelevant variables to zero (Jolliffe, 2002). Jolliffe (1995) pointed out the rotation method might have problems and the L 1 penalty function proposed by Jolliffe et al (2003) might cause bias on coefficient estimates.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic penalized principal component analysis

Park

Wang

2017

CSAM

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A variable selection method based on probabilistic principal component analysis (PCA) using penalized likelihood method is proposed. The proposed method is a two-step variable reduction method. The first step is based on the probabilistic principal component idea to identify principle components. The penalty function is used to identify important variables in each component. We then build a model on the original data space instead of building on the rotated data space through latent variables (principal components) because the proposed method achieves the goal of dimension reduction through identifying important observed variables. Consequently, the proposed method is of more practical use. The proposed estimators perform as the oracle procedure and are root-n consistent with a proper choice of regularization parameters. The proposed method can be successfully applied to high-dimensional PCA problems with a relatively large portion of irrelevant variables included in the data set. It is straightforward to extend our likelihood method in handling problems with missing observations using EM algorithms. Further, it could be effectively applied in cases where some data vectors exhibit one or more missing values at random.

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“…Since PCA yields nonzero loadings for entire set of variables, practical interpretation thereof is di¢ cult, and estimation e¢ ciency may become an issue. Because it allows for "sparsity", SPCA addresses these issues, leading to the estimation of more parsimonious latent factors than PCA or ICA (for further discussion, see Vines (2000), Jolli¤e et al (2003), and Zou et al (2006)). …”

Section: Introductionmentioning

confidence: 99%

Mining Big Data Using Parsimonious Factor and Shrinkage Methods

Kim

Swanson

2013

SSRN Journal

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A number of recent studies have focused on the usefulness of factor models in the context of prediction using "big data" (see e.g., Bai and Ng (2008), Dufour and Stevanovic (2010), Forni et al. (2000, Kim and Swanson (2014), Stock and Watson (2002b, and the references cited therein). We add to this literature by analyzing the predictive bene…ts associated with the use of independent component analysis (ICA) and sparse principal component analysis (SPCA), coupled with a variety of other factor estimation and data shrinkage methods, including bagging, boosting, and the elastic net, among others. We carry out a forecasting "horse-race", involving the estimation of 28 di¤erent baseline model types, each constructed using a variety of speci…cation approaches, estimation approaches, and benchmark econometric models; and all used in the prediction of 11 key macroeconomic variables relevant for monetary policy assessment. In numerous instances we …nd that a variety of benchmark autoregressive models and model averaging methods are mean square forecast error (MSFE) dominated by more complicated nonlinear methods. For example, simple averaging methods are MSFE "best" in only 9 of 33 key cases considered. However, in order to "beat" model averaging methods, we must combine new factor estimation methods with interesting new forms of shrinkage. For example, SPCA yields MSFE-best prediction models in many cases, particularly when coupled with shrinkage. In summary, we present empirical results that provide strong new evidence of the usefulness of sophisticated factor based forecasting methods, and as a corollary, of the use of "big data" in macroeconometric forecasting.

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Simple Principal Components

Cited by 84 publications

References 10 publications

Simplified EOFs-three alternatives to rotation

Simplified EOFs-three alternatives to rotation

Probabilistic penalized principal component analysis

Mining Big Data Using Parsimonious Factor and Shrinkage Methods

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