A robust principal component analysis

Ibazizen, Mohamed; Dauxois, Jacques

doi:10.1080/0233188031000065442

Cited by 7 publications

(4 citation statements)

References 5 publications

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“…We refer the interested reader to He and Ng (2003), Ibazizen and Dauxois (2003), Hubert, Rousseeuw and vanden Branden (2005), and Serneels and Verdonck (2008) for principal components; and to Yuan, Marshall and Bentler (2002) and Pison, Rousseeuw, Filzmoser, and Croux (2003) for factor analysis.…”

Section: Discussionmentioning

confidence: 99%

Smoking and Cancers: Case-Robust Analysis of a Classic Data Set

Bentler

Satorra

Yuan

2009

Structural Equation Modeling: A Multidisciplinary Journal

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A typical structural equation model is intended to reproduce the means, variances, and correlations or covariances among a set of variables based on parameter estimates of a highly restricted model. It is not widely appreciated that the sample statistics being modeled can be quite sensitive to outliers and influential observations leading to bias in model parameter estimates. A classic public epidemiological data set on the relation between cigarette purchases and rates of four types of cancer among states in the USA is studied with case-weighting methods that reduce the influence of a few cases on the overall results. The results support and extend the original conclusions; the standardized effect of smoking on a factor underlying deaths from bladder and lung cancer is .79.

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Section: Discussionmentioning

confidence: 99%

Smoking and Cancers: Case-Robust Analysis of a Classic Data Set

Bentler

Satorra

Yuan

2009

Structural Equation Modeling: A Multidisciplinary Journal

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“…For overcoming this problem, robust alternatives for these methods have been proposed in the literature, mainly by replacing the aforementioned empirical covariance operators by robust estimators. In this vein, robust versions of multivariate statistical methods have been introduced, especially for multiple regression ( [21]), principal components analysis ( [8], [10], [16], [22]), factor analysis ( [19]), linear discriminant analysis ( [6], [9], [14]), linear canonical analysis ( [5], [24]). Multiple-set linear canonical analysis (MSLCA) is an important multivariate statistical method that analyzes the relationship between more than two random vectors, so generalizing linear canonical analysis.…”

Section: Introductionmentioning

confidence: 99%

Robust multiple-set linear canonical analysis based on minimum covariance determinant estimator

Bivigou,

Nkiet

2018

Preprint

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By deriving influence functions related to multiple-set linear canonical analysis (MSLCA) we show that the classical version of this analysis, based on empirical covariance operators, is not robust. Then, we introduce a robust version of MSLCA by using the MCD estimator of the covariance operator of the involved random vector. The related influence functions are then derived and are shown to be bounded. Asymptotic properties of the introduced robust MSLCA are obtained and permit to propose a robust test for mutual non-correlation. This test is shown to be robust by studying the related second order influence function under the null hypothesis.

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“…Several ways of robustifying the classical PCA have been proposed in the literature (Jackson, 1991). Among many others, these approaches include employing robust estimate of the covariance matrix (Croux and Haesbroeck, 2000) or measure of variation that is more robust than the variance (Ibazizen and Dauxois, 2003). Despite their success in the case of PCA, it is not immediately clear how these approaches can be extended to the kernel PCA.…”

Section: Introductionmentioning

confidence: 99%

A note on robust kernel principal component analysis

Deng¹,

Yuan²,

Sudjianto³

2007

Prediction and Discovery

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Extending the classical principal component analysis (PCA), the kernel PCA (Schölkopf, Smola and Müller, 1998) effectively extracts nonlinear structures of high dimensional data. But similar to PCA, the kernel PCA can be sensitive to outliers. Various approaches have been proposed in the literature to robustify the classical PCA. However, it is not immediately clear how these approaches can be "kernelized" in practice. In this paper, we propose a robust kernel PCA procedure. We show that the proposed method can be easily computed. Simulations and a real example in the financial service also demonstrate the competitive performance of our approach when there are outlying observations.

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A robust principal component analysis

Cited by 7 publications

References 5 publications

Smoking and Cancers: Case-Robust Analysis of a Classic Data Set

Smoking and Cancers: Case-Robust Analysis of a Classic Data Set

Robust multiple-set linear canonical analysis based on minimum covariance determinant estimator

A note on robust kernel principal component analysis

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