Robust nonlinear principal components

Maronna, Ricardo A.; Méndez, Fernanda; Yohai, Vı́ctor J.

doi:10.1007/s11222-013-9442-0

Cited by 2 publications

(2 citation statements)

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“…Las referencia [31], por ejemplo, contiene un trabajo relacionado. PCP, sin embargo , puede fracasar en la detección de datos atípicos presentes en el complemento ortogonal del subespacio, tal como se muestra en [32] y [33]. She et al [33] investigan este problema al proponer el método ROCPCA.…”

Section: B Acp Robusto Contra Celdas Atípicasunclassified

Robust estimation of principal components: a literature review.

Cevallos-Valdiviezo¹,

Rodríguez-Cristiansen²,

Valdiviezo-Valenzuela³

2022

Proceedings of the 20th LACCEI International Multi-Conference for Engineering, Education and Technology: “Education, Research A

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In this work we do a short literature review on the most relevant methods for robust estimation of Principal Component Analysis (PCA). In particular, we review methods for PCA that are resistant against rowwise outliers, cellwise outliers and against both rowwise and cellwise outliers. It is well known that classical PCA breaks down in the presence of outliers. In practical applications, we suggest to fit a robust method for PCA estimation that is resistant to rowwise and cellwise outliers. We could later compare this result with the classical fit to evaluate the influence of outliers. Robust methodsfor PCA can also be used to detect outliers.

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Section: B Acp Robusto Contra Celdas Atípicasunclassified

Robust estimation of principal components: a literature review.

Cevallos-Valdiviezo¹,

Rodríguez-Cristiansen²,

Valdiviezo-Valenzuela³

2022

Proceedings of the 20th LACCEI International Multi-Conference for Engineering, Education and Technology: “Education, Research A

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“…However, PCP may fail to detect outliers in the orthogonal complement of the subspace (cfr. Maronna et al, 2015;She et al, 2016). Therefore, She et al (2016) introduced a robust orthogonal complement (ROCPCA) approach to deal with orthogonal complement outliers.…”

Section: Introductionmentioning

confidence: 99%

Fast computation of robust subspace estimators

Cevallos-Valdiviezo

Aelst

2019

Computational Statistics & Data Analysis

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Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to atypical data. Robust methods to estimate the low-dimensional subspace that best approximates the regular data have been proposed. However, for highdimensional data these algorithms become computationally expensive. Alternative algorithms for the robust subspace estimators are proposed that are better suited to compute the solution for high-dimensional problems. The main ingredients of the new algorithms are twofold. First, the principal directions of the subspace are estimated directly by iterating the first order solutions corresponding to the estimators. Second, to reduce the computation time even further five robust deterministic values are proposed to initialize the algorithms instead of using random starting values. It is shown that the new algorithms yield robust solutions and the computation time is largely reduced, especially for high-dimensional data.

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Robust nonlinear principal components

Cited by 2 publications

References 20 publications

Robust estimation of principal components: a literature review.

Robust estimation of principal components: a literature review.

Fast computation of robust subspace estimators

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