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Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies

Christophe Croux, +1 more
- 01 Sep 2000 - 
- Vol. 87, Iss: 3, pp 603-618
TLDR
In this paper, the influence functions and the corresponding asymptotic variances for these robust estimators of eigenvalues and eigenvectors are investigated by a simulation study, and it turns out that the theoretical results and simulations favor the use of S-estimators since they combine a high efficiency with appealing robustness properties.
Abstract
A robust principal component analysis can be easily performed by computing the eigenvalues and eigenvectors of a robust estimator of the covariance or correlation matrix. In this paper we derive the influence functions and the corresponding asymptotic variances for these robust estimators of eigenvalues and eigenvectors. The behaviour of several of these estimators is investigated by a simulation study. It turns out that the theoretical results and simulations favour the use of S-estimators, since they combine a high efficiency with appealing robustness properties. © 2000 Biometrika Trust.

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Citations
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Journal ArticleDOI

ROBPCA: A New Approach to Robust Principal Component Analysis

TL;DR: The ROBPCA approach, which combines projection pursuit ideas with robust scatter matrix estimation, yields more accurate estimates at noncontaminated datasets and more robust estimates at contaminated data.
Proceedings Article

Robust PCA via Outlier Pursuit

TL;DR: In this paper, an efficient convex optimization-based algorithm called Outlier Pursuit is presented, which under mild assumptions on the uncorrupted points (satisfied, e.g., by the standard generative assumption in PCA problems) recovers the exact optimal low-dimensional subspace, and identifies the corrupted points.
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Robust statistics for outlier detection

TL;DR: An overview of several robust methods and outlier detection tools for univariate, low‐dimensional, and high‐dimensional data such as estimation of location and scatter, linear regression, principal component analysis, and classification are presented.
Journal ArticleDOI

Robust PCA via Outlier Pursuit

TL;DR: In this paper, an efficient convex optimization-based algorithm that is called outlier pursuit is presented, which under some mild assumptions on the uncorrupted points (satisfied, e.g., by the standard generative assumption in PCA problems) recovers the exact optimal low-dimensional subspace and identifies the corrupted points.
Journal ArticleDOI

Principal Component Analysis on Spatial Data: An Overview

TL;DR: In this paper, the authors consider how one of the oldest and most widely applied statistical methods, principal components analysis (PCA), is employed with spatial data, and identify four main methodologies, which are defined as (1) PCA applied to spatial objects, (2) PCAs applied to raster data, (3) atmospheric science PCA, and (4)PCA on flows.
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