A Fast Algorithm for Robust Principal Components Based on Projection Pursuit

Croux, Christophe; Ruiz‐Gazen, Anne

doi:10.1007/978-3-642-46992-3_22

Cited by 81 publications

(84 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For a large sample size n with respect to the dimension p, the CR algorithm still performs quite well, as can be seen from the simulation results in Section 5. Note that the CR algorithm as proposed by [11] was not aimed at high dimensional applications. For n >> p we still recommend this algorithm as a fast and reasonably accurate way to find the robust principal components, but for p > n it should not be used.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Algorithms for Projection–Pursuit robust principal component analysis

Croux¹,

Filzmoser²,

Oliveira³

2007

Chemometrics and Intelligent Laboratory Systems

Self Cite

235

127

View full text Add to dashboard Cite

The results of a standard Principal Component Analysis (PCA) can be affected by the presence of outliers. Hence robust alternatives to PCA are needed. One of the most appealing robust methods for principal component analysis uses the Projection-Pursuit principle. Here, one projects the data on a lower-dimensional space such that a robust measure of variance of the projected data will be maximized. The Projection-Pursuit based method for principal component analysis has recently been introduced in the field of chemometrics, where the number of variables is typically large. In this paper, it is shown that the currently available algorithm for robust Projection-Pursuit PCA performs poor in presence of many variables. A new algorithm is proposed that is more suitable for the analysis of chemical data. Its performance is studied by means of simulation experiments and illustrated on some real data sets.

show abstract

Section: Discussionmentioning

confidence: 99%

“…In [10] simulated annealing was used, again yielding a slow algorithm that is not publicly available. On the other hand, [11] introduced an algorithm which is very simple, fast to compute and easy to implement. We call it the CR algorithm and consider it as the basis algorithm.…”

Section: Introductionmentioning

confidence: 99%

Algorithms for Projection–Pursuit robust principal component analysis

Croux¹,

Filzmoser²,

Oliveira³

2007

Chemometrics and Intelligent Laboratory Systems

Self Cite

235

127

View full text Add to dashboard Cite

show abstract

“…Unfortunately, in spite of the good statistical properties of the method, the algorithm they proposed was too complicated to be used in practice. A more tractable algorithm in these lines was first proposed by Croux and Ruiz-Gazen (1996) and later improved by Croux and Ruiz-Gazen (2005). To improve the performance of the algorithm for high-dimensional data a new improved version was proposed by Croux et al (2007).…”

Section: Projection Pursuit Methodsmentioning

confidence: 99%

An Object-Oriented Framework for Robust Multivariate Analysis

Todorov¹,

Filzmoser²

2009

J. Stat. Soft.

301

197

View full text Add to dashboard Cite

Taking advantage of the S4 class system of the programming environment R, which facilitates the creation and maintenance of reusable and modular components, an objectoriented framework for robust multivariate analysis was developed. The framework resides in the packages robustbase and rrcov and includes an almost complete set of algorithms for computing robust multivariate location and scatter, various robust methods for principal component analysis as well as robust linear and quadratic discriminant analysis. The design of these methods follows common patterns which we call statistical design patterns in analogy to the design patterns widely used in software engineering. The application of the framework to data analysis as well as possible extensions by the development of new methods is demonstrated on examples which themselves are part of the package rrcov.

show abstract

“…6-7) note that the Croux and Ruiz-Gazen (1996) and Hubert et al (2002) (So Eis the determinant ofsome robust covariance matrix that is computed with the Zj values.) As previously indicated, Eis taken to be the determinant of the covariance matrix described at the end of Section 3.…”

Section: Description Of the Robust Pca Methodsmentioning

confidence: 99%

Robust principal components: A generalized variance perspective

Wilcox

2008

Behav Res

View full text Add to dashboard Cite

This article compares several methods for performing robust principal component analysis, two of which have not been considered in previous articles. The criterion here, unlike that of extant articles aimed at comparing methods, is how well a method maximizes a robust version of the generalized variance of the projected data. This is in contrast to maximizing some measure of scatter associated with the marginal distributions of the projected scores, which does not take into account the overall structure of the projected data.

show abstract

A Fast Algorithm for Robust Principal Components Based on Projection Pursuit

Cited by 81 publications

References 7 publications

Algorithms for Projection–Pursuit robust principal component analysis

Algorithms for Projection–Pursuit robust principal component analysis

An Object-Oriented Framework for Robust Multivariate Analysis

Robust principal components: A generalized variance perspective

Contact Info

Product

Resources

About