Influence properties of partial least squares regression

Serneels, Sven; Croux, Christophe; Espen, Pierre J. Van

doi:10.1016/j.chemolab.2003.10.009

Cited by 21 publications

(12 citation statements)

References 17 publications

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“…Thereunto we have proposed to construct a squared influence diagnostic plot based on the actual values of the influence functions. The proposal of the SID is based on an analogous measure for PLS [7], although it is not the only possible influence assessment tool which can be derived from the influence function. Detection of influential samples for calibration and prediction has two major advantages:…”

Section: Discussionmentioning

confidence: 99%

“…In the context of bilinear partial least squares regression, the Squared Influence Diagnostic has been shown to perform as well as a widely used alternative [7]. The Squared Influence Diagnostic plot then consists of plotting the SID values versus the case index.…”

Section: Influence Diagnosismentioning

confidence: 99%

“…In a recent text-book on multi-way methods [6], the former reference [5] is cited in the context of influence analysis for linear regression; however, the reference is accompanied by the statement that there are many unresolved issues in two-way and especially multi-way analysis (including the influence functions of multi-way estimators). As concerns two-way estimators, the PLS influence function has recently been reported [7], as well as some proposals to visualize the results.…”

Section: Introductionmentioning

confidence: 99%

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Influence properties of trilinear partial least squares regression

Serneels

Geladi

Moens

et al. 2005

Journal of Chemometrics

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In this article we derive an algorithm to compute the influence function for tri-PLS1 regression. Based on the influence function, we propose the squared influence diagnostic plot to assess the influence of individual samples on calibration and prediction. We illustrate the applicability of the squared influence diagnostic plot for tri-PLS1 to two different data sets which have previously been reported in literature. Finally we note that from the influence function, a new estimate of prediction variance can be obtained.

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Section: Discussionmentioning

confidence: 99%

Section: Influence Diagnosismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Influence properties of trilinear partial least squares regression

Serneels

Geladi

Moens

et al. 2005

Journal of Chemometrics

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“…The non-robustness of PLS was justified theoretically in Reference [4]. Outliers are different from the majority of the data, but they are not necessarily incorrect.…”

Section: Introductionmentioning

confidence: 99%

Robust and classical PLS regression compared

Liebmann

Filzmoser

Вармуза

2010

Journal of Chemometrics

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a Classical PLS regression is a well-established technique in multivariate data analysis. Since classical PLS is known to be severely affected by the presence of outliers in the data or deviations from normality, several PLS regression methods with robust behavior towards data contamination have been proposed. We compare the performance of the classical SIMPLS approach with the partial robust M regression (PRM). Both methods are applied to three different data sets including outliers intentionally created. A simulated data set with known true model parameters allows insight in the modeling performance with increasing data contamination. QSPR data are modified with a cluster of outlying observations. A third data set from near infrared (NIR) spectroscopy is likely to include noise and experimental errors already in the original variables, and is further contaminated with outliers. To provide a sound comparison of the considered methods we apply repeated double cross validation. This validation procedure judiciously optimizes the model complexity (number of PLS components) and estimates the models' prediction performance based on test-set predicted errors. All studied robust regression models outperform the classical PLS models when outlying observations are present in the data. For uncontaminated data, the prediction performances of both the classical and the robust models are in the same range.

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“…The classical covariance is a nonrobust estimator; as all PLS estimates derive from this classical covariance it can be expected that the whole PLS procedure is nonrobust. Indeed, if one takes into consideration the PLS influence function (first derived by Serneels et al 69 ), it can be seen that the PLS influence functions are unbounded and thus that PLS is nonrobust.…”

Section: A Brief Introduction To Plsmentioning

confidence: 99%

Robust Multivariate Methods in Chemometrics

Filzmoser

Serneels

Maronna

et al. 2009

Comprehensive Chemometrics

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This chapter presents an introduction to robust statistics with applications of a chemometric nature. Following a description of the basic ideas and concepts behind robust statistics, including how robust estimators can be conceived, the chapter builds up to the construction (and use) of robust alternatives for some methods for multivariate analysis frequently used in chemometrics, such as principal component analysis and partial least squares. The chapter then provides an insight into how these robust methods can be used or extended to classification. To conclude, the issue of validation of the results is being addressed: it is shown how uncertainty statements associated with robust estimates, can be obtained.

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Influence properties of partial least squares regression

Cited by 21 publications

References 17 publications

Influence properties of trilinear partial least squares regression

Influence properties of trilinear partial least squares regression

Robust and classical PLS regression compared

Robust Multivariate Methods in Chemometrics

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