Robust methods for multivariate data analysis

Abstract

Outliers may hamper proper classical multivariate analysis, and lead to incorrect conclusions. To remedy the problem of outliers, robust methods are developed in statistics and chemometrics. Robust methods reduce or remove the effect of outlying data points and allow the 'good' data to primarily determine the result. This article reviews the most commonly used robust multivariate regression and exploratory methods that have appeared since 1996 in the field of chemometrics. Special emphasis is put on the robust versions of chemometric standard tools like PCA and PLS and the corresponding robust estimates of regression, location and scatter on which they are based.

A survey of functional principal component analysis

“…Pearson intended PCA as the correct solution to some of the problems that were of interest to biometrician at that time, although his study did not consider a practical method for calculating two or more components (Møller et al 2005). A detailed description of how to compute principal components came much later from Hotelling (1933).…”

Cross-connection detection in Australian dual reticulation systems by monitoring inherent fluorescent organic matter

“…Multivariate data analysis has been T, C Marine Coal [156] A Petroleum [157] T Groundwater Landfill leachate [103] T Potable Wastewater [158] T/C (ratio) PAHs [159] B, T, A Recycled water [116][117][118] T 1 widely applied within psychometrics [122] and chemometrics [123,124], where techniques such as principal component analysis (PCA), partial least-squares (PLS), Tucker decomposition and more specifically parallel factor (PARAFAC) analysis have become increasingly popular for their ability to decompose large and complicated datasets and extract relevant information. These multivariate approaches have been applied to fluorescence-based water research to detect the presence and quantify the underlying fluorescence characteristics of complex mixtures of DOM [98,125].…”

Robustified least squares support vector classification

“…Also in the chemometrical literature robust methods, defined in that sense, are already well established and proved to be useful which can be seen by the numerous publications in that field (see e.g. References [12][13][14][15][16][17]). …”