Robust Multivariate Methods in Chemometrics

Abstract

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.

Robust Methods in Analysis of Multivariate Food Chemistry Data

“…Over the past several years a number of book chapters, tutorials and review papers have been published, for example [61][62][63][64][65][66][67][68][69]. Over the past several years a number of book chapters, tutorials and review papers have been published, for example [61][62][63][64][65][66][67][68][69].…”

Projection-pursuit approach to robust linear discriminant analysis

“…Other relevant publications to robust discriminant analysis have also been published in the last decade: Pires [40] discusses theoretical and practical issues related to the projection-pursuit approach to robust discriminant analysis; Croux and Joossens [12] look at the behavior of the total probability of misclassification of robust linear and quadratic discriminant analysis; Croux and Joossens [13] analyze the influence of observations on error rates in quadratic discriminant analysis; Filzmoser et al [18] measure the performance of classical and robust Fisher discriminant analysis using the error rate as a performance criterion; Han and Jin [23] use robust linear discriminant analysis model to devise a face recognition technique with good recognition performance; Hubert et al [29] focus on high-breakdown robust multivariate methods including discriminant analysis; Croux et al [11] compute relative classification efficiencies of robust Fisher's linear discriminant analysis with respect to the classical method; Filzmoser et al [19] provide an insight of a number of robust methods that can be used or extended to classification, including discriminant analysis.…”

Classification of Lectins by Pattern Recognition Using Glyconanoparticles

“…Among the pattern recognition analysis tools, linear discriminant analysis (LDA) is a simple yet robust technique for analyte classification. 26-28 LDA was first discovered by Fisher in 1936 for taxonomic classification, 29 and through the years it has been successfully employed in a wide range of applications including sensing, material classification, and identification of disease cells. 30, 31 …”