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Chapter 3 Robust principal component analysis and constrained background bilinearization for quantitative analysis

Authors
Publisher
Elsevier Science & Technology
Identifiers
DOI: 10.1016/s0922-3487(06)80004-3

Abstract

Publisher Summary This chapter focuses on developing robust principal component analysis (PCA) and constrained background bilinearization for quantitative analysis. PCA is an important technique for high-dimensional data reduction and exploratory analysis. It is also the basis and an indispensable part of many multivariate quantitative methods developed in chemometrics, such as most curve resolution procedures, the widely used multivariate calibration methods, such as principal component regression (PCR) and partial least square regression (PLS), and many pattern recognition methods. There are several routines to obtain the robust PCA, which includes M-estimators based on the ellipsoidal distributions and the elementwise robust estimation of the disperse (covariance/correlation) matrix. More recently, a new type method for robust PCA with the use of projection pursuit (PP) has been proposed by Li and Chen. The Monte Carlo simulation has shown that the new procedures compare favorably with other robust methods. They provide results as good as the best of M-estimators in terms of efficiency of robustness and as good as the elementwise approaches with respect to the empirical breakdown point properties

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