Maximum likelihood principal component analysis

Maximum likelihood principal component analysis (1997)

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by Peter D. Wentzell , Darren T. Andrews , David C. Hamilton , Klaas Faber , Bruce R. Kowalski

Venue:	J. Chemometrics
Citations:	11 - 0 self

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Datum	Value	Source
TITLE	Maximum likelihood principal component analysis	INFERENCE
AUTHOR NAME	Peter D. Wentzell	SVM HeaderParse 0.2
AUTHOR AFFIL	1 Trace Analysis Research Centre, Department of Chemistry, Dalhousie University, Halifax	SVM HeaderParse 0.2
AUTHOR ADDR	Nova Scotia B3H 4J3,; Canada	SVM HeaderParse 0.2
AUTHOR NAME	Darren T. Andrews	SVM HeaderParse 0.2
AUTHOR NAME	David C. Hamilton	SVM HeaderParse 0.2
AUTHOR NAME	Klaas Faber	SVM HeaderParse 0.2
AUTHOR NAME	Bruce R. Kowalski	SVM HeaderParse 0.2
AUTHOR AFFIL	SUMMARY	SVM HeaderParse 0.2
ABSTRACT	The theoretical principles and practical implementation of a new method for multivariate data analysis, maximum likelihood principal component analysis (MLPCA), are described. MLCPA is an analog to principal component analysis (PCA) that incorporates information about measurement errors to develop PCA models that are optimal in a maximum likelihood sense. The theoretical foundations of MLPCA are initially established using a regression model and extended to the framework of PCA and singular value decomposition (SVD). An efficient and reliable algorithm based on an alternating regression method is described. Generalization of the algorithm allows its adaptation to cases of correlated errors provided that the error covariance matrix is known. Models with intercept terms can also be accommodated. Simulated data and near-infrared spectra, with a variety of error structures, are used to evaluate the performance of the new algorithm. Convergence times depend on the error structure but are typically around a few minutes. In all cases, models determined by MLPCA are found to be superior to those obtained by PCA when non-uniform error distributions are present, although the level of improvement depends on the error structure of the particular data set. © 1997 by John Wiley & Sons, Ltd. Journal of Chemometrics, Vol. 11, 339–366 (1997) (No. of Figures: 4 No. of Tables: 5 No. of References: 22) KEY WORDS principal component analysis; maximum likelihood; measurement errors; multivariate analysis; near-infrared spectroscopy; errors in variables 1.	SVM HeaderParse 0.2
YEAR	1997	INFERENCE
VENUE	J. Chemometrics	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	339--366	INFERENCE
VOLUME	11	INFERENCE
CITATIONS	21 found	ParsCit 1.0