MAXIMUM-LIKELIHOOD PRINCIPAL COMPONENT ANALYSIS

The theoretical principles and practical implementation of a new metho d for multivariate data analysis, maximum likelihood principal compone nt analysis (MLPCA), are described. MLCPA is an analog to principal co mponent 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 sin gular value decomposition (SVD). An efficient and reliable algorithm b ased on an alternating regression method is described. Generalization of the algorithm allows its adaptation to cases of correlated errors p rovided that the error covariance matrix is known. Models with interce pt terms can also be accommodated. Simulated data and near-infrared sp ectra, with a variety of error structures, are used to evaluate the pe rformance 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 s et. (C) 1997 by John Wiley & Sons, Ltd.