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SUMMARY 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(More)
The application of a new method to the multivariate analysis of incomplete data sets is described. The new method, called maximum likelihood principal component analysis (MLPCA), is analogous to conventional principal component analysis (PCA), but incorporates measurement error variance information in the decomposition of multivariate data. Missing(More)
The maximum likelihood PCA (MLPCA) method has been devised in chemometrics as a generalization of the well-known PCA method in order to derive consistent estimators in the presence of errors with known error distribution. For similar reasons, the total least squares (TLS) method has been generalized in the field of computational mathematics and engineering(More)
Most cells on earth exist in a quiescent state. In yeast, quiescence is induced by carbon starvation, and exit occurs when a carbon source becomes available. To understand how cells survive in, and exit from this state, mRNA abundance was examined using oligonucleotide-based microarrays and quantitative reverse transcription-polymerase chain reaction. Cells(More)
Two of the most widely employed multivariate calibration methods, principal components regression (PCR) and partial least squares regression (PLS), are compared using simulation studies of complex chemical mixtures which contain a large number of components. Details of the complex mixture model, including concentration distributions and spectral(More)
Procedures to compensate for correlated measurement errors in multivariate data analysis are described. These procedures Ž. are based on the method of maximum likelihood principal component analysis MLPCA , previously described in the literature. MLPCA is a decomposition method similar to conventional PCA, but it takes into account measurement uncertainty(More)
BACKGROUND Modeling of gene expression data from time course experiments often involves the use of linear models such as those obtained from principal component analysis (PCA), independent component analysis (ICA), or other methods. Such methods do not generally yield factors with a clear biological interpretation. Moreover, implicit assumptions about the(More)
—The transmittance spectra of a long-period fiber grating element immersed in different mixtures of water and dimethyl sulfoxide were recorded. The obtained data were compared with a theoretical model based on linearly polarized modes treated with a coupled-mode approach. Excellent agreement between the measurements and theoretical results was found over a(More)
The application of trilinear decomposition (TLD) to the analysis of fluorescence excitation-emission matrices of mixtures of polycyclic aromatic hydrocarbons (PAHs) is described. The variables constituting the third-order tensor are excitation wavelength, emission wavelength, and concentration of a fluorescence quencher (nitromethane). The addition of a(More)