Publications

Algorithms for multivariate image analysis and other large-scale applications of multivariate curve resolution (MCR) typically employ constrained alternating least squares (ALS) procedures in their solution. The solution to a least squares problem under general linear equality and inequality constraints can be reduced to the solution of a non-negativity-constrained least squares (NNLS) problem. Thus the efficiency of the solution to any constrained least square problem rests heavily on the underlying NNLS algorithm. We present a new NNLS solution algorithm that is appropriate to large-scale MCR and other ALS applications. Our new algorithm rearranges the calculations in the standard active set NNLS method on the basis of combinatorial reasoning. This rearrangement serves to reduce substantially the computational burden required for NNLS problems having large numbers of observation vectors. Copyright © 2005 John Wiley & Sons, Ltd.

Multivariate curve resolution (MCR) using constrained alternating least squares algorithms represents a powerful analysis capability for a quantitative analysis of hyperspectral image data. We will demonstrate the application of MCR using data from a new hyperspectral fluorescence imaging microarray scanner for monitoring gene expression in cells from thousands of genes on the array. The new scanner collects the entire fluorescence spectrum from each pixel of the scanned microarray. Application of MCR with nonnegativity and equality constraints reveals several sources of undesired fluorescence that emit in the same wavelength range as the reporter fluorphores. MCR analysis of the hyperspectral images confirms that one of the sources of fluorescence is due to contaminant fluorescence under the printed DNA spots that is spot localized. Thus, traditional background subtraction methods used with data collected from the current commercial microarray scanners will lead to errors in determining the relative expression of low-expressed genes. With the new scanner and MCR analysis, we generate relative concentration maps of the background, impurity, and fluorescent labels over the entire image. Since the concentration maps of the fluorescent labels are relatively unaffected by the presence of background and impurity emissions, the accuracy and useful dynamic range of the gene expression data are both greatly improved over those obtained by commercial microarray scanners.

Abstract not provided.

Hyperspectral Fourier transform infrared images have been obtained from a neoprene sample aged in air at elevated temperatures. The massive amount of spectra available from this heterogeneous sample provides the opportunity to perform quantitative analysis of the spectral data without the need for calibration standards. Multivariate curve resolution (MCR) methods with non-negativity constraints applied to the iterative alternating least squares analysis of the spectral data has been shown to achieve the goal of quantitative image analysis without the use of standards. However, the pure-component spectra and the relative concentration maps were heavily contaminated by the presence of system artifacts in the spectral data. We have demonstrated that the detrimental effects of these artifacts can be minimized by adding an estimate of the error covariance structure of the spectral image data to the MCR algorithm. The estimate is added by augmenting the concentration and pure-component spectra matrices with scores and eigenvectors obtained from the mean-centered repeat image differences of the sample. The implementation of augmentation is accomplished by employing efficient equality constraints on the MCR analysis. Augmentation with the scores from the repeat images is found to primarily improve the pure-component spectral estimates while augmentation with the corresponding eigenvectors primarily improves the concentration maps. Augmentation with both scores and eigenvectors yielded the best result by generating less noisy pure-component spectral estimates and relative concentration maps that were largely free from a striping artifact that is present due to system errors in the FT-IR images. The MCR methods presented are general and can also be applied productively to non-image spectral data.