Statistically weighted principal component analysis of rapid scanning wavelength kinetics experiments

Abstract

Prlnclpal component analysls Is used to develop a procedure for determlnlng the number of linearly Independent specles absorbing, fluorescing, or emitting llght In rapld scannlng wavelength klnetlcs experlments. The prlnclpal components of the data-second moment matrlx ghre for the specles nunber a lower estimate that Is sensltlve to the llnear dependence of the specles concentratlons; the prlnclpal components of the data-sample covarlance matrlx give a lower estimate that Is sensltlve to the llnear dependence of the tlme rates of change of the specles concentrations. An example Illustrates that the varlatlon of the experimental slgnal-to-noise ratlo wlth wavelength and tlme leads to Incorrect estlmates of the number of reactlng species. Thls error Is eliminated by statistically welghtlng the prlnclpal component calculatlons accordlng to a general model of error varlances.The development of sophisticated computer interfaced data collection systems has made scanning wavelength kinetics experiments practical for times as short as the stopped flow time scale (1-6)-In a typical scanning wavelength kinetics experiment, a spectral region is rapidly and repeatedly scanned while a spectrophotometric response such as absorbance, fluorescence, or chemiluminescence is measured at a fixed number of wavelength channels across the spectrum during each scan. If the time duration of each scan is short compared to the fastest spectrophotometrically detectable process in the reaction, the data can be regarded as a series of N consecutive, instantaneous spectra measured at p wavelength channels and can be represented by a (p X N ) matrix A, where A,j is the spectrophotometric response measured at wavelength channel i at the time of scan j .The reason for sampling this three-dimensional space of response-wavelength-time instead of the simpler two-dimensional space obtained in a fixed wavelength experiment is the need to characterize kinetic systems that contain more than one absorbing, fluorescing, or chemiluminescent solute. Whether the ultimate goal is to assay simultaneously several such solutes in a kinetic system with a known rate law, or to propose and test mechanisms for a complex reaction such as an enzyme system with detectable substrates, products, enzymes, and enzyme-bound intermediates, a necessary first step in data analysis is to determine how many detectable solutes occur in the reaction. The multivariate statistical method of principal component analysis, which has been applied to spectral studies of multicomponent equilibrium systems (7-IO), band resolution of IR spectra ( I I ) , analysis of potentiometric data ( E ) , and analysis of mass spectra (13, I4), is ideally suited for determining the number of detectable solutes in rapid scanning wavelength kinetics experiments.The analogy between spectral studies of multicomponent equilibrium systems and scanning wavelength kinetics experiments and the applicability of principal component analysis to both was pointed out and demonstrated by Sylvestre, Lawton, and Maggio...

Multivariate calibration of non-replicated measurements for the factored noise model

“…The development of this method combines ideas from the SWPCA method developed by Cochran and Horne [4] and the IPCA method developed by Narasimhan and Shah (2007).…”

“…In order to motivate our development, we first consider the case when the error variance factors are known and it is required to estimate a basis for the true data subspace. For this purpose the statistically weighted PCA method developed by Cochran and Horne [4] can be used, which is described in the following subsection.…”

“…The Statistically Weighted PCA (SWPCA) method developed in [4] applies PCA to appropriately weighted measurements in order to estimate the true data subspace. This method provides a consistent estimate of the true data subspace if the random errors in measurements follow the factored noise model.…”

“…It may be noted, that if the errors are uncorrelated, then the error covariance matrix is diagonal and this transformation is identical to a specific scaling of the measured data. Cochran and Horne [4] developed a statistically weighted principal component analysis (SWPCA) method using a scaling technique, when the error variances vary with respect to samples as well as wavelengths. A simplified model of the error variances is assumed in this approach by expressing the variance of measurement error of a sample i at a specific wavelength j as a product of two factors.…”

Data scaling for quantitative imaging XPS

“…Two methods have been used to redistribute Poisson noise throughout the data set, square root scaling [17] and optimal scaling. Keenan and Kotula [18,19] reported the use of optimal scaling for TOF-SIMS data, on the basis of a procedure developed by Cochran and Horne, [20] which proved to be superior in identifying low-intensity components. A recent review on the application of MVA techniques to TOF-SIMS analysis recommended the use of optimal scaling prior to the use of both PCA and MCR.…”