Factor analysis for signal modeling and noise characterization in spectro-kinetic data

Abstract

Measurement signals and noise (heteroscedastic and homoscedastic) in different evolutionary spectral kinetic data sets are modeled and characterized by applying maximum likelihood common factor analysis (MLFA) and principal axis factoring (PAF), as factor-based techniques. They decompose data into common and specific factors, that are assumed to be constant heteroscedastic. The digital filter is also used for characterization of noise in data and to confirm the obtained results from factor analysis techniques. No one of the applied methods requires the use of replicated measurements. Inverted Blackman windowed sinc (BWS) smoothing coefficients as high-pass digital filters are employed to provide point and bin estimates of noise from measurement vectors without any assumption about noise structure. The proportionality of noise to signals and their characteristics are also reported and are comparable when applying different methods.The proposed methods are compared using both simulated and experimental kinetic data sets. Experimental data includes fluorescence and UV–vis absorbance kinetic spectra. A simple solution for problem of MLFA application to fat data is proposed and successfully applied. Different types of independent noise including identical independent distribution (iid), constant heteroscedastic, and general heteroscedastic are added to the simulated data, in various levels.In the case of iid noise results from all methods are almost the same. In the presence of heteroscedastic noise results from MLFA and PAF are preferred to PCA regarding subspace angles and discrepancy function values. Employment of methods for highly overlapped, skinny, and fat data shows the superiority of MLFA to PAF and PCA. The independent noise characteristics obtained from factor analysis methods are comparable to that from digital filters.