error propagation in self-modeling curve resolution of size reduced data

Abstract: self-modeling curve resolution (smcr) analysis decomposes bilinear multivariate measurement matrices into more physically interpretable forms, such as spectral profiles, concentration profiles, elution profiles, and so on using a minimum amount of prior information about the process under investigation. by applying different constraints, smcr techniques don’t produce necessary a unique solution for every component in a system and a range of feasible solutions is possible [1]. evaluation of the error estimation and propagation of experimental errors is a key issue in the quality assessment of the results obtained by any chemometric methods and in particular for the mcr methods. different statistical procedures have been proposed to evaluate the error propagation for those cases where formulae for analytical evaluation of errors are not available owing to the strong non-linear behavior of the proposed model. among these procedures, monte carlo and numerical resampling methods have been proposed and become popular owing to their relatively easy implementation on today’s computers [2]. despite recent advances both in the field of self-modeling curve resolution (smcr) and on the practical side, (bio) chemical data sets and images are difficult to analyze because they are big and spatial spectral information is highly mixed. hence, there is a need for data compression and reduction techniques for which the preservation of essential information is guaranteed by low-level data transformation and minimum user involvement [3]. as the full and reduced data share the same vector space, mcr analysis can be equivalently performed on each data set [4].this work aims to investigate how the reduction of the data set dimensions affects the reliability of the feasible solutions. to study the effect of the reduction of the data set dimensions, several simulated data sets and their reduced sizes have been systematically investigated. the obtained results by simulated data sets showed that the reduction of the data sets dimensions increases the uncertainties of the feasible solutions.