application of the alternating conditional expectation (ace) algorithm for the determination of oxygenate compounds in gasoline samples using atr-ftir spectroscopy

This work aims to examine the nonparametric robust principal component analysis-alternatingconditional expectation (rpca-ace) algorithm combined with ftir spectroscopy as a rapid andaccurate analytical method for predicting the quality of gasoline samples based on oxygenatescontent (methanol, methyl tert-butyl ether, and isobutanol). the ace algorithm estimates a set ofoptimal transformations for independent and dependent variables in multiple regressions whichresults in a linear correlation between the transformed predictors and the transformed response,minimizing the error [1, 2]. in this study, the ace algorithm was applied to an empirical gasolinedataset and considered a series of possible transformations of the independent and dependentvariables to find the best transformations. among all possible transformations, the ace algorithmidentified a series of polynomials and a nearly linear transformation as the best transformationsfor the independent and dependent variables, respectively. the regression statistics for calibrationand prediction, including the correlation coefficient (???????????????? 2 =0.9692), root mean square error ofcalibration (rmsec=2.8638), and root mean square error of prediction (rmsep=4.0498) (%v/v)for oxygenates content, were calculated. the ace model showed improved regression resultscompared to the linear pls model (???????????????? 2 =0.9550, rmsec=3.9052, rmsep=5.1342) and pcrmodel (???????????????? 2 =0.9160, rmsec=6.5330, rmsep=7.0270). by applying the ace technique to thesynthetic fully non-linear dataset obtained from the equation ????′ = exp⁡(????) for the responsevariable, we demonstrated the power of the ace algorithm in multivariate analysis and its abilityto identify the exact functional relationship between independent and dependent variables to solvefully non-linear problems.