Detectability of concentration‐dependent factors by application of PCA. An indicator curve for the determination of important principal components and a post‐correction for transformation of principal components to factors

Abstract

A semi empirical model of light absorption for binary liquid mixtures, which includes linear, parabolic, and periodic terms of concentration-dependent factors, has been developed and applied for investigating the revealability of the factors. Concentration-dependent near infrared spectra of ethanol-water mixtures and a two-component model were decomposed by principal component analysis. Generated from the principal component analysis results and called the mean coefficient of determination, an indicator is introduced for separating the important or systematic principal components with deterministic information (factor PCs) from stochastic principal components originating from spectral noise (error PCs). Moreover, a post-correction method is proposed to pull the concentration-dependent factor effects out of the systematic principal components. The first PC of ethanol-water NIR mixture spectra defines the contributions of clusters of both water and ethanol molecules in the solution to resultant absorbance signals. The second PC includes partial absorptions from ethanol-water dimers and ethanol-water-ethanol trimers. The third PC is assumed to reflect concentration-dependent restructuring of mixture structure. KEYWORDS empirical absorption model, ethanol-water mixture, indicator MCD, PCA post-correction, V-plot | INTRODUCTIONPerhaps, the principal component analysis (PCA) is the most often applied multivariate data analysis method. As an almost required method, it appears in the assessments of concentration-dependent spectra of various aqueous solutions, as well as in those of two or more component liquid mixtures, too. 1-12 PCA is primarily utilized for the determination of systematic principal components (PCs) including deterministic information [13][14][15][16] and for the generation of the input matrix of discriminant analysis, 17-19 respectively. Mostly due to ambiguity of PCA results and lack of knowledge of the relationships between systematic PCs and the latent factors, the only PCA itself has not been applied to mapping the concentration-dependent factor effects. Based on the general transformation between decompositions of common factor analysis and PCA, 20 the idea was raised how the PCs of PCA could be traced back to the factor effects. The PCs involve the factor effects of examined phenomenon. In the cases of concentration-dependent spectra of aqueous solution, particularly some alcohol-water mixtures, we have tried to reveal the potential factors out of the PCA decompositions.