Poder discriminante de Fisher como critério de seleção de componentes principais em problemas de classificação usando PCA-LDA

Abstract

This work proposes a new algorithm that employs an adaptation of Fisher's discriminant criterion (named here as Discriminating Power, DISP) to choose principal components (obtained from Principal Component Analysis, PCA), which was used to build supervisedmodels for Linear Discriminant Analisys (LDA) for solving multivariate classification problems from food and fuel chemical data. This work fills a gap in analytical chemistry, adapting the successful approach originally proposed in the context of facial recognition, using Fisher's discriminability criterion. The proposed PCA-DISP-LDA algorithm was then applied to three different analytical problems, and a simulated case study involving: (I) classification of soybean oil in relation to expiration date by near-infrared (NIR) spectroscopy, (II)) identification of adulteration in biodiesel/diesel samples with soybean oil by VIS-NIR spectroscopy and (III) classification of cachaça samples regarding adulteration from aging in wooden barrels. The proposed method showed advantages in relation to techniques already established in the literature: conventional PCA-LDA, PCA-GA-LDA and PCA-SW-LDA, presenting results in terms of TCC, parsimony and operational simplicity superior to the mentioned methods, for cases in which that the PCs with higher values of explained variance do not have Fisher's discriminant power.