Scores selection via Fisher's discriminant power in PCA-LDA to improve the classification of food data

This paper proposes an adaptation of the Fisher's discriminability criterion (named here as discriminant power, DP) for choosing principal components (obtained from Principal Component Analysis, PCA), which will be used to construct supervised Linear Discriminant Analysis (LDA) models for solving classification problems of food data. The proposed PCA-DP-LDA algorithm was then applied to (i) simulated data, (ii) classify soybean oils with respect to expiration date, and (iii) identify cachaça adulteration with wood extracts that simulated aging. For comparison, PCA-DP-LDA was evaluated against conventional PCA-LDA (based on explained variance) and Partial Least Squares-Discriminant Analysis (PLS-DA). Among them, PCA-DP-LDA achieved the most parsimonious and interpretable results, with similar or better classification performance. Therefore, the new algorithm can be considered a good alternative to the already well-established discriminant methods, being potentially applied where the discriminability of the principal components may not follow the same behavior of the explained variance.