Tomáš Bílek

The geographical authentication of apples based on mineral profiles is complicated by substantial variability within and between production regions. This study examined the impact of geographical class definition and dataset structure on the classification of apple origin using linear discriminant analysis (LDA), and whether these effects could support a stepwise classification strategy. The mineral and isotopic profiles of four apple cultivars (‘Gala’, ‘Golden Delicious’, ‘Jonagold’, and ‘Idared’) originating from the Czech Republic and Poland were evaluated using five LDA models that differed in terms of geographical class definition, dataset size, and macro- versus micro-regional grouping. Exploratory analyses identified region-associated variation in twelve elemental and isotopic variables. Model performance was strongly affected by dataset structure and geographical class definition. Decomposing macro-regions into micro-regions did not universally improve classification, but it may reveal substantial intra-regional heterogeneity and the identification of specific collision regions that can be responsible for a considerable proportion of the classification uncertainty. Based on these findings, a conceptual hierarchical multiple-model framework is proposed, in which a broad reference model would provide an initial classification and samples assigned to collision regions are subsequently evaluated using dedicated local models. This strategy may represent a useful component of a broader approach to geographical authentication based on mineral profiles.

High-dimensional analytical datasets, such as those generated by inductively coupled plasma–mass spectrometry (ICP-MS), require robust computational frameworks for dimensionality reduction, classification, and model validation. This study presents a comparative evaluation of Linear Discriminant Analysis (LDA) and Partial Least Squares Discriminant Analysis (PLS-DA) algorithms applied to multivariate chemometric data for food origin authentication. The research employs a workflow that integrates Principal Component Analysis (PCA) for feature extraction, followed by supervised classification using LDA and PLS-DA. Model performance and stability were systematically assessed. The dataset comprised 28 apple samples from four geographical regions and was processed with normalization, scaling, and transformation prior to modeling. Each model was validated via leave-one-out cross-validation and evaluated using accuracy, sensitivity, specificity, balanced accuracy, detection prevalence, p-value, and Cohen’s Kappa. The results demonstrate that, as a linear projection-based classifier, LDA provides higher robustness and interpretability in small and unbalanced datasets. In contrast, PLS-DA, which is optimized for covariance maximization, exhibits higher apparent sensitivity but lower reproducibility under similar conditions. The study also emphasizes the importance of dimensionality reduction strategies, such as PCA-based variable selection versus latent space extraction in PLS-DA, in controlling overfitting and improving model generalizability. The proposed algorithmic workflow provides a reproducible and statistically sound approach for evaluating discriminant methods in chemometric classification.

One of the consequences of the globalisation of food markets is the effort enabling the control of food security and its origin. This might be traced by using different chemical composition analyses. However, for Central Europe, there is a lack of knowledge about the original reference values as well as their heterogeneity among the lands and countries. This study focused on characterizing the mineral profiles of apple tree fruits and comparing these profiles among different districts in Central Europe. The fruits of the apple cultivars ‘Gala’ and ‘Golden Delicious’ originated in the Czech Republic and Poland. The mineral and isotopic content of the apple fruit flesh was analysed using ICP-MS. The data were processed using the ANOVA test and compositely analysed using the PCA and LDA models. The results show relatively high variation in element distribution, particularly ⁸⁷Sr/⁸⁶Sr, Mn, Zn, Cu, Ca, P, and B, ranging between 20.6 and67.9% for both cultivars on average. However, their high variability within particular districts complicates the resolution of the LDA model. The reasons are linked to the geomorphological and pedological heterogeneity of the analysed districts as well as the particular sensitivity of the set of chosen primers to agronomic practices and tree performance. For this region, only partial separation among districts could be obtained by P, Ca, and Cu content, as well as the isotopic ratio of ¹⁰B/¹¹B. However, the resolution of the geographical discrimination needs to be improved by an enhanced set of primers, the use of more precise analytical techniques for the Sr isotopic ratio, or by multiple chemical analyses. Furthermore, the heterogeneity of the analysed districts could be tackled by more detailed analyses at the level of micro-regions.