## 2 Materials and Methods
### Multivariate Data Analysis  
Collected spectra were analyzed by a multivariate analysis software, Pirouette (Version 4.5, Bothell, WA, USA). The classification of authentic vs. tainted poppy seed oils was achieved using SIMCA, a supervised pattern recognition method. SIMCA classifies new and unknown samples into previously established classes--such as authentic or tainted/adulterated oils--based on prior knowledge regarding the category of the samples under consideration [27]. Interclass distances (ICDs) were calculated using between-class residuals, while the importance of the variables was determined by comparing the residual variance's average within each class to all classes and across classes [28]. ICD values greater than 3.0 indicate a significant separation between two sample groups as separate classes [29]. The major fatty acid composition of the tested poppy seed oil and possible adulterant oils was simultaneous and rapidly predicted using partial least square regression (PLSR). In order to overcome the high-collinearity problem generated by a spectrum with thousands of data points, PLSR combines the principles of multiple linear regression (MLR) and principal component analysis (PCA). PLSR is a quantitative approach that predicts dependent variables from a group of independent variables (predictors) by obtaining the greatest predictive power by extracting orthogonal elements (latent variables) [30]. Before constructing the SIMCA and the PLSR models, all spectral data were preprocessed through mean-centering to eliminate micro-multicollinearity, smoothing to address baseline noise, and normalization to identify systematic errors and biases unrelated to sample variance [31]. After evaluating the longer and shorter window options, a 25-point smoothing window was selected as optimal for reducing signal noise and enhancing essential spectral features. Prior to the multivariate analyses, irrelevant spectral regions, including peaks unrelated to lipids, were excluded to prevent interference in the analysis. Accordingly, only the spectral region between 3045-2800 cm\({}^{-1}\) and 1830-800 cm\({}^{-1}\) were included. To check the robustness of the models, the samples were randomly divided into PLSR calibration/training and independent validation sets. Accordingly, 80% of the total samples were used for calibration/training, while the remaining 20% were used for independent validation. The predictive performance of PLSR models was assessed using metrics such as outlier diagnostics, leverage, residual analysis, standard error of cross-validation (SECV), standard error of prediction (SEP), cross-validation correlation coefficients (RCV), prediction correlation coefficients (RPRE), residual predictive deviation (RPD), and range error ratio (RER). The authenticity of the samples was determined by evaluating the GC results and comparing those results with literature values. After assigning the samples to the authentic or adulterated groups, both multiple-class and single-class SIMCA approaches were applied. Samples were divided into training and external validation sets; the training set provides knowledge of the spectral characteristics associated with each distinct group (class), enabling the identification of potential discrimination discrepancies by supplying sample identity information to the model. In the multiple-class approach, the training set consisted of the randomly selected 20 authentic poppy seed oil samples and six tainted poppy seed oil samples. The training model was validated using an independent set of 10 authentic poppy seed oil samples from the market, three tainted poppy seed oil samples from the market, and the potential adulterants, including canola, maize (corn), soybean, and sunflower oils. In the single-class approach, the training model was generated using the same 20 authentic poppy seed oil samples used in the training set of the multiple-class approach.