## 1 Introduction
Even though the decision criterion in binary discriminant models is usually a single classification threshold, in that case an uncertainty range was set to identify boundary samples. In this way, the instrumental screening tool allowed classifying clear samples into EVOO, VOO or LOO and left the boundary ones that fall into the uncertain range to be further assessed and graded by the sensory panel, thus reducing its workload [14]. These satisfactory results prompted us to keep improving the tool to achieve a reliable instrumental screening tool as well as to bring its real future application one step closer. For this, it was still necessary to (i) improve the sample database, increasing sampling representativeness, (ii) set the terms for the validation of the analytical fingerprint method, and (iii) optimize and validate the classification strategy with the updated sample database. All these steps are addressed in this article as they need to be accomplished before the tool can be submitted to a system challenge (applying it to data obtained from different GC-MS instruments and labs) and eventually to an interlaboratory study. Regarding sampling, an increase in the number of samples, including samples from at least two crop years, aiming to add natural variability to the classification model, is broadly recommended [15]. A fingerprinting method needs to undergo a validation process in order to be transferred to routine analysis. The first step prior to interlaboratory validations or peer validation studies consistsof an in-house validation. First, this validation shall address the analytical fingerprint obtained by SPME-GC-MS to verify its repeatability and reproducibility and, subsequently, shall focus on the classification model. In target-based methods, validation procedures for both analytical methods and statistical models are well defined [33; 34], given that results are usually evaluated compound by compound using univariate statistics. In contrast, since data obtained by fingerprinting approaches are assessed on a pattern level using multivariate models [35], conventional performance criteria adopted for the former methods are not applicable as such to the latter. Specific guidelines are necessary for this purpose, but they are still lacking. Some authors proposed method validation strategies for non-targeted metabolomic analysis [36; 37], but they could adapt the target validation procedure because they sought the validation of biomarkers where target-like steps such as analyte quantification are carried out in the end. In contrast, the fingerprinting approach followed in the present study is not intended to carry out identification and quantification of single compounds. Indeed, as defined by [PERSON] et al. [35], the \"spectral or chromatographic fingerprint\" already represents the \"analyte\". Given the lack of clear-cut guidelines for the analytical validation of fingerprinting methods, we proposed and evaluated a procedure for the in-house assessment of the repeatability of the analytical signal, which is one of the constraints when transferring fingerprinting methods. Regarding the optimization and validation of the classification strategy, to maximize its performance, the models' uncertainty ranges were set by means of receiver operating characteristics (ROC) analysis [38] in which high sensitivity and specificity can be ensured. Moreover, both internal and external validation were performed in seven independent runs. This external validation also included the validation of the classification criteria based on the uncertainty ranges from ROC analysis, to assess up to which extent they were influenced by the samples in the training set and how the uncertainty ranges performed in classifying new samples.