## 1 Introduction  
Extra virgin olive oil (EVOO) is at the forefront of research due to its high consumption in the Mediterranean and worldwide. Its consumption is associated with lower risk of cancer, cardiovascular disease and other diseases [1]. Apart from its nutritional value, olive oil is highly appreciated by consumers for its unique sensory characteristics that are related to the volatile composition, the high content of oleic acid and the presence of phenolic compounds [2, 3]. There is also a very significant economic and social role played by olive oil production in the Mediterranean. According to the International Olive Oil Council, 2022 [4], world olive oil production has tripled in the last 60 years. Specifically for the crop year 2020/21, the production reached 3010,000 tons, of which Spain produced 46.15%, Greece ranks second with 9.14% of the world olive oil production and Italy third with 9.09%. Since the Greek olive oil industry exports approximately 35% of its annual production, characterization and standardization of its olive oil are crucial in order to benefit from significant price increases [5]. Volatile compounds are low-molecular-mass compounds that easily vaporize at ambient temperature, and when they reach the olfactory receptors, they cause an odor sensation [6]. A great number of volatile compounds have been reported in the volatile fraction of EVOOs belonging to several chemical classes, especially carbonyl compounds, alcohols, esters, hydrocarbons and other compounds such as acids, ethers, terpenes and furan derivatives [7]. The C6 and C5 compounds, especially C6 unsaturated and saturated aldehydes, represent the most important fraction of volatile compounds that contribute to green odor notes and are enzymatically produced from polyunsaturated fatty acids through the lipoxygenase (LOX) pathway [8]. Thus, the positive aroma perceptions in olive oil are attributed to the action of the endogenous plant enzymes, whereas the negative notes result are from chemical oxidation and the microbial activity [6]. During the olive fruit storage, the concentration of aldehydes and esters decreases and off-flavor compounds with low odor thresholds are generated [9]. Cultivar, geographic region, climatic and agronomic conditions (e.g., irrigation and fertilization), fruit maturity and processing method (e.g., malaxation time and temperature) influence the volatile composition of olive oil [10; 11; 12]. Since consumers are increasingly showing the need to purchase certified EVOOs produced in certain regions and avoid food fraud, quality assessment of olive oil and authenticity is at the core of scientific research [13; 14; 15]. Various instrumental techniques have been applied regarding the non-volatile and volatile fraction of olive oil to prevent adulteration and false labeling. The determination of fatty acid and sterol composition via gas chromatography equipped with a flame ionization detector has been widely used [16], as well as spectroscopic techniques, including nuclear magnetic resonance (NMR), Fourier transform infrared spectroscopy (FT-IR), fluorescence spectroscopy, near infrared spectroscopy (NIR) and mass spectrometry [13]. The application of chemometrics for the characterization and authentication of EVOOs using volatile composition data is quite common in the literature [13; 14; 17; 18]. In comparison to other methods that are widely used for the determination of volatile compounds, headspace solid-phase microextraction (HS-SPME) combined with gas chromatography-mass spectrometry (GC-MS) is generally considered more sensitive, faster, fully automatable and cost effective, while providing the advantages of an untargeted approach [18]. To fully utilize the large amount of data produced from olive oil profiling, chemometric tools are required. Principal component analysis (PCA), linear and partial least squares discriminant analysis (LDA, PLS-DA) [13] and orthogonal PLS-DA (OPLS-DA) [19] are most commonly used.