The high price of marketing of extra virgin olive oil (EVOO) requires the introduction of cost-effective and sustainable procedures that facilitate its authentication, avoiding fraud in the sector. Contrary to classical techniques (such as chromatography), near-infrared (NIR) spectroscopy does not need derivatization of the sample with proper integration of separated peaks and is more reliable, rapid, and cost-effective. In this work, principal component analysis (PCA) and then redundancy analysis (RDA)�which can be seen as a constrained version of PCA�are used to summarize the high-dimensional NIR spectral information. Then PCA and RDA factors are contemplated as explanatory variables in models to authenticate oils from qualitative or quantitative analysis, in particular, in the prediction of the percentage of EVOO in blended oils or in the classification of EVOO or other vegetable oils (sunflower, hazelnut, corn, or linseed oil) by the use of some machine learning algorithms. As a conclusion, the results highlight the potential of RDA factors in prediction and classification because they appreciably improve the results obtained from PCA factors in calibration and validation.