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The periodic table of the elements is the most important generalization in chemistry, and is often regarded as a special representative case in the study of the relationship between chemistry and physics. The study of contradictions in the periodic table has been the subject of much research, such as the study of the position of lutetium and the position of hydrogen, but without being able to clarify the problem. In this work, we have attempted to tackle this problem, using a data mining approach and applying multivariate analysis techniques such as Principal Component Analysis (PCA) and regression (PLS). The results obtained show the great similarity between lutetium and the transition metals of the third period of the periodic table, indicating that the position of lutetium must be below yttrium next to hafnium, while for hydrogen it was found that it does not conform to any group of the periodic table, it is a special element.