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The bi-dimensional F1-Transform was applied in image analysis to improve the performances of the F-transform method; however, due to its high computational complexity, the multidimensional F1-transform cannot be used in data analysis problems, especially in the presence of a large number of features. In this research, we proposed a new classification method based on the multidimensional F1-Transform in which the Principal Component Analysis technique is applied to reduce the dataset size. We test our method on various well-known classification datasets, showing that it improves the performances of the F-transform classification method and of other well-known classification algorithms; furthermore, the execution times of the F1-Transform classification method is similar to the ones obtained executing F-transform and other classification algorithms. [ABSTRACT FROM AUTHOR]