F-transform, dimensionality reduction, Laplacianeigenmaps, fuzzy partition, PCA, pattern recognition

Two distinguished properties of the F-transform:the best approximation in a local sense and the reductionin dimension imply the fact that the F-transform has manysuccessful applications. In the first part, we propose another wayof computing the F-transform components of a functional data.This way is based on the particular dimensionality reductionalgorithm named Laplacian eigenmaps. In the second part,we strengthen the effect of F-transform-based dimensionalityreduction by applying the PCA reduction method over theF0- or F1- transform results. We demonstrate the efficiency ofthe proposed combinations F0zT+PCA and F1zT+PCA on theproblem of patter recognition in a large database. We compareboth combinations with other relevant techniques (besides other,LENET-like CNN) and show that they outperform them fromthe computation time and success rate points of view.