Reduction with Application to Pattern Recognition in Large Databases

Two distinguished properties of the F-transform: the best approximation in a local sense and the reduction in dimension imply the fact that the F-transform has many successful applications. In the first part, we propose another way of computing the F-transform components of a functional data. This way is based on the particular dimensionality reduction algorithm named Laplacian eigenmaps. In the second part, we strengthen the effect of F-transform-based dimensionality reduction by applying the PCA reduction method over the $F^{0}-$ or $F^{1}-$ transform results. We demonstrate the efficiency of the proposed combinations $F^{0}zT+PCA$ and $F^{1}zT+PCA$ on the problem of patter recognition in a large database. We compare both combinations with other relevant techniques (besides other, LENET-like CNN) and show that they outperform them from the computation time and success rate points of view.