Regularization; Dimensionality reduction; Weighted graph; Data processing; F-transform; LLE

Three techniques of data analysis are examined: dimensionality reduction, locally linear embedding and the F-transform. We show that all of them can be connected using the notion of a fuzzy partition and the corresponding construction of a non-local Laplace operator. The article is endowed with results of two comprehensible numerical experiments that compare achieved outputs. An important conclusion is that the outputs correspond to values of the first degree F-transform components.