Deterministic Decoupling of Global Features for Data Analysis

 We introduce a method for deterministic decoupling of global features with application to data analysis. We propose a new formalism that is based on defining transformations on submanifolds, by following trajectories along the features’ gradients. Through these transformations, we define a type of normalization that, we demonstrate, allows for decoupling differentiable features. We apply this to sampling moments, obtaining a quasi-analytic solution for the orthokurtosis, a normalized version of the kurtosis that is not just decoupled from mean and variance, but also from skewness. We also apply the proposed method, up to sixth-order moments, in the original data domain and at the output of a filter bank, to regression and texture classification problems, consistently obtaining strong improvements in performance as compared to using classical (non-decoupled) features