We semiclassicalise the theory of quantum group principal bundles to level Poisson geometry. The total space X is a manifold with Poisson-compatible contravariant connection, fibre Poisson-Lie in sense Drinfeld bicovariant and base has an inherited structure connection. latter are known be semiclassical data for differential calculus. illustrated by q-Hopf fibration on standard q-sphere. also c...

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, intuitive accessible manner, basic principles underlying PCA its applications. Next, present a systematic, though no exclusive, survey some representative works illustrating poten...

This paper presents a new approach for dimension reduction of data observed on spherical surfaces. Several techniques have been developed in recent years non-euclidean analysis. As pioneer work, (Hauberg 2016) attempted to implement principal curves Riemannian manifolds. However, this uses approximations process manifolds, resulting distorted results. study proposes project onto continuous curv...