Construction Of Pseudo Hyperbolic Hull And Its Application

This article points to the concept of convex sets in projective space, and it dissertates upon the notion and construction method with which pseudo hyperbolic hull transforms from classical convex polygon by projective transformation in projective space. It mainly includes the following four aspects.Firstly, it dissertates upon the basic theory and algorithm of convex hull and the basic concept of projective transformation, and gives the matrix representation methods of projective transformation as well.Secondly, it deduces the transformation matrix which transforms from convex hull to pseudo hyperbolic hull in one-dimensional and two-dimensional cases, which has proved the corresponding relations between the infinity point and the straight line in convex hull and pseudo hyperbolic hull. At the same time, it elaborates on the visibility of pseudo hyperbolic hull, puts forward the construction algorithm of pseudo hyperbolic hull on Euclidean plane, and finally goes through the programming verification.Thirdly, on the basis of one-dimensional and two-dimensional pseudo hyperbolic hulls, this article, according to the derivation method of transformation matrix on two-dimensional plane, obtains the transformation matrix in three-dimensional space, and it makes a conjecture on the extension to high-dimensional space. It figures out the construction algorithm of pseudo hyperbolic hull in Euclidean space, and goes through the programming verification at last.Fourthly, it gives a full display to the application outlook of pseudo hyperbolic hull in the "channel" and "clustering" issues. The application examples of route planning in the "channel" issue have been given and the application examples of support vector machine in the "channel" issue have also been given.Based on the study of pseudo hyperbolic hull, this article derives the transformation matrix which transforms from convex hull to pseudo hyperbolic hull and brings forward the algorithm of pseudo hyperbolic hull in low-dimensional space, which provides a theoretical basis for the expansion of high- dimensional space and also provides a broad prospect for its applications.