Reasearch On The Fiber Bundle Learning Algorithms Based On Manifold Learning

Facing the data with high-dimensional, nonlinear and non-struction, a serious problems we should solve is how to find the rules behind the data sets. Manifold learning is a dimensional reducion method oriented to such high-dimensional data. By the way of finding the low-dimensional manifold in the high-dimensional space and the correspondance imbedding projection, it accomplish the goal of reduction. Fiber bundle theory, as the chief content of integral differential geometry, combining the topology and differential geometry, is the important part of research of geometry in 20th century. Its special way of contacting and processing different geometry space and geometry values in different space provides the feasibility method to research the globe and local relation of data sets. This paper will introduce the fiber bundle theory into manifold learning. The primary work is as follows:We constrcut the fiber bundle learning model, propose the representation and basic conception of fiber bundle based on manifold learning, give two contretely models based on the typical fiber bundle: tangent bundle and principle bundle, propose the fiber bundle learning algorithms included vection field reduction algorithm based on the local principle direction of tangent bundle and principle curve construction algorithm based on conncection of tangent bundle, illustrate their effect by the results of experiments, and apply the fiber bundle algorithm on partten recognize.All in all, characteristic of the paper represent as follow:(1) Give the tangent bundle modle and principle bundle model of fiber bundle representation and relate algorithms;(2) Find the applicatiable examples for proposed models and algorithms.