Research On Tangent Bundle Manifold Learning And Its Application

With the arrival of information age, we face with difficult problems such as dealing with high-dimetional and nonlinear of the data. How to find hidden laws from these data is an urgent problem which needs to be done. Substantial progresses have already been made on some of the traditional linear dimentionality reduction methods, but these works are far from dealing with complex data such as data with multi-manifolds structure. We try to do some significant works, include the following aspects:(1) Analysis of manifold learning algorithm with its problem in neighborhood selection and the related solutions.(2) Presenting the manifold learning based on tangent bundle model and its relevant algorithm.(3) Proving the usefulness of the manifold learning based on tangent bundle algorithm in handwriting recognition, face recognition, and medical data analysis.