Researches On Affine Connection Learning Algorithm

Manifold learning method is one of the learning methods which is concerned by thepeople in recent years. To affine operator on manifold or manifold tangent bundle as thestarting point, this paper puts forward the affine connection algorithm. The results obtainedin this article include:(1) It presents dimensionality reduction method based on the data structure of the tensorand is combined with affine operator on the tangent bundle to build an affineconnection learning algorithm.(2) Processing the data on manifold structures and discussing from the horizontal spaceand vertical space, it proposes a contact algorithm on the frame bundle.To sum up, the innovation of this paper is mainly reflected the following:(1) The article uses tensor structure on the manifold as basic elements for data processingwhich has the advantage of maintaining the inner space’s structure of the original dataand intrinsic geometric relations.(2) Affine operator can transform between the different manifold tangent space and thistransformation can maintain the original data characteristics constant so that it can beprocessed in the same tangent space; it also has advantages of less training sample andsmall time complexity.(3) The algorithm of the paper can maintain the constant nature of different manifoldstructures, which improves the classification accuracy of the current manifold dataand enhances the effectiveness of dimension reduction algorithm...