Investigation Of The Divergence Function And Its Application

Information Geometry was first mentioned by the Japanese professor Amari. it is used in many fields, such as in information science and physics. Their theories is benefit to elaborate information systems, intelligent systems, control systems, physical systems, mathematical systems.The Research about information geometry has been a great development in a foreign country, however the research in our country is pessimistical.Currently,the information geometric is not only used in pattern recognition, signal processing, control theory, but also has achieved a certain development in control theory, Li group, Lie algebra, thermodynamic systems, and neural networks.The differentiable manifold has the concept of divergence,divergence operator,correspondingly, statistical manifolds also has divergence function. This paper is aimed to classify the divergence function,explore the applications of divergence function, and make a further promotion for the nature of divergence function.Divergence function is a great topic in information geometry,which is of great signification and has widely use in the index family,Logarithmic families and normal distribution manifold moderate and so on.The main contents of this paper are:The first part is introduces about the background of this study, presented the basic knowledge about differentiable manifolds and related statistical manifold.The second part is about α-connection,index family,blended family.The third part introduces the basic knowledge about divergence function.The fourth part is about the applications and promotion for divergence function.