An overview on theory and application of information geometry method

LIU Cong

doi:10.3969/j.issn.1673-0569.2017.03.003

Abstract：Information geometry is the fundamental and cutting -edge discipline rapidly developed in recent years, which is a new set of theoretical system that explores statistical problems on Riemannian manifolds of prob -ability distributions by using the methods of modern differential geometry .Meanwhile , as an interdisciplinary re-search subject with profound theoretical foundation , information geometry theory provides a new concept for sol-ving statistical problems and a new approach for studying systems theory , information science , neural networks , statistical inference and other research fields .Just because of powerful theory and technology advantages in sol-ving scientific problems with information geometry method , which attracts a lot of researchers and results in a great many of studies in various fields of natural sciences .Firstly, this article introduces some basic concepts of information geometry , including statistical manifold , Riemannian metric , affine connection and Kullback -Leibler divergence .The two important theorems based on dual flat manifold are also introduced .Then, the new application of information geometry to various areas such as neural networks , statistical inference , systems theo-ry, communications and coding , physics and medical imaging are reviewed .And the research prospect of infor-mation geometry is also discussed in the last .