Chinese Journal of Computers   Full Text
  TitleSurvey on Lie Group Machine Learning
  AuthorsLI Fan-Zhang HE Shu-Ping QIAN Xu-Pei
  Address(School of Computer Science and Technology, Machine Learning and Data Analysis, Research Center, Soochow University, Suzhou, Jiangsu 215006)
  Year2010
  IssueNo.7(11151126)
  Abstract &
  Background
Abstract This paper summarizes the relevant research of Lie group machine learning, including: conceptions of Lie group machine learning, assumption axioms, algebra learning model, geometric learning model, geometric learning algorithms of Dynkin diagram, learning algorithms of orbits generated and so on. Especially, this paper gives out specific design of quantum group classifier and sympletic group classifier. Keywords Lie group machine learning; assumption axiom; Lie group; classifier Background As a new approach to learning in machine learning field, Lie group machine learning, on the one hand, keeps the merits of manifolds; On the other hand, it borrows the idea of Lie group. And so a learning paradigm with innovative feature was formed. Since reported in 1994, Lie group machine learning has draw widespread attention at home and abroad, such as Finland, Canada, Ireland, Italy, USA. Compared with manifold leaning method, it has an obvious advantage. As can be seen from the concept of Lie Group, it includes the contents of differentiable manifold and group; differentiable manifold contains topological manifold and differential structure. In addition, seen from cognitive process, when identifying any object in the objective world, human brain first look to a stable point in symbolizing problems, second analyzes the image structure in turn. In Lie group structure, minimum generator is this stable point for the cognitive models. As long as the minimum generator is found, one can analyses the image by Lie group method. So Lie group learning method not only is up to the cognitive and leaning rule, but also meets the conditions of solving realistic problem by computer.