Research And Application On Lie Group Machine Learning Models

This paper introduces Lie group to machine learning, which combines the definition of machine learning by Simon, demonstrates the intrinsic relations between Lie group and machine learning and builds the basic theoretical framework of Lie group machine learning. The content is as follows:1. The basic conceptions of Lie group machine learning are given;2. The models of Lie group machine learning are given, including the algebra model and the geometric model;3. The geometry algorithms of Dynkin diagrams in Lie group machine learning are given;4. The method to design the linear classifiers of Lie group machine learning is given and the SO(3) Classifier of Lie group machine learning is designed;5. The computer aided system of the classification of crystals based on Lie group machine learning is completed.Through the work of this paper, on one hand, the content of Lie group machine learning is enriched and the theoretical basis for the future research of Lie group machine learning is founded; on the other hand, the application is found for Lie group machine learning: the method of Lie group machine learning is introduced to the classification of crystals and the computer aided system of the classification of crystals based on Lie group machine learning is completed on the whole.