Multiply Lie Group Kernel Covering Learning Algorithm And Its Application

Lie Group Machine Learning was presented in 2004 and it raises the concern of more and more researchers.This paper further studies the narrow scope of the mapping and the problem of road crossing and road selection in the Multiply Connected Lie Group Covering Learning Algorithm.After three years of efforts,the main results include:1.In order to solve the problem of road crossing in the lie group covering learning algorithm,this paper considers the idea of kernel function.We transforms the traditional kernel function into lie group kernel function.Finally,we propose the multi-lie group kernel covering learning algorithm by combine the kernel thought and covering learning algorithm.2.We should select right kernels according to the sample itself or the distribution.So,we consider to introduce the graphic embedding method and map the original lie group space to the target lie group space by using lie homology mapping to weaken the road crossing.In order to obtain a better relative optimal road representation,we use the sample's neighborhood information as a rule to select the cut point and adjust the coverage domain center.Finally,we propose a road selection algorithm.3.We apply the above algorithm to some dataset of vector or matrix form.The validity of those algorithms is verified by experiments.In this paper,we propose a multi-lie group kernel covering learning algorithm and some optimized learning algorithm.Finally,some examples are given to demonstrate the method which provides the application background for these methods.