李群均值学习算法

首先分析李群均值的计算方法，在此基础上，进一步提出李群均值学习算法，其思想是在李群流形上寻找一个由总体样本内均值的李代数元素决定的单参数子群，这个单参数子群是原李群上的一条测地线，定义样本到测地线投影的概念，同时将李群样本向该测地线投影，并尽可能使投影后各类别间的散度与类内散度比值最大化，从而实现非线性李群空间的类别判别。实验表明，基于李群均值的学习算法和KNN、FLDA算法相比，具有较好的分类效果。

Lie Group Means Learning Algorithm

The method of mean computation on Lie group manifold is analyzed, and Lie group mean learning algorithm is proposed. The main idea of the algorithm is to find a one-parameter sub-group on the original Lie group which is decided by a Lie algebra element of intrinsic mean of all samples. The one-parameter sub-group is a geodesic on the original Lie group. Then, the projection of the sample to the geodesic is defined, and all samples to the geodesic are projected. In order to implement the discrimination in nonlinear Lie group space after projection, the ratio of between-class variance and within-class variance is maximized. The experimental results show that Lie group based algorithm is better than KNN, FLDA algorithms in classification performance.