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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.
First of all, the method of calculating the mean of Lie group is analyzed. On the basis of this, the algorithm of Lie group averaging is further proposed. The idea is to find a single parameter subgroup which is determined by the Lie algebraic elements in the whole sample. Subgroups are a geodesic line on the original Lie group, which defines the concept of the projection of the sample to the geodesic. At the same time, the projection of the Lie group samples onto the geodesic line, and the degree of divergence among the categories after projection, The divergence ratio is maximized so as to realize the classification of nonlinear Lie group space.Experiments show that the learning algorithm based on Lie group means has better classification results than KNN and FLDA algorithms.