Abstract 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.
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2012, Vol. 25 
