Research On Lie Group Mean Learning Algorithm And Its Application

This paper based on Lie group mean computation theory, and proposed Lie-Fisher algorithm, which mainly finds a one-parameter sub group decided by a Lie algebra element of intrinsic mean of all samples, and this one-parameter sub group is a geodesic on the original Lie group. Moreover, we defined the projection of sample to geodesic, and projected all samples to a geodesic. In order to implement the discrimination in nonlinear Lie group space after projection, the ratio of between-class variance to within-class variance is maximized. In accordance with the matrix Lie group dot project theory, we also designed kernel functions based on matrix Lie group, and further proposed KLieDA algorithm with the help of KFDA and these kernel functions. A large number of experiments showed that Lie-Fisher based on Lie group mean is better than KNN, FLDA algorithms in classification performance, and both KLieDA and SVM based on Lie group kernels also have excellent recognition rate of handwritten classification.The contributions and innovations of this paper are as follows.(1) The proposed Lie-Fisher learning algorithm solves the problem that geodesic is used to classify on Lie group manifold.(2) The several deduced Lie group kernel functions can be easily combined with the existing kernel-based algorithms, such as KFDA, SVM, and KPCA.(3) The proposed KlieDA algorithm solves the problem of nonlinear matrix samples’ classification through the kernel theory.(4) The experiments demonstrate that the region covariance features of the handwritten images are located in Lie group manifold space, but they have a very good linear distribution characteristic.