关键词: 李群, 李群核, 李群均值, 李群协方差特征, 分类器

Abstract: This paper analyzes the geometry structure of Lie group manifold, kernel function and principles of KFDA (kernel Fisher linear discriminant analysis), derives the measure of matrix Lie group dot-product space, then derives five Lie group kernel functions and designs KLieDA (kernel Lie group linear discriminant analysis) algorithm. Lie group kernel functions are more adaptive kernel functions. Due to the geometry of Euclidean space is a subset of Lie group, Lie group functions apply to not only the sample sets of matrix Lie group but also the sample sets of conventional vector form. The experiments show that KLieDA algorithm, based on theories of Lie group functions and Lie groups mean, is a fast and efficient Lie group sample classifier. Additionally, in the experiment section, the paper does a handwritten classification through SVM (support vector machine) based on Lie group kernel functions, and the results show that the region image covariance Lie group feature of the handwritten has a good linear distribution.

Key words: Lie group, Lie group kernel, Lie group mean, Lie group covariance feature, classifier