关键词: 李群, 流形结构, 覆盖学习算法, 核函数

Abstract: Lie group not only has algebraic structures, but also has manifold structures. Data are mapped to multiply Lie group, according to the track ralation of Lie group samples on the manifold, these tracks which are homotopic can be covered. So, these covering areas can present the category information. This paper proposes a new covering algorithm called multiply Lie group kernel covering learning algorithm that uses kernel function to make the covering area have more divisibility and the edge of covering area smooth. The experimental results on the MNIST datasets show that the proposed algorithm has better classification performance with comparison to the other algorithm called multiply connected Lie group covering learning algorithm.

Key words:  Lie group, manifold, covering learning algorithm, kernel function