Abstract: As a novel learning method, Lie group machine learning has attracted much attention in academia. According to the connectivity of Lie group, this paper tries to map the research objects with different category characteristics into the space of multiply connected Lie group. Based on the homotopy equivalence of attachments on each simple connected Lie group, this paper explores the equivalent representation of the optimal path for each of the different categories by covering ideas, so as to present the category information of images by employing its multiple-valued representation. Therefore, this paper proposes a new covering learning algorithm on multiply connected Lie group. The experimental results on the datasets of MPEG7_CE-Shape01_Part_B and MNIST show that the proposed algorithm has better classification performance with comparisons to the other two algorithms based on the Lie group means.

Key words: Lie group machine learning, multiple connected Lie group, Lie group covering learning algorithm

摘要： 李群机器学习作为一种新的学习范式已被学术界广泛关注。根据李群的连通性质，将具有不同类别特征的研究对象映射到多连通李群空间，并从各个单连通李群空间上连线的同伦等价出发，运用覆盖的思想寻找对应不同类别的最优道路等价表示，从而用多连通李群的多值表示来呈现图像的类别信息，因此提出了多连通李群覆盖学习算法。在MPEG7_CE-Shape01_Part_B图像库的图像和MNIST手写体数字图像上进行了实验验证，结果表明与两种基于李群均值的学习算法相比，多连通李群覆盖学习算法具有较好的分类效果。

关键词: 李群机器学习, 多连通李群, 李群覆盖学习算法