关键词: 李群机器学习, 多连通李群, 李群覆盖学习算法

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