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中文摘要：
在之前的研究中,已经针对李群多连通空间上具有不同类别特征的研究对象,提出了多连通覆盖学习算法,成功地将覆盖学习应用到多连通李群空间.主要针对多连通覆盖学习算法中连通道路的交叉问题,考虑在李群空间上寻找一条测地曲线,使得映射后不同单连通空间上的道路的关联度最小化、同一单连通空间上的道路的关联度最大化,从而实现连通空间上类别判别性能的优化.首先回顾李群连通性质的相关知识;然后,简单介绍了多连通覆盖学习算法,并针对问题给出新的优化算法;最终,通过与经典覆盖学习算法、李群均值算法以及原始算法的比较实验,证明了该优化算法具有更好的分类性能.
英文摘要：
The present paper focuses on the problem of the connected road intersection of multiply connected Lie group covering learning which was recently shown to possess a cover learning based on the connectivity of Lie group on the author＇s previous studies. It discusses a geodesic curve for optimal mapping of roads to minimize the correlation of roads from different connected spaces and maximize the correlation of roads within the same connected space. A review on some relevant notions from Lie-group connectivity theory is provided, followed by a brief introduction of multiply connected covering learning algorithm. New path optimization algorithms are then proposed. Some numerical experiments compared with classical covering learning methods, Lie group means learning algorithms and the author＇s previous algorithm serve to illustrate the better classification performance of the presented optimization algorithms.
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