李群上的路签名
Path Signatures on Lie Groups
摘要：
路径特征是时间序列分析的非参数工具，可以为欧氏时间序列数据形成一个通用的特征映射。我们提升的路径签名理论的李群值的时间序列的设置，适应这些工具的时间序列与潜在的几何约束。我们证明了这种广义路径签名具有普适性和特征性。为了证明普遍性，我们分析了计算机视觉中的人类动作识别问题，使用$SO(3)$表示时间序列，提供与其他浅层学习方法相当的性能，同时提供易于解释的特征集。我们还提供了一个两个样本的假设检验李群值随机游动，以说明其特性。最后，我们提供了这些方法的算法和Julia实现。
英文摘要：
Path signatures are powerful nonparametric tools for time series analysis, shown to form a universal and characteristic feature map for Euclidean valued time series data. We lift the theory of path signatures to the setting of Lie group valued time series, adapting these tools for time series with underlying geometric constraints. We prove that this generalized path signature is universal and characteristic. To demonstrate universality, we analyze the human action recognition problem in computer vision, using $SO(3)$ representations for the time series, providing comparable performance to other shallow learning approaches, while offering an easily interpretable feature set. We also provide a two-sample hypothesis test for Lie group-valued random walks to illustrate its characteristic property. Finally we provide algorithms and a Julia implementation of these methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
