论文标题
谎言组的路径签名
Path Signatures on Lie Groups
论文作者
论文摘要
路径签名是用于时间序列分析的强大非参数工具，显示出为欧几里得有价值的时间序列数据构成通用和特征的特征图。我们将路径签名理论提升为谎言组有价值的时间序列的设置，并将这些工具适应时间序列，并具有潜在的几何约束。我们证明这种广义路径签名是普遍的和特征的。为了展示普遍性，我们使用$ SO（3）$表示时间序列分析了人类的行动识别问题，提供了与其他浅层学习方法相当的性能，同时提供了易于解释的功能集。我们还为Lie组值随机步道提供了两样本假设检验，以说明其特征性能。最后，我们提供了这些方法的算法和朱莉娅实施。
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.
