Title: Riemannian Time Warping: Multiple Sequence Alignment in Curved Spaces Show Chinese title

Title: 黎曼时间扭曲：弯曲空间中的多重序列比对

Abstract: Temporal alignment of multiple signals through time warping is crucial in many fields, such as classification within speech recognition or robot motion learning. Almost all related works are limited to data in Euclidean space. Although an attempt was made in 2011 to adapt this concept to unit quaternions, a general extension to Riemannian manifolds remains absent. Given its importance for numerous applications in robotics and beyond, we introduce Riemannian Time Warping (RTW). This novel approach efficiently aligns multiple signals by considering the geometric structure of the Riemannian manifold in which the data is embedded. Extensive experiments on synthetic and real-world data, including tests with an LBR iiwa robot, demonstrate that RTW consistently outperforms state-of-the-art baselines in both averaging and classification tasks. Show Chinese abstract

Abstract: 通过时间扭曲对多个信号进行时间对齐在许多领域中至关重要，例如在语音识别中的分类或机器人运动学习。 几乎所有相关工作都局限于欧几里得空间中的数据。 尽管2011年曾尝试将这一概念适应到单位四元数，但对黎曼流形的通用扩展仍然缺失。 鉴于其在机器人技术及其他众多应用中的重要性，我们引入了黎曼时间扭曲（RTW）。 这种新方法通过考虑数据嵌入的黎曼流形的几何结构，高效地对齐多个信号。 在合成数据和真实世界数据上的大量实验，包括与LBR iiwa机器人的测试，表明RTW在平均和分类任务中始终优于最先进的基线方法。