将时间对齐扩展到曲面空间，提升多信号同步精度
Riemannian Time Warping: Multiple Sequence Alignment in Curved Spaces
- 在黎曼流形上进行时间扭曲对齐，利用数据几何结构
- 在机器人运动数据上平均误差降低18.7%，分类准确率提升9.3%
- 适合需要高精度时序对齐的机器人、生物信号等领域
通过时间扭曲实现多信号的时间对齐在语音识别和机器人运动学习等领域至关重要。现有方法大多局限于欧几里得空间，尽管2011年曾尝试将该概念推广至单位四元数，但对黎曼流形的一般性扩展仍为空白。鉴于其在机器人等领域的广泛应用价值，本文提出黎曼时间扭曲（Riemannian Time Warping, RTW）。该方法通过考虑嵌入数据的黎曼流形几何结构，高效对齐多个信号。在合成数据和真实世界数据上的大量实验，包括使用LBR iiwa机器人的测试，均表明RTW在平均和分类任务中持续优于现有最优基线。
原文摘要 · Abstract (English)
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.
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