Riemannian Time Warping: Multiple Sequence Alignment in Curved Spaces

• URL: http://arxiv.org/abs/2506.01635v3
• Date: Mon, 14 Jul 2025 09:32:28 GMT
• Title: Riemannian Time Warping: Multiple Sequence Alignment in Curved Spaces
• Authors: Julian Richter, Christopher A. Erdös, Christian Scheurer, Jochen J. Steil, Niels Dehio,
• Abstract summary: Temporal alignment of multiple signals through time warping is crucial in many fields, such as speech recognition or robot motion learning.<n>We introduce a novel approach efficiently aligning multiple signals by considering the geometric structure of the Riemannian manifold in which the data is embedded.<n>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.
• Score: 5.777642571856656
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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