On the Existence of a Sample Mean in Dynamic Time Warping Spaces
This work addresses a foundational gap for researchers in pattern recognition and clustering using DTW, though it is incremental as it builds on prior approximate methods.
The paper tackles the problem of proving the existence of a sample mean in dynamic time warping (DTW) spaces, which had not been previously established, and presents sufficient conditions for its existence.
The concept of sample mean in dynamic time warping (DTW) spaces has been successfully applied to improve pattern recognition systems and generalize centroid-based clustering algorithms. Its existence has neither been proved nor challenged. This article presents sufficient conditions for existence of a sample mean in DTW spaces. The proposed result justifies prior work on approximate mean algorithms, sets the stage for constructing exact mean algorithms, and is a first step towards a statistical theory of DTW spaces.