On the Existence of a Sample Mean in Dynamic Time Warping Spaces

2016/10/14 by Brijnesh J. Jain, David Schultz, Jain, Brijnesh J. +1
Computer Science · Mathematics · #Computer Vision and Pattern Recognition (cs.CV) #Data Mining Algorithms and Applications #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Morphological variations and asymmetry #Optimization and Control (math.OC) #Time Series Analysis and Forecasting

paper · pdf · doi:10.48550/arxiv.1610.04460

openalex publication_date 2016/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces
• Dynamic programming algorithm optimization for spoken word recognition

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