A New Clustering Strategy for Geo-Referenced Time Series Based on Optimal Transport

Abstract

Advances in spatio-temporal data collection have created a demand for efficient methods to analyze geo-referenced time series (GTS), which capture changes over time at specific spatial locations. Traditional clustering methods often struggle to handle the high-dimensional, complex nature of GTS. This paper proposes a novel approach for clustering GTS using a new dissimilarity measure, the Bi-Gromov Dynamic Time Warping (Bi-GDTW) distance. This method combines the alignment-based Dynamic Time Warping framework with Gromov–Wasserstein distance to account for both temporal and spatial dependencies in the data. The proposed measure supports clustering through algorithms such as K-means, enabling effective pattern discovery in GTS datasets. The paper explores the theoretical foundations of Optimal Transport and its integration with time series analysis, introducing Bi-GDTW as a comprehensive tool for capturing spatio-temporal patterns. Through applications on simulated and real-world datasets, the results demonstrate the effectiveness of this approach in addressing challenges in GTS clustering, offering new possibilities for analyzing structured sequential data. The research has implications for various fields, including environmental monitoring, urban studies, and socio-economic analysis, and provides a foundation for extending these techniques to other sequential datasets with underlying topological structures.