Geospatial Clustering of GNSS Stations Using Unsupervised Learning: A Statistical Framework to Enhance Deformation Analysis for Environmental Risk Management

The global expansion of continuous GNSS networks has generated large-scale spatiotemporal datasets whose analysis requires robust mathematical and statistical tools. This study introduces a geospatial, multivariate statistical framework for classifying 21,548 GNSS stations from the University of Nevada repository. The methodology integrates harmonic regression, stochastic noise modeling, quality assessment, and slope estimation into a unified feature space suitable for high-dimensional analysis. Using unsupervised learning clustering computed with our custom-developed code, based entirely on free and open-source software, we identify homogeneous station groups that reflect dominant signal properties—periodicity, noise structure, data quality, and long-term velocity—together with their spatial context. The resulting clusters exhibit strong mathematical coherence and reveal continental-scale patterns driven by seasonal forcing, tectonic regime, climatic variability, and monument stability. By grouping stations with similar statistical behavior, the proposed framework improves reference-site selection, enhances deformation-field interpretation, and supports the detection of anomalous or hazard-related behavior. Overall, this approach provides a scalable, data-driven mathematical tool for analyzing complex spatiotemporal signals and contributes to more reliable deformation modeling and environmental risk assessment.