ℓ1 trend clustering: Trend estimation, clustering, and change detection for spatial-temporal ground displacement data from satellite remote sensing

This study proposes ℓ 1 trend clustering, a novel method for analyzing spatiotemporal ground displacements obtained from satellite remote sensing techniques such as InSAR. The method integrates two machine learning algorithms— k -means clustering and ℓ 1 trend filtering—into a unified framework that simultaneously performs clustering, trend estimation, and change point detection. The effectiveness of ℓ 1 trend clustering was evaluated through three numerical examples, where it successfully estimated the true number of clusters, identified representative trends, and detected change points in noisy time-displacement curves. Additionally, its applicability was demonstrated using real subsurface settlement data from InSAR. The results indicate that ℓ 1 trend clustering can effectively distinguish areas of high and low settlement risk while accurately estimating representative trends. ℓ 1 trend clustering offers a simple yet powerful approach for analyzing spatiotemporal data from satellite remote sensing and can contribute to more accurate geotechnical risk assessment and improved geoinfrastructure management.