Scanner : Simultaneously temporal trend and spatial cluster detection for spatial-temporal data

Identifying the underlying trajectory pattern in the spatial-temporal data analysis is a fundamental but challenging task. In this paper, we study the problem of simultaneously identifying temporal trends and spatial clusters of spatial-temporal trajectories. To achieve this goal, we propose a novel method named spatial clustered and sparse nonparametric regression ($\mathrm{Scanner}$). Our method leverages the B-spline model to fit the temporal data and penalty terms on spline coefficients to reveal the underlying spatial-temporal patterns. In particular, our method estimates the model by solving a doubly-penalized least square problem, in which we use a group sparse penalty for trend detection and a spanning tree-based fusion penalty for spatial cluster recovery. We also develop an algorithm based on the alternating direction method of multipliers (ADMM) algorithm to efficiently minimize the penalized least square loss. The statistical consistency properties of $\mathrm{Scanner}$ estimator are established in our work. In the end, we conduct thorough numerical experiments to verify our theoretical findings and validate that our method outperforms the existing competitive approaches.