An Adaptive Sampling Strategy for Monitoring Clustered Anomalies in Large-Scale Spatial Domains

Timely detection of emerging anomalies, such as solar flares, wildfires and environmental pollution, is critical for early hazard mitigation. However, achieving this objective often requires high sampling rates over large-scale spatial domains, leading to prohibitively high costs in data acquisition, communication, and processing. Adaptive sampling, which selectively observes a subset of informative locations at each acquisition time, has emerged as a cost-effective alternative. Rather than relying on precise dependence structures of anomalies, we exploit weak geometric clustering information and propose a novel adaptive sampling scheme that significantly outperforms existing approaches in detecting anomalies with diverse and unknown clustering patterns. Departing from conventional exploration strategies confined to multi-armed bandit paradigms, our method integrates a spatiotemporal distance metric into a minimax optimization framework originally developed for space-filling designs. This formulation achieves more uniform coverage of the monitoring domain within sliding windows, thereby ensuring that any emergent cluster can be rapidly intercepted by the sampling process. In addition, we introduce a standardized kernel-weighted mean estimator with appropriate regularization and transform the resulting online estimates based on partial observations into weighting factors for the spatiotemporal distance metric. This yields an adaptive sampling criterion that effectively balances local exploitation and global exploration. Theoretical analysis and simulation studies confirm the effectiveness and robustness of the proposed method, and a case study on solar flare detection further demonstrates its practical value.