Fast localization of anomalous patches in spatial data under dependence

2026-03-29

AI Summary

This work addresses the challenge of efficiently localizing an unknown number of anomalous regions in large-scale spatially dependent data. The authors propose SPLADE, a two-stage method that integrates intelligent sampling with boundary estimation to simultaneously and consistently estimate both the number and boundaries of multiple axis-aligned anomalous patches under general spatial dependence structures—without requiring full spatial grid segmentation. By leveraging a uniform Gaussian approximation and an efficient search strategy, SPLADE substantially improves computational efficiency and localization accuracy. Experimental results demonstrate that SPLADE outperforms existing approaches on both synthetic and real-world video surveillance datasets, achieving faster runtime, higher localization precision, and robustness to strong spatial dependencies.

Abstract

We propose a scalable, provably accurate method for localizing an unknown number of multiple axis-aligned anomalous patches in spatial data under a general class of spatial dependence. Motivated by the practical need to detect localized changes rather than completely segment large spatial grids, we first introduce both a naive and a significantly faster intelligent-sampling-based estimator for a single patch. We then extend this methodology to the highly challenging multiple-patch setting and propose a two-stage Spatial Patch Localization of Anomalies under DEpendence procedure (SPLADE). Under mild conditions on signal strength, separation from the boundary, inter-patch separation, and a uniform Gaussian approximation, we establish simultaneous consistency for the estimated number of patches and for each individual patch boundary. Extensive numerical results based on synthetic data scenarios demonstrate that the proposed method exhibits significant computational and accuracy gains over competing approaches, as well as robustness to moderate and severe spatial dependence. Finally, we demonstrate the real-world utility of the proposed method by applying it to frame-to-frame video surveillance data, where it accurately detects small, closely separated subjects, a task where existing methods are significantly slower and highly prone to spurious detections due to not accounting for spatial dependence. A second application on 3D fibrous media is deferred to the Appendix.

Problem

• anomalous patches
• spatial dependence
• localization
• multiple anomalies
• spatial data

Innovation

• anomaly localization
• spatial dependence
• intelligent sampling
• SPLADE
• patch detection