Fast localization of anomalous patches in spatial data under dependence

TL;DR

The paper introduces a scalable and accurate method for localizing multiple anomalous patches in spatial data with dependence, improving speed and robustness over existing approaches.

Contribution

It develops SPLADE, a novel two-stage procedure for detecting multiple patches under dependence, with proven consistency and practical effectiveness.

Findings

Method achieves significant computational and accuracy improvements.

Robust to moderate and severe spatial dependence.

Successfully applied to video surveillance data for detecting small, close subjects.

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.