Optimal Spatial Anomaly Detection

2025-10-25

AI Summary

This study addresses spatial mean anomaly detection in multidimensional grid data, aiming to accurately localize both the position and extent of anomalous regions. We propose a dual-penalty optimization framework that uniquely couples an $L_0$-norm penalty—enforcing sparsity—with a geometric structural constraint based on the minimum convex hull area, thereby ensuring consistent estimation of the number of anomalies while enhancing localization accuracy. To handle the inherent nonconvexity, we develop a dynamic programming–based approximation algorithm. Extensive Monte Carlo simulations validate the method’s statistical properties, including consistency and finite-sample performance. In comparative experiments, our approach significantly outperforms existing benchmarks. Applied to European Space Agency sea surface temperature data, it successfully identifies high-precision marine heatwave events. The method thus bridges theoretical rigor—via principled sparsity–geometry integration—with practical utility in real-world geospatial anomaly detection.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

There has been a growing interest in anomaly detection problems recently, whilst their focuses are mostly on anomalies taking place on the time index. In this work, we investigate a new anomaly-in-mean problem in multidimensional spatial lattice, that is, to detect the number and locations of anomaly ''spatial regions'' from the baseline. In addition to the classic minimisation over the cost function with a $L_0$ penalisation, we introduce an innovative penalty on the area of the minimum convex hull that covers the anomaly regions. We show that the proposed method yields a consistent estimation of the number of anomalies, and it achieves near optimal localisation error under the minimax framework. We also propose a dynamic programming algorithm to solve the double penalised cost minimisation approximately, and carry out large-scale Monte Carlo simulations to examine its numeric performance. The method has a wide range of applications in real-world problems. As an example, we apply it to detect the marine heatwaves using the sea surface temperature data from the European Space Agency.

Problem

• Detect spatial anomalies in multidimensional lattice data
• Estimate number and locations of anomalous spatial regions
• Introduce convex hull penalty for improved anomaly localization

Innovation

• Penalizes minimum convex hull area
• Uses dynamic programming algorithm
• Detects anomalies in spatial lattice