An algorithm for real-time anomaly detection

Real-world statistical systems are often complex, and efficiently detecting minor anomalies can be the key to avoiding catastrophe. For example, small timescale changes in the current and voltage output of an inverter can indicate a short circuit. However, many methods for detecting anomalies are insufficient, relying too heavily on simple models and prior knowledge, or struggling to handle noisy data.

Zhang et al. developed an efficient, adaptive algorithm for identifying such anomalies, called the exception maximization outlier detection (EMOD) algorithm. By treating all datasets as a blend of primarily normal data with a few abnormalities sprinkled in, EMOD can identify hidden outliers without needing to know specific details about the data’s behavior.

“As new observations arrive, EMOD updates this understanding in near-real time… It’s continuously refining its understanding of what’s ‘normal’ versus ‘abnormal,’” said author Mingyuan Zhang.

When applied to circuitry, the team found EMOD can quickly and accurately deliver alerts when a complex circuit system’s output indicates a short, with few missed or false detections. Moreover, it works continuously and does not erroneously report abnormalities after the circuit has returned to its working state.

EMOD is not limited to short circuits. The researchers also effectively applied their algorithm to study insured unemployment data in the United States at the height of the COVID-19 pandemic, a critical indicator of economic markets. Any time-series dataset that needs anomaly detection can utilize EMOD.

“I’m most eager to see EMOD applied to monitoring complex real-world systems—especially those where anomalies can have critical consequences,” said Zhang, pointing to examples such as detecting chemical anomalies in rivers for early signs of pollution, or real-time analyses of medical device signals for quick diagnoses.

Source: “Machine learning for complex systems with abnormal pattern by exception maximization outlier detection,” by Zhikun Zhang, Yiting Duan, Xiangjun Wang, and Mingyuan Zhang, Chaos (2025). The article can be accessed at https://doi.org/10.1063/5.0250852 .

This paper is part of the Advances in Mathematics and Physics: from Complexity to Machine Learning Collection, learn more here .