Leveraging Data Seasonality and Matrix Profile for Anomaly Detection: Application to Climate Time Series

Seasonal time series analysis is fundamental in domains such as climate science, where detecting and understanding anomalies, patterns, and data changes are essential. The classical Matrix Profile approach does not consider the data's seasonality, failing to detect seasonal anomalies and patterns. This paper introduces the Interval Matrix Profile, a novel extension of the Matrix Profile specifically designed for analyzing periodic and seasonal time series data. The Interval Matrix Profile enables flexible interval-based comparisons across seasons, allowing the detection of anomalies that conventional approaches miss. We further propose the constrained k Nearest Neighbor Interval Matrix Profile, designed to identify anomalies that may appear across multiple periods, a common characteristic of abnormal climate events and extreme weather phenomena. Our approach leverages a scalable block-based algorithm that achieves significant performance gains through caching, vectorization, and parallelism. Additionally, we introduce a novel methodology to detect the first or last occurrence of a pattern, enabling the discovery of pattern emergence or disappearance within seasonal time series. The algorithms are demonstrated in case studies on temperature climate time series. They effectively capture seasonal anomalies and find pattern disappearance. Our results illustrate that the IMP consistently outperforms the classical Matrix Profile in the accuracy of seasonal anomaly detection and computational efficiency.