Granular Computing-Based Time Series Anomaly Pattern Detection with Semantic Interpretation

Time series analysis may suffer from the “curse of dimensionality” due to its high-dimensionality characteristics. In terms of this issue, information granulation offers an effective vehicle to process time series at a higher level of abstraction. To take this advantage, this study conducts an interpretable time series anomaly pattern detection under the framework of granular computing, where each time series is granulated into a series of semantics according to its patterns and the anomaly ones are identified based on the obtained semantics. First, the time series is partitioned into a predefined number of segments and trend-based information granules are formed for the data points in each time interval. Guided by the principle of justifiable granularity, the granular results maintaining the main features of the original time series realize informative feature extraction and meaningful dimensionality reduction. Then, to realize semantic anomaly pattern detection, the Axiomatic Fuzzy Set (AFS) theory is generalized to construct and compute with semantic time series, and an AFS-based anomaly score is proposed to discover anomaly patterns. In the experiments, the proposed method is conducted on both UCR data sets and real-world time series, where the detected anomaly patterns are equipped with well-defined semantics.