A novel multi-level framework for anomaly detection in time series data

Anomaly detection is a challenging problem in science and engineering that appeals to numerous scholars. It is of great relevance to detect anomalies and analyze their potential implications. In this study, a multi-level anomaly detection framework with information granules of higher type and higher order is developed based on the principle of justifiable granularity and Fuzzy C-Means (FCM) clustering algorithm, including two different types of approaches, namely abstract level approach (ALA) and detailed level approach (DLA). The ALA approach is implemented at a comparatively abstract level (viz., level-1), in which two distinct types of information granules of order-1 (viz., information granules of type-1 and type-2) are employed for anomaly detection. The DLA approach is formulated and derived from the ALA approach at a more detailed level (viz., level-2), which generates more detailed information granules, namely information granules of order-2, through successive splitting information granules and the FCM clustering algorithm to refine the problem at various levels. Furthermore, a similarity measurement algorithm is designed for anomaly detection utilizing information granules of higher type and higher order. Comprehensive performance indexes are produced to quantify the performance of the proposed framework compared with the methods of two single-level approaches and two multi-level approaches. Synthetic data and several real-world data coming from various areas are engaged to demonstrate and support the superiority of the proposed approaches over other classical methods in terms of detection accuracy and data anomaly resolution.