Abstract
Since time series are characterized by a substantial volume of data, high levels of noise and the correlation between data in the time series attributes, it becomes challenging to mine crucial information from the series and apply it to anomaly detection. In this study, inspired by the concept of information granularity being applied to the process of system modelling, a granular Markov model is proposed for time series anomaly detection. Anomalies are generally caused by the changes in amplitude and shape; in this study we take both the original time series data and their amplitude change data into consideration. First, we utilize an interval information granularity representation based on the principle of justifiable granularity to represent the original time series data in an abstract manner to arrive at the corresponding representation results- that is, interval information granules. Then, based on the results of the interval information granularity representation and the Fuzzy C Means (FCM) clustering algorithm, a granular Markov model is developed to produce anomaly scores to quantify possible anomalies. Compared with state-of-the-art methods, experimental studies completed for a large number of datasets demonstrate that the proposed method can significantly improve the anomaly detection process with higher data anomaly resolution. The obtained results are consistent across all datasets.