A Piecewise Aggregate pattern representation approach for anomaly detection in time series

In the area of time series representation, the Piecewise Aggregate Approximation (PAA) method has established itself quite visibly resulting in a number of useful results. However, the PAA technique usually leads to some losses of information. In order to overcome this issue, we propose a representation approach called Piecewise Aggregate Pattern Representations (PAPR). In the PAPR method, the range of values assumed in the temporal segment is divided into several regions with equal probability. In the sequel, some statistics of the regions, such as the number, the mean and the variance of points falling within each region, are determined. A matrix (pattern) containing all these statistical characteristics is constructed to represent the corresponding segment of the time series. We incorporate the PAPR method into anomaly detection by computing the similarity of patterns and using a Random Walk (RW) model, as a classifier, to determine the similarity values. Finally, the connectivity and anomaly ranks of patterns are obtained with the use of the RW model. The overall anomaly detection approach is referred to as PAPR-RW. Experimental studies are reported for synthetic data sets and two publicly available data sets: electrocardiograms (ECGs) data and the video surveillance data. Compared with the PAA-based method, the PAPR-RW approach exhibits a higher level of robustness and detects anomalies more accurately.