Exploiting self-similarity for change detection

Time-series data are often characterized by a large degree of self-similarity, which arises in application domains featuring periodicity or seasonality. While self-similarity has shown to be an effective prior for modeling real data in the signal and image-processing literature, it has received much less attention in time-series literature, where only few works leveraging the self-similarity for anomaly detection have been presented. Here we introduce a novel change-detection test to detect structural changes in time series by analyzing their self-similarity. The core of the proposed solution is the definition of a change indicator to quantitatively assesses the self-similarity of the time-series data over time. In particular, the change indicator is obtained by comparing each patch to be analyzed with its most similar counterpart in a change-free training set. Experimental results on the flow measurements in the water distribution network of the Barcelona city show the effectiveness of the proposed solution.