Table 2. Overview of the proposed method.

The GraphTS Method.
input: time series T, anomaly length ℓ, input window length wg
output: subsequence anomalies
Step 1 2D visualization of time series (Algorithm 1 2Dviz). Transfer all subsequences of length wg in T into a 2D spatial-temporal space, where subsequence with similar patterns are projected into similar spatial locations;
Step 2 Construction of graph (Algorithm 2 ConGraph). Construct a directed graph based on the 2D spatial-temporal space where spatial information is used to create the node set and temporal information is used to extract the edge set. The nodes represent the various subsequence patterns of length wg in time series and edges represent the number of successive occurrences of these patterns;
Step 3 Subsequence anomaly detection (Algorithm 3 AnomalyScore). Calculate the abnormality score for each subsequence of length ℓ based on their path in the constructed graph and return a ranked list of abnormal subsequences in T.