  In the realm of time series analysis, accurately measuring similarity is
crucial for applications such as forecasting, anomaly detection, and
clustering. However, existing metrics often fail to capture the complex,
multidimensional nature of time series data, limiting their effectiveness and
application. This paper introduces the Structured Similarity Index Measure for
Time Series (TS3IM), a novel approach inspired by the success of the Structural
Similarity Index Measure (SSIM) in image analysis, tailored to address these
limitations by assessing structural similarity in time series. TS3IM evaluates
multiple dimensions of similarity-trend, variability, and structural
integrity-offering a more nuanced and comprehensive measure. This metric
represents a significant leap forward, providing a robust tool for analyzing
temporal data and offering more accurate and comprehensive sequence analysis
and decision support in fields such as monitoring power consumption, analyzing
traffic flow, and adversarial recognition. Our extensive experimental results
also show that compared with traditional methods that rely heavily on
computational correlation, TS3IM is 1.87 times more similar to Dynamic Time
Warping (DTW) in evaluation results and improves by more than 50% in
adversarial recognition.
