TS3IM: Unveiling Structural Similarity in Time Series through Image Similarity Assessment Insights

TL;DR

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 limitations by assessing structural similarity in time series.

Abstract

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.

Figures (6)

• Figure 1: The upper line is an example of SSIM. Except for contrast, almost all other structural information of the two pictures is the same, but SSIM still captured this information and reflected it in the score. Subsequently, the following line delineates instances of the time series field. The sequence changes values at 2 time steps and one of them changes drastically, but it can be seen from the results that the existing relative similarity method CCF cannot accurately capture the structural nuances of the sequence, while TS3IM is able to.
• Figure 2: Diagram of the TS3IM measurement system.
• Figure 3: Confusion matrices for the Pearson correlation coefficients: TS3IM-DTW Fig. \ref{['fig-ts3im']}, CCF-DTW Fig. \ref{['fig-ccf']}.
• Figure 4: Two plots depicting two sets of time series data, each comprising X and Y sequences.
• Figure 5: Two subsequence plots from Fig. \ref{['fig-plot2']}, representing the subsequences at [140, 200] and [250, 320], respectively.