Free congruence: an exploration of expanded similarity measures for time series data

Abstract

\u200b \u200bTime series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often involve point-to-point distance measures including Euclidean distance and Dynamic Time Warping. Such similarity measures fundamentally require the fluctuation of values in the time series being compared to follow a corresponding order or cadence for similarity to be established. Other existing approaches use local statistical tests to detect structural changes in time series. This paper is spurred by the exploration of a broader definition of similarity, namely one that takes into account the sheer numerical resemblance between sets of statistical properties for time series segments irrespectively of value labeling. Further, the presence of common pattern components between time series segments was examined even if they occur in a permuted order, which would not necessarily satisfy the criteria of more conventional point-to-point distance measures. The newly defined similarity measures were tested on time series data representing over 20 years of cooperation intent expressed in global media sentiment. Tests determined whether the newly defined similarity measures would accurately identify stronger resemblance, on average, for pairings of similar time series segments (exhibiting overall decline) than pairings of differing segments (exhibiting overall decline and overall rise). The ability to identify patterns other than 1 the obvious overall rise or decline that can accurately relate samples is regarded as a first step towards assessing the value of the newly explored similarity measures for classification or prediction. Results were compared with those of Dynamic Time Warping on the same data for context. Surprisingly, the test for numerical resemblance between sets of statistical properties established stronger resemblance for pairings of decline years with greater statistical significance than Dynamic Time Warping on the particular data and sample size used.