Multi-variate time series similarity measures and their robustness against temporal asynchrony

The amount of time series data generated is increasing due to the integration of sensor technologies with everyday applications, such as gesture recognition, energy optimization, health care, video surveillance. The use of multiple sensors simultaneously

for capturing different aspects of the real world attributes has also led to an increase in dimensionality from uni-variate to multi-variate time series. This has facilitated richer data representation but also has necessitated algorithms determining similarity between two multi-variate time series for search and analysis.

Various algorithms have been extended from uni-variate to multi-variate case, such as multi-variate versions of Euclidean distance, edit distance, dynamic time warping. However, it has not been studied how these algorithms account for asynchronous in time series. Human gestures, for example, exhibit asynchrony in their patterns as different subjects perform the same gesture with varying movements in their patterns at different speeds. In this thesis, we propose several algorithms (some of which also leverage metadata describing the relationships among the variates). In particular, we present several techniques that leverage the contextual relationships among the variates when measuring multi-variate time series similarities. Based on the way correlation is leveraged, various weighing mechanisms have been proposed that determine the importance of a dimension for discriminating between the time series as giving the same weight to each dimension can led to misclassification. We next study the robustness of the considered techniques against different temporal asynchronies, including shifts and stretching.

Exhaustive experiments were carried on datasets with multiple types and amounts of temporal asynchronies. It has been observed that accuracy of algorithms that rely on data to discover variate relationships can be low under the presence of temporal asynchrony, whereas in case of algorithms that rely on external metadata, robustness against asynchronous distortions tends to be stronger. Specifically, algorithms using external metadata have better classification accuracy and cluster separation than existing state-of-the-art work, such as EROS, PCA, and naive dynamic time warping.