In recent years Dynamic Time Warping (DTW) has emerged as the distance measure of choice for virtually all time series data mining applications. For example, virtually all applications that process data from wearable devices use DTW as a core sub-routine. This is the result of significant progress in improving DTW’s efficiency, together with multiple empirical studies showing that DTW-based classifiers at least equal (and generally surpass) the accuracy of all their rivals across dozens of datasets. Thus far, most of the research has considered only the one-dimensional case, with practitioners generalizing to the multi-dimensional case in one of two ways, dependent or independent warping. In general, it appears the community believes either that the two ways are equivalent, or that the choice is irrelevant. In this work, we show that this is not the case. The two most commonly used multi-dimensional DTW methods can produce different classifications, and neither one dominates over the other. This seems to suggest that one should learn the best method for a particular application. However, we will show that this is not necessary; a simple, principled rule can be used on a case-by-case basis to predict which of the two methods we should trust at the time of classification. Our method allows us to ensure that classification results are at least as accurate as the better of the two rival methods, and, in many cases, our method is significantly more accurate. We demonstrate our ideas with the most extensive set of multi-dimensional time series classification experiments ever attempted.

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The ability to make predictions about future events is at the heart of much of science; so, it is not surprising that prediction has been a topic of great interest in the data mining community for the last decade. Most of the previous work has attempted to predict the future based on the current value of a stream. However, for many problems the actual values are irrelevant, whereas the shape of the current time series pattern may foretell the future. The handful of research efforts that consider this variant of the problem have met with limited success. In particular, it is now understood that most of these efforts allow the discovery of spurious rules. We believe the reason why rule discovery in real-valued time series has failed thus far is because most efforts have more or less indiscriminately applied the ideas of symbolic stream rule discovery to real-valued rule discovery. In this work, we show why these ideas are not directly suitable for rule discovery in time series. Beyond our novel definitions/representations, which allow for meaningful and extendable specifications of rules, we further show novel algorithms that allow us to quickly discover high quality rules in very large datasets that accurately predict the occurrence of future events.