Novel Tools and Algorithms for Time Series Analysis
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Novel Tools and Algorithms for Time Series Analysis

  • Author(s): AlaeeJordehi, Sara
  • Advisor(s): Keogh, Eamonn
  • et al.
Creative Commons 'BY' version 4.0 license
Abstract

In recent years, time series motif discovery has emerged as perhaps the most important primitive for many analytical tasks, including clustering, classification, rule discovery, segmentation, and summarization. In parallel, it has long been known that Dynamic Time Warping (DTW) is superior to other similarity measures such as Euclidean Distance under most settings. However, due to the computational complexity of both DTW and motif discovery, virtually no research efforts have been directed at combining these two ideas. The current best mechanisms to address their lethargy appear to be mutually incompatible.In addition, time series classification is an important task in its own right, and it is often a precursor to further downstream analytics. To date, virtually all works in the literature have used either shape-based classification using a distance measure or feature-based classification after finding some suitable features for the domain. It seems to be underappreciated that in many datasets it is the case that some classes are best discriminated with features, while others are best discriminated with shape. Thus, making the shape vs. feature choice will condemn us to poor results, at least for some classes. To address these issues, in this dissertation, we present the first efficient, scalable and exact method to find time series motifs under DTW. Our method automatically performs the best trade-off of time-to-compute versus tightness-of-lower-bounds for a novel hierarchy of lower bounds that we introduce. As we shall show through extensive experiments, our algorithm prunes up to 99.99% of the DTW computations under realistic settings and is up to three to four orders of magnitude faster than the brute force search, and two orders of magnitude faster than the only other competitor algorithm. This allows us to discover DTW motifs in massive datasets for the first time. As we will show, in many domains, DTW-based motifs represent semantically meaningful conserved behavior that would escape our attention using all existing Euclidean distance-based methods. For time series classification, we propose a new model for classifying time series that allows the use of both shape and feature-based measures, when warranted. Our algorithm automatically decides which approach is best for which class, and at query time chooses which classifier to trust the most. We evaluate our idea on real world datasets and demonstrate that our ideas produce statistically significant improvement in classification accuracy.

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