A Novel Distance Measure and Semantic Segmentation for Time Series Data
At their core, many time series data mining algorithms reduce to reasoning about the shapes of time series subsequences. This requires an effective distance measure, and for last two decades most algorithms use Euclidean Distance or DTW as their core subroutine. We argue that these distance measures are not as robust as the community seems to believe. The undue faith in these measures perhaps derives from an overreliance on the benchmark datasets and self-selection bias. The community is simply reluctant to address more difficult domains, for which current distance measures are ill-suited.
In addition, unsupervised semantic segmentation in the time series domain is a much studied problem due to its potential to detect unexpected regularities and regimes in poorly understood data. However, the current techniques have several shortcomings, which have limited the adoption of time series semantic segmentation beyond academic settings for four primary reasons. First, most methods require setting/learning many parameters and thus may have problems generalizing to novel situations. Second, most methods implicitly assume that all the data is segmentable and have difficulty when that assumption is unwarranted. Thirdly, many algorithms are only defined for the single dimensional case, despite the ubiquity of multi-dimensional data. Finally, most research efforts have been confined to the batch case, but online segmentation is clearly more useful and actionable.
To address these issues, in this dissertation, we introduce a novel distance measure MPdist. we show that our proposed distance measure is much more robust than current distance measures. For example, it can handle data with missing values or spurious regions. Furthermore, it allows us to successfully mine datasets that would defeat any Euclidean or DTW distance-based algorithm. Additionally, we show that our distance measure can be computed so efficiently as to allow analytics on very fast arriving streams.
For semantic segmentation, we also present a multi-dimensional algorithm, which is domain agnostic, has only one, easily-determined parameter, and can handle data streaming at a high rate. In this context, we test the algorithm on the largest and most diverse collection of time series datasets ever considered for this task and demonstrate the algorithm’s superiority over current solutions.