GRAIL: Efficient Time-Series Representation Learning.

The analysis of time series is becoming increasingly prevalent across scientific disciplines and industrial applications. The effectiveness and the scalability of time-series mining techniques critically depend on design choices for three components responsible for (i) representing; (ii) comparing; and (iii) indexing time series. Unfortunately, these components have to date been investigated and developed independently, often resulting in mutually incompatible methods. The lack of a unified approach has hindered progress towards fast and accurate analytics over massive time-series collections. To address this major drawback, we present GRAIL, a generic framework to learn compact time-series representations that preserve the properties of a user-specified comparison function. Given the comparison function, GRAIL (i) extracts landmark time series using clustering; (ii) optimizes necessary parameters; and (iii) exploits approximations for kernel methods to construct representations in linear time and space by expressing each time series as a combination of the landmark time series. We extensively evaluate GRAIL for querying, classification, clustering, sampling, and visualization of time series. For these tasks, methods leveraging GRAIL's representations are significantly faster and at least as accurate as state-of-the-art methods operating over the raw time series. GRAIL shows promise as a new primitive for highly accurate, yet scalable, time-series analysis.