With the emergence of the Internet of Things (IoT), time series streams have become ubiquitous in our daily life. Recording such data is rarely a perfect process, as sensor failures frequently occur, yielding occasional blocks of data that go missing in multiple time series. These missing blocks do not only affect real-time monitoring but also compromise the quality of online data analyses. Effective streaming recovery (imputation) techniques either have a quadratic runtime complexity, which is infeasible for any moderately sized data, or cannot recover more than one time series at a time.
In this paper, we introduce a new online recovery technique to recover multiple time series streams in linear time. Our recovery technique implements a novel incremental version of the Centroid Decomposition technique and reduces its complexity from quadratic to linear. Using this incremental technique, missing blocks are efficiently recovered in a continuous manner based on previous recoveries. We formally prove the correctness of our new incremental computation, which yields an accurate recovery. Our experimental results on real-world time series show that our recovery technique is, on average, 30% more accurate than the state of the art while being vastly more efficient.
Efficient EMD-based Similarity Search via Batch Pruning and Incremental Computation