Discovering All-chain Set with Direction and Graduality Characteristics over Streaming Time Series

Since its introduction over five years ago, time series chain has become a fundamental tool for time series analytics, finding diverse uses in dozens of domains. Recent work has generalized the definition of time series chain, and introduced a novel definition of time series chain with directionality and graduality characteristics (TSC-DG) which can significantly enhance both robustness and usability of the original time series chain. However, previous studies on TSCDG process fixed-length time series. In this work, we focus on the issue of all-chain set with direction and graduality characteristics (all-TSCS-DG) mining over streaming time series for the first time, where all-TSCS-DG is the core of current TSCDG researches. We propose an improved Naive algorithm (IN) to solve this problem. Compared to the Naive, the IN guarantees the same space costs and results firstly, secondly is the IN takes two additional optimal strategies to further improve the time efficiency. The basic ideas of these two strategies are both incremental computing. The first one can make the IN update the IB structure at each time-tick incrementally, where the IB is an important data structure that is used to obtain the all-TSCS-DG. The second one makes the IN obtain mining results at current time-tick based on the ones at the last time-tick incrementally. Extensive experiments on real dataset demonstrate the efficiency and effectiveness of the IN.