A fast algorithm for complex discord searches in time series: HOT SAX Time

Time series analysis is quickly proceeding towards long and complex tasks. In recent years, fast approximate algorithms for discord search have been proposed in order to compensate for the increasing size of the time series. It is more interesting, however, to find quick exact solutions. In this research, we improved HOT SAX (Heuristically Ordered Time series using Symbolic Aggregate ApproXimation) by exploiting two main ideas: the warm-up process, and the similarity between sequences close in time. These improvements can reduce the size of the discord search space by orders of magnitude when compared with HOT SAX. The resulting algorithm, called HOT SAX Time (HST), has been validated with real and synthetic time series, and successfully compared with HOT SAX, RRA (Rare Rule Anomaly), SCAMP (SCAlable Matrix Profile), and DADD (Disk Aware Discord Discovery). The complexity of a discord search has been evaluated with a new indicator, the cost per sequence (cps), which allows one to compare searches on time series of different lengths. Numerical evidence suggests that two conditions are involved in determining the complexity of a discord search in a non-trivial way: the length of the discords, and the noise/signal ratio. This is the first exact discord search algorithm that has been demonstrated being more than 100 times faster than HOT SAX.