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 by exploiting two main ideas: the warm-up process, and the similarity between sequences close in time. The resulting algorithm, called HOT SAX Time (HST), has been validated with real and synthetic time series, and successfully compared with HOT SAX, RRA, SCAMP, and DADD. 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. In the case of complex searches, HST can be more than 100 times faster than HOT SAX, thus being at the forefront of the exact discord search.