Stream Monitoring under the Time Warping Distance

The goal of this paper is to monitor numerical streams, and to find subsequences that are similar to a given query sequence, under the DTW (dynamic time warping) distance. Applications include word spotting, sensor pattern matching, and monitoring of bio-medical signals (e.g., EKG, ECG), and monitoring of environmental (seismic and volcanic) signals. DTW is a very popular distance measure, permitting accelerations and decelerations, and it has been studied for finite, stored sequence sets. However, in many applications such as network analysis and sensor monitoring, massive amounts of data arrive continuously and it is infeasible to save all the historical data. We propose SPRING, a novel algorithm that can solve the problem. We provide a theoretical analysis and prove that SPRING does not sacrifice accuracy, while it requires constant space and time per time-tick. These are dramatic improvements over the naive method. Our experiments on real and realistic data illustrate that SPRING does indeed detect the qualifying subsequences correctly and that it can offer dramatic improvements in speed over the naive implementation.