Efficiently Finding Arbitrarily Scaled Patterns in Massive Time Series Databases

The problem of efficiently finding patterns in massive time series databases has attracted great interest, and, at least for the Euclidean distance measure, may now be regarded as a solved problem. However in recent years there has been an increasing awareness that Euclidean distance is inappropriate for many real world applications. The limitations of Euclidean distance stems from the fact that it is very sensitive to distortions in the time axis. A partial solution to this problem, Dynamic Time Warping (DTW), aligns the time axis before calculating the Euclidean distance. However, DTW can only address the problem of local scaling. As we demonstrate in this work, uniform scaling may be just as important in many domains, including applications as diverse as bioinformatics, space telemetry monitoring and motion editing for computer animation. In this work, we demonstrate a novel technique to speed up similarity search under uniform scaling. As we will demonstrate, our technique is simple and intuitive, and can achieve a speedup of 2 to 3 orders of magnitude under realistic settings.