Similarity Search Over Time-Series Data Using Wavelets

We consider the use of wavelet transformations as a dimensionality reduction technique to permit efficient similarity search over high-dimensional time-series data. While numerous transformations have been proposed and studied, the only wavelet that has been shown to be effective for this application is the Haar wavelet. In this work, we observe that a large class of wavelet transformations (not only orthonormal wavelets but also bi-orthonormal wavelets) can be used to support similarity search. This class includes the most popular and most effective wavelets being used in image compression. We present a detailed performance study of the effects of using different wavelets on the performance of similarity search for time-series data. We include several wavelets that outperform both the Haar wavelet and the best known non-wavelet transformations for this application. To ensure our results are usable by an application engineer, we also show how to configure an indexing strategy for the best performing transformations. Finally, we identify classes of data that can be indexed efficiently using these wavelet transformations.