Fast Summarization of Long Time Series with Graphics Processor

Summarization of a long time series often occurs in analytical applications related to decision-making, modeling, planning, and so on. Informally, summarization aims at discovering a small-sized set of typical patterns (subsequences) to briefly represent the long time series. Apparent approaches to summarization like motifs, shapelets, cluster centroids, and so on, either require training data or do not provide an analyst with information regarding the fraction of the time series that a typical subsequence found corresponds to. Recently introduced, the time series snippet concept overcomes the above-mentioned limitations. A snippet is a subsequence that is similar to many other subsequences of the time series with respect to a specially defined similarity measure based on the Euclidean distance. However, the original Snippet-Finder algorithm has cubic time complexity concerning the lengths of the time series and the snippet. In this article, we propose the PSF (Parallel Snippet-Finder) algorithm that accelerates the original snippet discovery schema with GPU and ensures acceptable performance over very long time series. As opposed to the original algorithm, PSF splits the calculation of the similarity of all the time series subsequences to a snippet into several steps, each of which is performed in parallel. Experimental evaluation over real-world time series shows that PSF outruns both the original algorithm and a straightforward parallelization.