FRESH: Fréchet Similarity with Hashing
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Massive datasets of curves, such as time series and trajectories, are continuously generated by mobile and sensing devices. A relevant operation on curves is similarity search: given a dataset S of curves, construct a data structure that, for any query curve q, finds the curves in S similar to q. Similarity search is a computational demanding task, in particular when a robust distance function is used, such as the continuous Fréchet distance. In this paper, we propose FRESH, a novel approximate solution to find similar curves under the continuous Fréchet distance. FRESH leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and a subsequent pruning step based on a pipeline of curve simplifications. By relaxing the requirement of exact and deterministic solutions, FRESH reaches high performance and outperforms the state-of-the-art approaches. The experiments indeed show that, with a recall larger than 80 precision 100 baseline given by the best solutions developed for the ACM SIGSPATIAL 2017 challenge on the Fréchet distance. Furthermore, the improvement peaks up to two orders of magnitude, and even more, by relaxing the precision.
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