A Practical Index Structure Supporting Fréchet Proximity Queries among Trajectories

Abstract

We present a scalable approach for range and k nearest neighbor queries under computationally expensive metrics, like the continuous Fréchet distance on trajectory data. Based on clustering for metric indexes, we obtain a dynamic tree structure whose size is linear in the number of trajectories, regardless of the trajectory’s individual sizes or the spatial dimension, which allows one to exploit low “intrinsic dimensionality” of datasets for effective search space pruning. Since the distance computation is expensive, generic metric indexing methods are rendered impractical. We present strategies that (i) improve on known upper and lower bound computations, (ii) build cluster trees without any or very few distance calls, and (iii) search using bounds for metric pruning, interval orderings for reduction, and randomized pivoting for reporting the final results. We analyze the efficiency and effectiveness of our methods with extensive experiments on diverse synthetic and real-world datasets. The results show improvement over state-of-the-art methods for exact queries, and even further speedups are achieved for queries that may return approximate results. Surprisingly, the majority of exact nearest-neighbor queries on real datasets are answered without any distance computations.

Exploring Sub-skeleton Trajectories for Interpretable Recognition of Sign Language

“…CF and DF are metrics and can take advantage of metric indexing [9] which provides very fast query times for k-Nearest Neighbor computations. The CF distance is generally regarded to capture visual similarity more precisely than DF, especially if the sampling rate is very sparse, since it takes the continuity of the shapes into account.…”

“…The testing sets always contain the remainder of the whole data set and the DM methods compute the full number of distance columns. For the metric distance measure CF, we use the k Nearest-Neighbor search structure from [9]. The results in Figure 5 show average wall-clock time per query, overall classification accuracy, and average number of necessary distance computations per query for our 1NN-s (blue) and DM methods (black).…”

On Practical Nearest Sub-Trajectory Queries under the Fréchet Distance

“…ese are (B1) adjusting the decision algorithm of Alt and Godau [1], (B2) adapting the approximate Fréchet distance algorithm of Driemel et al [13], and (B3) using the metric indexing technique from [18].…”

“…Our integrated, third technique combines both and additionally uses simpli cations to accelerate the freespace technique and heuristics [5,18] to accelerate the pruning technique (cf. Section 5.4).…”

“…is includes B3, the recent practical metric index method of [18] that is speci cally designed for trajectory proximity searches, but results in a data structure of quadratic size in the sub-trajectory se ing (cf. Section 6).…”