Detecting Commuting Patterns by Clustering Subtrajectories

Abstract

In this paper we consider the problem of detecting commuting patterns in a trajectory. For this we search for similar subtrajectories. To measure spatial similarity we choose the Fréchet distance and the discrete Fréchet distance between subtrajectories, which are invariant under differences in speed. We give several approximation algorithms, and also show that the problem of finding the 'longest' subtrajectory cluster is as hard as MaxClique to compute and approximate.

A GPU Approach to Subtrajectory Clustering Using the Fréchet Distance

“…In the case when at least one of the subtrajectories in a cluster has to start and end at vertices of the trajectory the algorithm requires Oðn 2 'Þ time and Oðn' 2 Þ space, which is also the version we will focus on in this paper. The algorithm in [1] can be modified to return many different outputs depending on the settings, however, in general it reports a set of subtrajectory clusters where each cluster C in the set contains at least s subtrajectories of T , at least one of the subtrajectories has length ' and the Fr echet distance between any two subtrajectories in C is at most 2". Due to this the algorithm is a 2-distance approximation algorithm.…”

“…In most realistic settings the input data can be compressed to 5-10 percent of its original size, thus developing a practical approach for trajectory clustering using the continuous Fr echet distance is a crucial open problem. Note that due to the complexity of the implementation only the algorithm using the discrete Fr echet distance was implemented and tested in [1]. See also [2].…”

“…More formally, following the definition from [1], the input is a moving point object in d-dimensional euclidean space, called an entity, whose location is known at n consecutive time-steps. We assume that an entity moves between two consecutive time steps on a straight line.…”

“…The problem was considered in [1] in which the authors also developed approximation algorithms using both the discrete Fr echet distance and the continuous Fr echet distance. Their algorithms have a running time of Oð'n 2 Þ and Oðn 3 sÁ 2 aðn=sÞ ðlog n logðn=sÞ þ sÞÞ when using the discrete and continuous Fr echet distance (to be defined), respectively.…”

How to Walk Your Dog in the Mountains with No Magic Leash

“…The Fréchet distance and its variants (e.g. dynamic time-warping [28]) have been used as a similarity measure in various applications such as matching of time series in databases [29], comparing melodies in music information retrieval [36], matching coastlines over time [32], as well as in map-matching of vehicle tracking data [5,39], and moving objects analysis [7,8]. See [2,3] for algorithms for computing the Fréchet distance.…”