## Abstract

We present efficient algorithms for segmenting and classifying trajectories based on a movement model parameterised by a single parameter, like the Brownian bridge movement model. Segmentation is the problem of subdividing a trajectory into interior-disjoint parts such that each part is homogeneous in its movement characteristics. We formalise this using the likelihood of the model parameter, and propose a new algorithm for trajectory segmentation based on this. We consider the case where a discrete set of m parameter values is given and present an algorithm to compute an optimal segmentation with respect to an information criterion in O(nm) time for a trajectory with n sampling points. We also present an algorithm that efficiently computes the optimal segmentation if we allow the parameter values to be drawn from a continuous domain. Classification is the problem of assigning trajectories to classes of similar movement characteristics. The set of trajectories might for instance be the subtrajectories resulting from segmenting a trajectory, thus identifying movement phases. We give an algorithm to compute the optimal classification with respect to an information criterion in O(m^{2}+ kmlog m) time for m parameter values and k trajectories, assuming bitonic likelihood functions. We also show that classification is NP-hard if the parameter values are allowed to vary continuously and present an algorithm that solves the problem in polynomial time under mild assumptions on the input.

Original language | English |
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Pages (from-to) | 2422-2452 |

Number of pages | 31 |

Journal | Algorithmica |

Volume | 80 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1 Aug 2018 |

## Keywords

- Classification
- Movement model
- Segmentation
- Trajectory analysis