Elastic Translation Invariant Matching of Trajectories

Abstract

Abstract.We investigate techniques for analysis and retrieval of object trajectories. We assume that a trajectory is a sequence of two or three dimensional points. Trajectory datasets are very common in environmental applications, mobility experiments, video surveillance and are especially important for the discovery of certain biological patterns. Such kind of data usually contain a great amount of noise, that makes all previously used metrics fail. Therefore, here we formalize non-metric similarity functions based on the Longest Common Subsequence (LCSS), which are very robust to noise and furthermore provide an intuitive notion of similarity between trajectories by giving more weight to the similar portions of the sequences. Stretching of sequences in time is allowed, as well as global translating of the sequences in space. Efficient approximate algorithms that compute these similarity measures are also provided. We compare these new methods to the widely used Euclidean and Dynamic Time Warping distance functions (for real and synthetic data) and show the superiority of our approach, especially under the strong presence of noise. We prove a weaker version of the triangle inequality and employ it in an indexing structure to answer nearest neighbor queries. Finally, we present experimental results that validate the accuracy and efficiency of our approach.

Dynamics-aware similarity of moving objects trajectories

“…Firstly, we plan to adapt our results to the, so called, decision problem, which is, given two trajectories, and a constant ε does there exist transformation that will yield a similarity distance ≤ ε? An important issue is the actual similarity-based query processing for massive trajectories' datasets, which ultimately demands an efficient indexing structures [28,29]. Another avenue that we are planning to pursue is exploring the map-available data when the objects are constrained to move on road networks [18] and see whether some pre-processing can be done that will speed up the calculations of the similarity distances among trajectories, especially for real-time tracking data [30].…”

“…Recent efforts from the MOD and GIS communities have targeted the problems of similarity of spatial and spatiotemporal mobility patterns [9,20,14,28,29]. In particular, [14] proposed a Finite State Automaton based algorithm which, given a zone-based partition of the spatial domain, reduces the problems of routes and trajectories matching to the problem of recognizing regular expressions.…”

“…Although the works have addressed larger categories of queries than we do, e.g., subsections of trajectories matching whereas we consider at most a containment of a shorter-trip into the longer-trip trajectory, our work uses a more intuitive distance-measure and does not require a discretization of the spatial dimension. More recent extensions [28,29] proposed similarity measures based on the Longest Common Subsequence (LCSS) and addressed the problem of indexing large datasets for the purpose of the efficient evaluation of the similarity-based spatio-temporal queries. We have not addressed the problem of indexing in this work, however, we proposed a different distance function and we took into consideration the rotation in the spatial dimension.…”

Textual Approximation Methods for Time Series Classification: TAX and l-TAX

“…Other textual approximation methods including those in [30]- [34] are based on application-domain dependent symbolic representation of a time series from significant knowledge on the time series features, which are quite unlike our method as our goal is to build a domain independent model. Non-metric similarity functions based on the Longest Common Subsequence are presented in [27], where the authors proposed a method that performs significantly well for noisy data. For noisy data exact similarity computation is inefficient.…”

Probabilistic Framework for Automated Analysis of Exposure to Road Collisions

“…To apply the probabilistic safety framework presented in this paper, it is necessary to be able to predict road users' future positions. Motion patterns, represented by actual prototype trajectories without any special preprocessing, are learnt incrementally using the Longest Common Sub-sequence Similarity (LCSS) (26). The description of the motion pattern learning algorithm is beyond the scope of this paper and is described in detail in (27).…”