Finding long and similar parts of trajectories

A natural time-dependent similarity measure for two trajectories is their average distance at corresponding times. We give algorithms for computing the most similar subtrajectories under this measure, assuming the two trajectories are given as two polygonal, possibly self-intersecting lines. When a minimum duration is specified for the subtrajectories, and they must start at exactly corresponding times in the input trajectories, we give a linear-time algorithm for computing the starting time and duration of the most similar subtrajectories. The algorithm is based on a result of independent interest: We present a linear-time algorithm to find, for a piece-wise monotone function, an interval of at least a given length that has minimum average value. When the two subtrajectories can start at different times in the two input trajectories, it appears difficult to give an exact algorithm for the most similar subtrajectories problem, even if the duration of the desired two subtrajectories is fixed to some length. We show that the problem can be solved approximately, and with a performance guarantee. More precisely, we present (1 + e)-approximation algorithms for computing the most similar subtrajectories of two input trajectories for the case where the duration is specified, and also for the case where only a minimum on the duration is specified

Corridor Detection from Large GPS Trajectories Datasets

Given the widespread use of mobile devices that track their geographical location, it has become increasingly easy to acquire information related to users' trips in real time. This availability has triggered several studies based on user's position, such as the analysis of flows of people in cities, and also new applications, such as route recommendation systems. Given a dataset of geographical trajectories in an urbanmetropolitan area,we propose a algorithmto detect corridors. Corridors can be defined as geographical paths, with a minimum length, that are commonly traversed by a minimum number of different users. We propose an efficient strategy based on the Apriori algorithm to extract frequent trajectory patterns from the geo-spatial dataset. By discretizing the data and adapting the roles of itemsets and baskets of this algorithm to our context, we find the longest corridors formed by cells shared by a minimum number of trajectories. After that, we refine the results obtained with a subsequent filtering step, by using a Radius Neighbors Graph. To illustrate the algorithm, the GeoLife dataset is analyzed by following the proposed method. Our approach is relevant for transportation analytics because it is the base to detect lacking lines in public transportation systems and also to recommend to private users which route to take when moving from one part of the city to another on the basis of behavior of the users who provided their logs

Computing a Subtrajectory Cluster from c-packed Trajectories

We present a near-linear time approximation algorithm for the subtrajectory cluster problem of $c$-packed trajectories. The problem involves finding $m$ subtrajectories within a given trajectory $T$ such that their Fr\'echet distances are at most $(1 + \varepsilon)d$, and at least one subtrajectory must be of length~$l$ or longer. A trajectory $T$ is $c$-packed if the intersection of $T$ and any ball $B$ with radius $r$ is at most $c \cdot r$ in length. Previous results by Gudmundsson and Wong \cite{GudmundssonWong2022Cubicupperlower} established an $\Omega(n^3)$ lower bound unless the Strong Exponential Time Hypothesis fails, and they presented an $O(n^3 \log^2 n)$ time algorithm. We circumvent this conditional lower bound by studying subtrajectory cluster on $c$-packed trajectories, resulting in an algorithm with an $O((c^2 n/\varepsilon^2)\log(c/\varepsilon)\log(n/\varepsilon))$ time complexity

Clustering Trajectories for Map Construction

We propose a new approach for constructing the underlying map from trajectory data. Our algorithm is based on the idea that road segments can be identified as stable subtrajectory clusters in the data. For this, we consider how subtrajectory clusters evolve for varying distance values, and choose stable values for these. In doing so we avoid a global proximity parameter. Within trajectory clusters, we choose representatives, which are combined to form the map. We experimentally evaluate our algorithm on vehicle and hiking tracking data. These experiments demonstrate that our approach can naturally separate roads that run close to each other and can deal with outliers in the data, two issues that are notoriously difficult in road network reconstruction

Knowledge discovery from trajectories

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial TechnologiesAs a newly proliferating study area, knowledge discovery from trajectories has attracted more and more researchers from different background. However, there is, until now, no theoretical framework for researchers gaining a systematic view of the researches going on. The complexity of spatial and temporal information along with their combination is producing numerous spatio-temporal patterns. In addition, it is very probable that a pattern may have different definition and mining methodology for researchers from different background, such as Geographic Information Science, Data Mining, Database, and Computational Geometry. How to systematically define these patterns, so that the whole community can make better use of previous research? This paper is trying to tackle with this challenge by three steps. First, the input trajectory data is classified; second, taxonomy of spatio-temporal patterns is developed from data mining point of view; lastly, the spatio-temporal patterns appeared on the previous publications are discussed and put into the theoretical framework. In this way, researchers can easily find needed methodology to mining specific pattern in this framework; also the algorithms needing to be developed can be identified for further research. Under the guidance of this framework, an application to a real data set from Starkey Project is performed. Two questions are answers by applying data mining algorithms. First is where the elks would like to stay in the whole range, and the second is whether there are corridors among these regions of interest

Distributed Mining of Popular Paths in Road Networks

International audienceWe consider the problem of finding large scale mobility patterns. A common challenge in mobility tracking systems is that large quantity of data is spread out spatially and temporally across many tracking sensors. We thus devise a spatial sampling and information exchange protocol that provides probabilistic guarantees on detecting prominent patterns. For this purpose, we define a general notion of significant popular paths that can capture many different types of motion. We design a summary sketch for the data at each tracking node, which can be updated efficiently, and then aggregated across devices to reconstruct the prominent paths in the global data. The algorithm is scalable, even with large number of mobile targets. It uses a hierarchic query system that automatically prioritizes important trajectories – those that are long and popular. We show further that this scheme can in fact give good results by sampling relatively few sensors and targets, and works for streaming spatial data. We prove differential privacy guarantees for the randomized algorithm. Extensive experiments on real GPS data show that the method is efficient and accurate, and is useful in predicting motion of travelers even with small samples