Scientists study trajectory data to understand trends in movement patterns, such as human mobility for traffic analysis and urban planning. There is a pressing need for scalable and efficient techniques for analyzing this data and discovering the underlying patterns. In this paper, we introduce a novel technique which we call vector-field @math -means. The central idea of our approach is to use vector fields to induce a similarity notion between trajectories. Other clustering algorithms seek a representative trajectory that best describes each cluster, much like @math -means identifies a representative "center" for each cluster. Vector-field @math -means, on the other hand, recognizes that in all but the simplest examples, no single trajectory adequately describes a cluster. Our approach is based on the premise that movement trends in trajectory data can be modeled as flows within multiple vector fields, and the vector field itself is what defines each of the clusters. We also show how vector-field @math -means connects techniques for scalar field design on meshes and @math -means clustering. We present an algorithm that finds a locally optimal clustering of trajectories into vector fields, and demonstrate how vector-field @math -means can be used to mine patterns from trajectory data. We present experimental evidence of its effectiveness and efficiency using several datasets, including historical hurricane data, GPS tracks of people and vehicles, and anonymous call records from a large phone company. We compare our results to previous trajectory clustering techniques, and find that our algorithm performs faster in practice than the current state-of-the-art in trajectory clustering, in some examples by a large margin.
Like Rinzivillo et al., our overall approach falls within the broader category of visual and exploratory movement analysis , which exploits humans' ability to visually detect patterns, and then steer the visualization and analysis to those regions of greatest interest. is it? Andrienko and Andrienko @cite_25 @cite_49 @cite_38 have lead the field in this area. Their work has focused on human-in-the-loop analysis systems, but has also included more general aggregation and visualization of movement data @cite_19 , and most recently the identification of important locations and events by analyzing movement data @cite_21 @cite_1 .
@cite_38 @cite_21 @cite_1 @cite_19 @cite_49 @cite_25
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Nowadays, human movement in urban spaces can be traced digitally in many cases. It can be observed that movement patterns are not constant, but vary across time and space. In this work, we characterize such spatio-temporal patterns with an innovative combination of two separate approaches that have been utilized for studying human mobility in the past. First, by using non-negative tensor factorization (NTF), we are able to cluster human behavior based on spatio-temporal dimensions. Second, for characterizing these clusters, we propose to use HypTrails, a Bayesian approach for expressing and comparing hypotheses about human trails. To formalize hypotheses, we utilize publicly available Web data (i.e., Foursquare and census data). By studying taxi data in Manhattan, we can discover and characterize human mobility patterns that cannot be identified in a collective analysis. As one example, we find a group of taxi rides that end at locations with a high number of party venues on weekend nights. Our findings argue for a more fine-grained analysis of human mobility in order to make informed decisions for e.g., enhancing urban structures, tailored traffic control and location-based recommender systems. With widespread availability of low cost GPS devices, it is becoming possible to record data about the movement of people and objects at a large scale. While these data hide important knowledge for the optimization of location and mobility oriented infrastructures and services, by themselves they lack the necessary semantic embedding which would make fully automatic algorithmic analysis possible. At the same time, making the semantic link is easy for humans who however cannot deal well with massive amounts of data. In this paper, we argue that by using the right visual analytics tools for the analysis of massive collections of movement data, it is possible to effectively support human analysts in understanding movement behaviors and mobility patterns. We suggest a framework for analysis combining interactive visual displays, which are essential for supporting human perception, cognition, and reasoning, with database operations and computational methods, which are necessary for handling large amounts of data. We demonstrate the synergistic use of these techniques in case studies of two real datasets. We propose a visual analytics procedure for analyzing movement data, i.e., recorded tracks of moving objects. It is oriented to a class of problems where it is required to determine significant places on the basis of certain types of events occurring repeatedly in movement data. The procedure consists of four major steps: (1) event extraction from trajectories; (2) event clustering and extraction of relevant places; (3) spatio-temporal aggregation of events or trajectories; (4) analysis of the aggregated data. All steps are scalable with respect to the amount of the data under analysis. We demonstrate the use of the procedure by example of two real-world problems requiring analysis at different spatial scales. We propose a novel approach to understanding activities from their partial observations monitored through multiple non-overlapping cameras separated by unknown time gaps. In our approach, each camera view is first decomposed automatically into regions based on the correlation of object dynamics across different spatial locations in all camera views. A new Cross Canonical Correlation Analysis (xCCA) is then formulated to discover and quantify the time delayed correlations of regional activities observed within and across multiple camera views in a single common reference space. We show that learning the time delayed activity correlations offers important contextual information for (i) spatial and temporal topology inference of a camera network; (ii) robust person re-identification and (iii) global activity interpretation and video temporal segmentation. Crucially, in contrast to conventional methods, our approach does not rely on either intra-camera or inter-camera object tracking; it thus can be applied to low-quality surveillance videos featured with severe inter-object occlusions. The effectiveness and robustness of our approach are demonstrated through experiments on 330 hours of videos captured from 17 cameras installed at two busy underground stations with complex and diverse scenes.