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.
Vector fields have been widely used in scientific visualization and even by some researchers doing trajectory clustering analysis to show speed and direction of animal movements @cite_30 and wind @cite_32 . In these cases, they have only been used to visualize the results, rather than as an integral part of the underlying clustering technique.
@cite_30 @cite_32
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Abstract This work presents an exploratory data analysis of the trajectories of deer and elk moving about in the Starkey Experimental Forest and Range in eastern Oregon. The animals’ movements may be affected by habitat variables and the behavior of the other animals. In the work of this paper a stochastic differential equation-based model is developed in successive stages. Equations of motion are set down motivated by corresponding equations of physics. Functional parameters appearing in the equations are estimated nonparametrically and plots of vector fields of animal movements are prepared. Residuals are used to look for interactions amongst the movements of the animals. There are exploratory analyses of various sorts. Statistical inferences are based on Fourier transforms of the data, which are unequally spaced. The sections of the paper start with motivating quotes and aphorisms from the writings of John W. Tukey. Abstract A new probabilistic clustering method, based on a regression mixture model, is used to describe tropical cyclone (TC) propagation in the western North Pacific (WNP). Seven clusters were obtained and described in Part I of this two-part study. In Part II, the present paper, the large-scale patterns of atmospheric circulation and sea surface temperature associated with each of the clusters are investigated, as well as associations with the phase of the El Nino–Southern Oscillation (ENSO). Composite wind field maps over the WNP provide a physically consistent picture of each TC type, and of its seasonality. Anomalous vorticity and outgoing longwave radiation indicate changes in the monsoon trough associated with different types of TC genesis and trajectory. The steering winds at 500 hPa are more zonal in the straight-moving clusters, with larger meridional components in the recurving ones. Higher values of vertical wind shear in the midlatitudes also accompany the straight-moving tracks, compared to...