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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Spatio-temporal and geo-referenced datasets are growing rapidly, with the rapid development of some technology, such as GPS, satellite systems. At present, many scholars are very interested in the clustering of the trajectory. Existing trajectory clustering algorithms group similar trajectories as a whole and can't distinguish the direction of trajectory. Our key finding is that clustering trajectories as a whole could miss common sub-trajectories and trajectory has direction information. In many applications, discovering common sub-trajectories is very useful. In this paper, we present a trajectory clustering algorithm CTHD (clustering of trajectory based on hausdorff distance). In the CTHD, the trajectory is firstly described by a sequence of flow vectors and partitioned into a set of sub-trajectory. Next the similarity between trajectories is measured by their respective Hausdorff distances. Finally, the trajectories are clustered by the DBSCAN clustering algorithm. The proposed algorithm is different from other schemes using Hausdorff distance that the flow vectors include the position and direction. So it can distinguish the trajectories in different directions. The experimental result shows the phenomenon. While crowds of various subjects may offer applicationspecific cues to detect individuals, we demonstrate that for the general case, motion itself contains more information than previously exploited. This paper describes an unsupervised data driven Bayesian clustering algorithm which has detection of individual entities as its primary goal. We track simple image features and probabilistically group them into clusters representing independently moving entities. The numbers of clusters and the grouping of constituent features are determined without supervised learning or any subject-specific model. The new approach is instead, that space-time proximity and trajectory coherence through image space are used as the only probabilistic criteria for clustering. An important contribution of this work is how these criteria are used to perform a one-shot data association without iterating through combinatorial hypotheses of cluster assignments. Our proposed general detection algorithm can be augmented with subject-specific filtering, but is shown to already be effective at detecting individual entities in crowds of people, insects, and animals. This paper and the associated video examine the implementation and experiments of our motion clustering framework. In this paper, we propose a trajectory clustering algorithm suited for video surveillance systems. Trajectories are clustered on-line, as the data are collected, and clusters are organized in a tree-like structure that, augmented with probability information, can be used to perform behaviour analysis, since it allows the identification of anomalous events. When analyzing multidimensional, quantitative data, the comparison of two or more groups of dimensions is a common task. Typical sources of such data are experiments in biology, physics or engineering, which are conducted in different configurations and use replicates to ensure statistically significant results. One common way to analyze this data is to filter it using statistical methods and then run clustering algorithms to group similar values. The clustering results can be visualized using heat maps, which show differences between groups as changes in color. However, in cases where groups of dimensions have an a priori meaning, it is not desirable to cluster all dimensions combined, since a clustering algorithm can fragment continuous blocks of records. Furthermore, identifying relevant elements in heat maps becomes more difficult as the number of dimensions increases. To aid in such situations, we have developed Matchmaker, a visualization technique that allows researchers to arbitrarily arrange and compare multiple groups of dimensions at the same time. We create separate groups of dimensions which can be clustered individually, and place them in an arrangement of heat maps reminiscent of parallel coordinates. To identify relations, we render bundled curves and ribbons between related records in different groups. We then allow interactive drill-downs using enlarged detail views of the data, which enable in-depth comparisons of clusters between groups. To reduce visual clutter, we minimize crossings between the views. This paper concludes with two case studies. The first demonstrates the value of our technique for the comparison of clustering algorithms. In the second, biologists use our system to investigate why certain strains of mice develop liver disease while others remain healthy, informally showing the efficacy of our system when analyzing multidimensional data containing distinct groups of dimensions.