We define several new models for how to define anomalous regions among enormous sets of trajectories. These are based on spatial scan statistics, and identify a geometric region which captures a subset of trajectories which are significantly different in a measured characteristic from the background population. The model definition depends on how much a geometric region is contributed to by some overlapping trajectory. This contribution can be the full trajectory, proportional to the time spent in the spatial region, or dependent on the flux across the boundary of that spatial region. Our methods are based on and significantly extend a recent two-level sampling approach which provides high accuracy at enormous scales of data. We support these new models and algorithms with extensive experiments on millions of trajectories and also theoretical guarantees.
A few papers have attempted to port scan statistics to trajectories, with goal of finding spatial anomalous regions. Pang al @cite_4 discretized cities into grids and recorded traffic conditions in each cell. They then computed a likelihood ratio test over all sub-grids to detect the most anomalous region. And Liu al @cite_19 partitions a city into regions defined by the road network, and their adjacency defines a graph. Then spatial anomalous links in this graph are scanned over various times to find a time @math region of high traffic. But neither of these approaches directly operate on the trajectories, and fix regions ahead of time which restricts the set and nature of possible anomalies.
@cite_19 @cite_4
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As the development of crowdsourcing technique, acquiring amounts of data in urban cities becomes possible and reliable, which makes it possible to mine useful and significant information from data. Traffic anomaly detection is to find the traffic patterns which are not expected and it can be used to explore traffic problems accurately and efficiently. In this paper, we propose LoTAD to explore anomalous regions with long-term poor traffic situations. Specifically, we process crowdsourced bus data into TS-segments (Temporal and Spatial segments) to model the traffic condition. Later, we explore anomalous TS-segments in each bus line by calculating their AI (Anomaly Index). Then, we combine anomalous TS-segments detected in different lines to mine anomalous regions. The information of anomalous regions provides suggestions for future traffic planning. We conduct experiments with real crowdsourced bus trajectory datasets of October in 2014 and March in 2015 in Hangzhou. We analyze the varieties of the results and explain how they are consistent with the real urban traffic planning or social events happened between the time interval of the two datasets. At last we do a contrast experiment with the most ten congested roads in Hangzhou, which verifies the effectiveness of LoTAD. Finding anomalous regions within spatial data sets is a central task for biosurveillance, homeland security, policy making, and many other important areas. These communities have mainly settled on spatial scan statistics as a rigorous way to discover regions where a measured quantity (e.g., crime) is statistically significant in its difference from a baseline population. However, most common approaches are inefficient and thus, can only be run with very modest data sizes (a few thousand data points) or make assumptions on the geographic distributions of the data. We address these challenges by designing, exploring, and analyzing sample-then-scan algorithms. These algorithms randomly sample data at two scales, one to define regions and the other to approximate the counts in these regions. Our experiments demonstrate that these algorithms are efficient and accurate independent of the size of the original data set, and our analysis explains why this is the case. For the first time, these sample-then-scan algorithms allow spatial scan statistics to run on a million or more data points without making assumptions on the spatial distribution of the data. Moreover, our experiments and analysis give insight into when it is appropriate to trust the various types of spatial anomalies when the data is modeled as a random sample from a larger but unknown data set. We present GraphScan, a novel method for detecting arbitrarily shaped connected clusters in graph or network data. Given a graph structure, data observed at each node, and a score function defining the anomalousness of a set of nodes, GraphScan can efficiently and exactly identify the most anomalous (highest-scoring) connected subgraph. Kulldorff’s spatial scan, which searches over circles consisting of a center location and its k − 1 nearest neighbors, has been extended to include connectivity constraints by FlexScan. However, FlexScan performs an exhaustive search over connected subsets and is computationally infeasible for k > 30. Alternatively, the upper level set (ULS) scan scales well to large graphs but is not guaranteed to find the highest-scoring subset. We demonstrate that GraphScan is able to scale to graphs an order of magnitude larger than FlexScan, while guaranteeing that the highest-scoring subgraph will be identified. We evaluate GraphScan, Kulldorff’s spatial scan (searching over circles)... The detection and localization of anomalous behaviors in crowded scenes is considered, and a joint detector of temporal and spatial anomalies is proposed. The proposed detector is based on a video representation that accounts for both appearance and dynamics, using a set of mixture of dynamic textures models. These models are used to implement 1) a center-surround discriminant saliency detector that produces spatial saliency scores, and 2) a model of normal behavior that is learned from training data and produces temporal saliency scores. Spatial and temporal anomaly maps are then defined at multiple spatial scales, by considering the scores of these operators at progressively larger regions of support. The multiscale scores act as potentials of a conditional random field that guarantees global consistency of the anomaly judgments. A data set of densely crowded pedestrian walkways is introduced and used to evaluate the proposed anomaly detector. Experiments on this and other data sets show that the latter achieves state-of-the-art anomaly detection results.