The explosion in the availability of GPS-enabled devices has resulted in an abundance of trajectory data. In reality, however, majority of these trajectories are collected at a low sampling rate and only provide partial observations on their actually traversed routes. Consequently, they are mired with uncertainty. In this paper, we develop a technique called Infer Tra to infer uncertain trajectories from network-constrained partial observations. Rather than predicting the most likely route, the inferred uncertain trajectory takes the form of an edge-weighted graph and summarizes all probable routes in a holistic manner. For trajectory inference, Infer Tra employs Gibbs sampling by learning a Network Mobility Model (NMM) from a database of historical trajectories. Extensive experiments on real trajectory databases show that the graph-based approach of Infer Tra is up to 50 more accurate, 20 times faster, and immensely more versatile than state-of-the-art techniques.
More recently, a technique @cite_6 was designed to study the trajectory inference problem in a setting where trajectories are not constrained by a network. Due to the focus on network-free trajectories, @cite_6 is not applicable to our problem.
@cite_6
2004284939 2031397756 2952024198 2141596757
In order to track moving objects in long range against occlusion, interruption, and background clutter, this paper proposes a unified approach for global trajectory analysis. Instead of the traditional frame-by-frame tracking, our method recovers target trajectories based on a short sequence of video frames, e.g., 15 frames. We initially calculate a foreground map at each frame obtained from a state-of-the-art background model. An attribute graph is then extracted from the foreground map, where the graph vertices are image primitives represented by the composite features. With this graph representation, we pose trajectory analysis as a joint task of spatial graph partitioning and temporal graph matching. The task can be formulated by maximizing a posteriori under the Bayesian framework, in which we integrate the spatio-temporal contexts and the appearance models. The probabilistic inference is achieved by a data-driven Markov chain Monte Carlo algorithm. Given a period of observed frames, the algorithm simulates an ergodic and aperiodic Markov chain, and it visits a sequence of solution states in the joint space of spatial graph partitioning and temporal graph matching. In the experiments, our method is tested on several challenging videos from the public datasets of visual surveillance, and it outperforms the state-of-the-art methods. This paper examines techniques for finding falsifying trajectories of hybrid systems using an approach that we call trajectory splicing. Many formal verification techniques for hybrid systems, including flowpipe construction, can identify plausible abstract counterexamples for property violations. However, there is often a gap between the reported abstract counterexamples and the concrete system trajectories. Our approach starts with a candidate sequence of disconnected trajectory segments, each segment lying inside a discrete mode. However, such disconnected segments do not form concrete violations due to the gaps that exist between the ending state of one segment and the starting state of the subsequent segment. Therefore, trajectory splicing uses local optimization to minimize the gap between these segments, effectively splicing them together to form a concrete trajectory. We demonstrate the use of our approach for falsifying safety properties of hybrid systems using standard optimization techniques. As such, our approach is not restricted to linear systems. We compare our approach with other falsification approaches including uniform random sampling and a robustness guided falsification approach used in the tool S-Taliro. Our preliminary evaluation clearly shows the potential of our approach to search for candidate trajectory segments and use them to find concrete property violations. We present an interpretable framework for path prediction that learns scene-specific causations behind agents' behaviors. We exploit two sources of information: the past motion trajectory of the agent of interest and a wide top-down view of the scene. We propose a Clairvoyant Attentive Recurrent Network (CAR-Net) that learns "where to look" in the large image when solving the path prediction task. While previous works on trajectory prediction are constrained to either use semantic information or hand-crafted regions centered around the agent, our method has the capacity to select any region within the image, e.g., a far-away curve when predicting the change of speed of vehicles. To study our goal towards learning observable causality behind agents' behaviors, we have built a new dataset made of top view images of hundreds of scenes (e.g., F1 racing circuits) where the vehicles are governed by known specific regions within the images (e.g., upcoming curves). Our algorithm successfully selects these regions, learns navigation patterns that generalize to unseen maps, outperforms previous works in terms of prediction accuracy on publicly available datasets, and provides human-interpretable static scene-specific dependencies. The advances in location-acquisition technologies have led to a myriad of spatial trajectories. These trajectories are usually generated at a low or an irregular frequency due to applications' characteristics or energy saving, leaving the routes between two consecutive points of a single trajectory uncertain (called an uncertain trajectory). In this paper, we present a Route Inference framework based on Collective Knowledge (abbreviated as RICK) to construct the popular routes from uncertain trajectories. Explicitly, given a location sequence and a time span, the RICK is able to construct the top-k routes which sequentially pass through the locations within the specified time span, by aggregating such uncertain trajectories in a mutual reinforcement way (i.e., uncertain + uncertain → certain). Our work can benefit trip planning, traffic management, and animal movement studies. The RICK comprises two components: routable graph construction and route inference. First, we explore the spatial and temporal characteristics of uncertain trajectories and construct a routable graph by collaborative learning among the uncertain trajectories. Second, in light of the routable graph, we propose a routing algorithm to construct the top-k routes according to a user-specified query. We have conducted extensive experiments on two real datasets, consisting of Foursquare check-in datasets and taxi trajectories. The results show that RICK is both effective and efficient.