Trajectory big data have significant applications in many areas, such as traffic management, urban planning and military reconnaissance. Traditional visualization methods, which are represented by contour maps, shading maps and hypsometric maps, are mainly based on the spatiotemporal information of trajectories, which can macroscopically study the spatiotemporal conditions of the entire trajectory set and microscopically analyze the individual movement of each trajectory; such methods are widely used in screen display and flat mapping. With the improvement of trajectory data quality, these data can generally describe information in the spatial and temporal dimensions and involve many other attributes (e.g., speed, orientation, and elevation) with large data amounts and high dimensions. Additionally, these data have relatively complicated internal relationships and regularities, whose analysis could cause many troubles; the traditional approaches can no longer fully meet the requirements of visualizing trajectory data and mining hidden information. Therefore, diverse visualization methods that present the value of massive trajectory information are currently a hot research topic. This paper summarizes the research status of trajectory data-visualization techniques in recent years and extracts common contemporary trajectory data-visualization methods to comprehensively cognize and understand the fundamental characteristics and diverse achievements of trajectory-data visualization.

Modern positioning and sensor technology enable the acquisition of movement positions and attributes on an unprecedented scale. Therefore, a large amount of trajectory data can be used to analyze various movement phenomena. In cartography, a common way to visualize and explore trajectory data is to use the 3D cube (e.g., space-time cube), where trajectories are presented as a tilted 3D polyline. As larger movement datasets become available, this type of display can easily become confusing and illegible. In addition, movement datasets are often unprecedentedly massive, high-dimensional, and complex (e.g., implicit spatial and temporal relations and interactions), making it challenging to explore and analyze the spatiotemporal movement patterns in space. In this paper, we propose 4D time density as a visualization method for identifying and analyzing spatiotemporal movement patterns in large trajectory datasets. The movement range of the objects is regarded as a 3D geographical space, into which the fourth dimension, 4D time density, is incorporated. The 4D time density is derived by modeling the movement path and velocity separately. We present a time density algorithm, and demonstrate it on the simulated trajectory and a real dataset representing the movement data of aircrafts in the Hong Kong International and the Macau International Airports. Finally, we consider wider applications and further developments of time density.

As a frontier research topic in the field of scientific visualization, trajectory data visualization extracts valuable patterns and knowledge from trajectory data for decision support via spatiotemporal trajectory visualization techniques. We propose the concept of multivariate trajectory data and interpret two categories of attributes that are based on geographical space and abstract space. Properly analyzing multivariate trajectory data depends on many factors such as visualization task and data sparsity. Therefore, we generalize rich interactions to explore the evolution of trajectory events and transform the issue into a more intelligibly perceptual task, which derives our discussion regarding advantages and limitations of the analytical methods. This review endeavors to provide a quick and thorough cognition and comprehension with regard to fundamental features and numerous outcomes in visual analytics for trajectory data, seeks to promote comparisons and criticisms about the descriptive framework for multivariate spatiotemporal trajectory data visualization, and aims to encourage the exploration of emerging methods and techniques.

This paper proposes a novel modeling concept, the “public opinion digital twin,” for public opinion analysis. The public opinion digital twin can be regarded as an experimental sandbox for social science. By digitalizing public data acquired from cyberspace into digital models, the modeling enables practical simulation, data analytics, scenario reflection, and decision support in a digital space with fine controllability, so that all possible evolutions of the research target can be analyzed. By simply inputting or filtering variables, any number of future scenarios are simulated, the effect models of each strategy for coping with public opinion are presented, and the optimized solution can be derived from continuous deep learning. If a robust digital twin is established and the required digital replicas are constantly updated, the system can perform risk assessments and trend predictions for social events. In this case, public opinion information can provide intelligent decision support for governments or enterprises and significantly facilitate social loss aversion, which will greatly advance the revolution in production, dissemination, and guidance.

This paper presents an approximation algorithm for word-replacement under a bi-gram language model. Words replacement is an key step in the decoding part of statistical machine translation. However, the word or phrase replacement step is often done at the same time with the target language generating process in machine translation while our algorithm focus on the special replacement model without the target language generating process. We firstly make a reduction from the famous NP-Complete problem Hamiltonian Path Problem to the word-replacement problem. Then we apply the approximation algorithm for Hamiltonian Path on the word-replacement problem, which gives us a good performance in the designed experiment.