This work proposes the use of Information Theory for the characterization of vehicles behavior through their velocities. Three public data sets were used: (i) Mobile Century data set collected on Highway I-880, near Union City, California; (ii) Borlange GPS data set collected in the Swedish city of Borlange; and (iii) Beijing taxicabs data set collected in Beijing, China, where each vehicle speed is stored as a time series. The Bandt-Pompe methodology combined with the Complexity-Entropy plane were used to identify different regimes and behaviors. The global velocity is compatible with a correlated noise with f − k Power Spectrum with k ≥ 0. With this we identify traffic behaviors as, for instance, random velocities (k ≃ 0) when there is congestion, and more correlated velocities (k ≃ 3) in the presence of free traffic flow. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015
@cite_35 characterized time series of vehicle velocities using Complex Networks. They transformed the time series into a new series based on the reconstruction of the phase space. Then, complex networks of traffic flow were built and analyzed considering the degree distribution, density, and clustering coefficient. The results detected that the networks present communities structures, i.e., the nodes of the networks are grouped so that each group is highly connected. The data set used was collected in the city of Harbin, China, during one complete day with sampling at 2 , resulting in @math samples.
@cite_35
2058532765 40609341 2001667451 2009664208
A complex network is a powerful tool to research complex systems, traffic flow being one of the most complex systems. In this paper, we use complex network theory to study traffic time series, which provide a new insight into traffic flow analysis. Firstly, the phase space, which describes the evolution of the behavior of a nonlinear system, is reconstructed using the delay embedding theorem. Secondly, in order to convert the new time series into a complex network, the critical threshold is estimated by the characteristics of a complex network, which include degree distribution, cumulative degree distribution, and density and clustering coefficients. We find that the degree distribution of associated complex network can be fitted with a Gaussian function, and the cumulative degree distribution can be fitted with an exponential function. Density and clustering coefficients are then researched to reflect the change of connections between nodes in complex network, and the results are in accordance with the observation of the plot of an adjacent matrix. Consequently, based on complex network analysis, the proper range of the critical threshold is determined. Finally, to mine the nodes with the closest relations in a complex network, the modularity is calculated with the increase of critical threshold and the community structure is detected according to the optimal modularity. The work in our paper provides a new way to understand the dynamics of traffic time series. The traffic networks reflect the pulse and structure of a city and shows some dynamic characteristic. Previous research in mining structure from networks mostly focus on static networks and fail to exploit the temporal patterns. In this paper, we aim to solve the problem of discovering the urban spatio-temporal structure from time-evolving traffic networks. We model the time-evolving traffic networks into a 3-order tensor, each element of which indicates the volume of traffic from i-th origin area to j-th destination area in k-th time domain. Considering traffic data and urban contextual knowledge together, we propose a regularized Non-negative Tucker Decomposition (rNTD) method, which discovers the spatial clusters, temporal patterns and relations among them simultaneously. Abundant experiments are conducted in a large dataset collected from Beijing. Results show that our method outperforms the baseline method. Determining interrelatedness structure of various entities from multiple time series data is of significant interest to many areas. Knowledge of such a structure can aid in identifying cause and effect relationships, clustering of similar entities, identification of representative elements and model reduction. The majority of existing results are based on correlation based indices which effectively assume a static relationship between the time series data and are not suitable for detecting interrelatedness when the time series are dynamically related or when the time series involve loops. In this paper, a methodology for identifying the interrelatedness structure of dynamically related time series data is presented that also allows for the presence of loops in the connectivity structure. A linear dynamic graph model is presented where it is assumed that each time series data is the sum of an independent stochastic noise source and a dynamically weighted sum of other time series data. A link is assumed to be present between two time series if the weight of a time series, which is a linear time-invariant filter, is nonzero in the formation of the other. Reconstruction of the link connectivity structure under various scenarios is considered. It is shown that when the linear dynamic graph is allowed to admit non-causal weights, then the links structure can be recovered with the possibility of identifying spurious connections. However, it is shown that the spurious links remain local, where, a spurious link is restricted to be within one hop of a true link. Furthermore, strategies for exact reconstruction of the link structure when the weights are restricted to be causal are developed. The main tools for determining the network topology are based on variations of Wiener filtering. A significant insight provided by the article is that, in the class of network models considered in the paper, the Wiener filter estimating a stochastic process based on other processes remains local in the sense that the Wiener filter utilizes only measurements local to the node being estimated. Networks are present in many fields such as finance, sociology, and transportation. Often these networks are dynamic: they have a structural as well as a temporal aspect. In addition to relations occurring over time, node information is frequently present such as hierarchical structure or time-series data. We present a technique that extends the Massive Sequence View ( msv) for the analysis of temporal and structural aspects of dynamic networks. Using features in the data as well as Gestalt principles in the visualization such as closure, proximity, and similarity, we developed node reordering strategies for the msv to make these features stand out that optionally take the hierarchical node structure into account. This enables users to find temporal properties such as trends, counter trends, periodicity, temporal shifts, and anomalies in the network as well as structural properties such as communities and stars. We introduce the circular msv that further reduces visual clutter. In addition, the (circular) msv is extended to also convey time-series data associated with the nodes. This enables users to analyze complex correlations between edge occurrence and node attribute changes. We show the effectiveness of the reordering methods on both synthetic and a rich real-world dynamic network data set.