Statistical and Nature-Inspired Modeling of Vehicle Flows by Using Finite Mixtures of Simple Circular Normal Distributions

The representation, visualization, and modeling of traffic data is at the heart of intelligent transportation systems. Different types of traffic data exist, and novel ways of their accurate representation and modeling, which are useful for further analyses, simulations, and optimizations, are sought. In this work, location-specific traffic flows are represented by finite mixtures of circular normal (von Mises) statistical distributions. The parameters of the distributions are learned from empirical data by two variants of the expectation-maximization (EM) algorithm and by a nature-inspired method, differential evolution (DE). A proposed statistical model and a fitting strategy are evaluated on real-world data sets describing traffic flows in New York City. The experimental results show that the EM algorithm is able to find model parameters that correspond to input data and that are better than their analytic estimates, while DE evolves even more accurate models. The models based on circular distributions can be represented by circular plots as a novel type of visually appealing and easily interpretable fingerprints of the underlying traffic flow patterns.