Wavelets on graphs with application to transportation networks

The technological advancements in Intelligent Transport Systems have made it possible to acquire large amounts of traffic data in real-time. As a result, various data-mining techniques are being used to extract useful traffic patterns. The research presented in this article focuses on the detection of disruptive traffic events such as congestion. In most transportation studies, traffic parameters are typically modeled as time series. However, these techniques fail to incorporate the spatial dependencies between different traffic variables. In this work, the traffic quantities such as speeds are considered as the signals defined at the vertices of a network line graph. Furthermore, the graph wavelet operators are applied to the spatial signals to generate the wavelet coefficients at different wavelet scales. By analyzing these wavelet coefficients, useful information such as origin, propagation, and the span of traffic congestion are inferred. For analysis, we consider two major expressways in Singapore. The analysis shows that the abrupt changes in the speed can be captured by using the wavelet coefficients at the higher scales. On the other hand, the high magnitude coefficients at the lower wavelet scales reflect the smooth flow of the traffic across the network.