Multivariate count time series segmentation with “sums and shares” and Poisson lognormal mixture models: a comparative study using pedestrian flows within a multimodal transport hub

This paper deals with a clustering approach based on mixture models to analyze multidimensional mobility count time-series data within a multimodal transport hub. These time series are very likely to evolve depending on various periods characterized by strikes, maintenance works, or health measures against the Covid19 pandemic. In addition, exogenous one-off factors, such as concerts and transport disruptions, can also impact mobility. Our approach flexibly detects time segments within which the very noisy count data is synthesized into regular spatio-temporal mobility profiles. At the upper level of the modeling, evolving mixing weights are designed to detect segments properly. At the lower level, segment-specific count regression models take into account correlations between series and overdispersion as well as the impact of exogenous factors. For this purpose, we set up and compare two promising strategies that can address this issue, namely the “sums and shares” and “Poisson log-normal” models. The proposed methodologies are applied to actual data collected within a multimodal transport hub in the Paris region. Ticketing logs and pedestrian counts provided by stereo cameras are considered here. Experiments are carried out to show the ability of the statistical models to highlight mobility patterns within the transport hub. One model is chosen based on its ability to detect the most continuous segments possible while fitting the count time series well. An in-depth analysis of the time segmentation, mobility patterns, and impact of exogenous factors obtained with the chosen model is finally performed.