Multi-resolution and spatial Independent Component Analysis approaches for geo-referred and time-varying mobile phone data

The aim of this work is to provide different statistical tools to catch meaningful and useful information from geo-referred quantities varying along time. In particular a mobile-phone traffic dataset is analyzed to decompose the spatiotemporal information in order to identify spatial and temporal patterns. Two different approaches have been followed. The first one is an Independent Component Analysis (ICA) approach, where sources are assumed to be spatial stochastic processes on a lattice, in order to take into account the spatial dependence between pixels. This method is called spatial colored Independent Component Analysis (Shen, Truong, Zanini, 2014). The second one is a multi-resolution approach, where a temporal sparsity to the final representation is imposed through a wavelet-inspired data-driven procedure. This method is called Hierarchical Independent Component Analysis (Secchi, Vantini, Zanini, 2014). Results highlight urban features related to residential, leisure and mobility activities.