Network models of spatial interactions, human mobility and navigation ability

Thesis

Networks provide a useful mathematical model for systems that are composed of agents, also called nodes, that interact in a pairwise fashion. Inside a spatial network, nodes are embedded in space and they typically interact much more strongly within their close surrounding, resulting in a special pattern of connections. Geographers, physicists and applied mathematicians have a set of tools at their disposal to understand these systems, and there is a close relationship between spatial networks and population-level models that were originally meant to represent human mobility, but that have been generalised to model more abstract spatial flows.

Over the last decade, there has been an effort to adapt network tools for community detection — whose aim is to describe a system in terms of its mesoscale organisation into groups or communities — to spatial networks. So far, the methods that have been proposed are based on the modularity function, a heuristic function that compares network partitions against a suitable null model. However, a mesoscale description that is gaining traction relies instead on the stochastic block model (SBM), a generative model that can be fitted to an observation using statistical inference. We propose a methodology to leverage an SBM for the case of spatial networks.

We are guided in this by an application to study a network linking customers to the stores they have shopped in, built from anonymised shopping records belonging to a large UK retailer. We also characterise customer shopping behaviours, specially from the lens of their mobility. Lastly, we study a dataset that was collected to assess spatial navigation, and we propose new metrics that are used in comparing the trajectories of healthy individuals, at-genetic-risk patients and patients diagnosed with dementia. Our hope is that this early proposal can be refined in the future by medical practitioners and used to detect early-onset Alzheimer’s Disease.

Authors: Leal Cervantes, R

• DOI: 10.5287/ora-6rojrjkgb
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: spatial networks; network science; human mobility
• Subjects: Computer networks; Information networks; Social networks