An Overview of Methods for Activity Graph Study of Movements

Graph-based data structures have emerged as a fundamental tool across a wide range of applications, offering an intuitive and powerful way to visualize, model, and analyze complex information systems. One notable application is the study of discrete movement patterns observed between defined key points or locations. By representing these movements as graph structures, underlying trends, identify benchmarks, and establish predictive models can be uncovered. Such analyses are crucial for understanding and modelling the behaviours of various populations, including individuals with movement or decision-making impairments, where tailored interventions or designs might be required. This paper provides an overview of graph-based methodologies employed in the literature to analyze and model movement data. Specifically, it focuses on three techniques: a) Markov Chains, which model probabilistic transitions and sequence dependencies within the movement data; b) PageRank, originally devisedm for web-page ranking but adapted here to evaluate importance of nodes within a movement graph and c) Graph Signal Processing, as an approach that facilitates the analysis of signals distributed over graph structures to detect patterns and anomalies. Each method is detailed and demonstrated through illustrative examples, highlighting its unique contributions to the study of movement patterns.