Topological determinants of brain imaging data
Brain imaging data such as EEG and fMRI represent a challenge for statisticians as well as clinicians due to their pervasive yet still unknown dependency structure. The emerging field of topological data analysis (TDA) can provide new insights on provides new insights on brain activity; as it characterize data through connected structures of any dimension (i.e. connected components in dimension 0, loops in dimension 1 and so on), in fact, TDA provides information not only what on areas of the brain are connected (i.e. work together) but also what kind of connection relates them.
Topological features can be considered as an alternative representation of the association between brain areas, hence understanding the determinants of the topology of brain imaging data can inform us on the determinants of brain activity itself. This allows to capture more complex forms of dependence, such as cyclical dependence, which is typically neglected by existing network-based methods for brain imaging data.
Our goal is to provide a toolbox to investigate and assess the impact of external covariates on topological invariants, with a special emphasis on their persistence, i.e. how prominent they are in the characterisation of the brain activity. In addition, we plan to release opensource software for the implementation of our proposed methodology.