Developing statistical and machine learning methods based on topological data analysis (TDA) to understand brain disorders

Topological data analysis (TDA) is an umbrella term for a set of computational topology tools tracking multidimensional holes (connected components, cycles, voids etc.) in data objects. It has recently found applications in a wide variety of research areas, such as astronomy, genomics, neuroscience, and road network. Under the TDA-Brain initiative, we are interested in building topological learning methods, i.e. statistical and machine learning tools that utilize the topological structures and features in neuroimaging data depicted by TDA. Our goal is to obtain fresh insight into brain network disorders, such as epilepsy and post-stroke aphasia, with topological learning of multimodal neuroimaging data.