Abstract: 

Many previous studies on networks have mainly focused on analyzing graph theory features that are parameter dependent. Persistent homology provides a more coherent mathematical framework that is invariant to the choice of parameters. Instead of looking at networks at a fixed scale, persistent homology charts the topological changes of networks over every possible parameter. In doing so, it reveals the most persistent topological features that are robust to parameter changes. In this talk, we present novel topological inference and learning frameworks that can integrate networks of different sizes, topologies or modalities through persistent homology. This is possible through the Wasserstein distances defined on persistent diagrams. The method is applied for determining the heritability of functional brain networks (Songdechakraiwut et al. 2021, MICCAI 116-176) and modeling higher order brain connectivity via Hodge Laplacian (Anand et al. 2021, arXiv:2110.14599). This is joint work with Dr. Vijay Anand.

Bio:

Dr. Chung’s main research area is computational neuroimging, where noninvasive brain imaging modalities such as magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI) are used to map spatiotemporal dynamics of the human brain. Computational neuroimaging deals with the computational problems arising from the quantification of the structure and the function of the human brain. Dr. Chung’s research has been concentrated on the methodological development of quantifying anatomical shape variations and function brain networks in both normal and clinical populations using various mathematical and statistical techniques. A major challenge in the field is caused by the massive amount of nonstandard high dimensional non-Euclidean imaging data that are difficult to analyze using available techniques. This requires new computational solutions that are formulated in a differential geometric or algebraic topological setting in addressing more complex scientific hypotheses. Other than computational neuroimaging, Dr. Chung’s interests lie in persistent homology, deformable shape models, functional data analysis and network sciences.