Topological inference and learning for graphs
Moo K. Chung
University of Wisconsin-Madison
Date: Wednesday, October 6, 2021
Time: 4:00 pm - 5:00 pm
Abstract: Many previous studies on networks have mainly focused analyzing graph theory features that are often 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, topology or modalities through persistent homology. This is possible through the Kolmogorov-Smirnov and Wasserstein distances defined on persistent homological features. The use of Kolmogorov-Smirnov and Wasserstein distances bypass the intrinsic computational bottleneck associated with persistent homology. The methods are applied for determining the conformational changes of the spike protein of COVID-19 virus (Chung et al. 2021, arXiv:2105:00351) and the heritability of functional brain networks (Songdechakraiwutet al. 2021, arXiv:2012.0067).
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