Leveraging Topological Structure in Data Analysis, Machine Learning, and Visualization
Date:
Talk at Seattle Children's Research Institute, March 2023, Seattle, Washington
Abstract:
In this talk I outlined my past and current research in developing methods to leverage topological structure in different stages of data analysis, machine learning, and visualization pipelines. Topological techniques can be particularly powerful in characterizing complex, high-dimensional data. In the first part of the talk, I described ways to construct topological signatures of data (images, networks, point clouds) and utilizing them in statistical analysis, machine learning, and interactive visual analysis. I presented our work in collaboration with neuroscientists where we explored the utility of topological features to study structural and functional brain network abnormalities in autism spectrum disorders. In the second part of the talk, I presented our work extending graph learning algorithms to simplicial complexes and hypergraphs which are generalizations of graphs that allow us to capture multilateral relationships between nodes. I presented methods for unsupervised and semisupervised learning on simplicial complexes, specifically, spectral clustering and label propagation. Then I presented our work on performing computations such as averaging, interpolating, and sketching on ensembles of combinatorial objects (trees) using an optimal transport based framework. I presented our recent results on using this framework to identify a small representative basis set from a large collection of merge trees obtained from scientific simulations. Lastly, I talked about a future research direction which builds on different elements mentioned before to create a novel hypergraph based framework for genome-wide, cross-species, multiomics analysis.
