Gromov-Wasserstein Bound between Reeb and Mapper Graphs
We treat Reeb and Mapper graphs as metric measure spaces and give an upper bound on the Gromov-Wasserstein distance between the two.
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Publications and Preprints
Deep Mapper: Efficient Visualization of Plausible Conformational Pathways
Joint work with Fujitsu Ltd. - Now accepted at ECAI 2024!
We introduce a novel variant of the Mapper algorithm in order to find plausible protein conformational pathways. When applied to a 50S-ribosomal dataset, this proves to be more efficient than existing methods, while successfully recovering well-recognized pathways.
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Differentiable Mapper for Topological Optimization of Data Representation
Now accepted at ICML 2024!
The Mapper algorithm has been known to be a powerful tool in visualization and data analytics, but suffers from dependence on many hand-turning parameters. In this work, we propose a relaxation and generalization of the Mapper so that the parameters can be optimized using gradient descent. Convergence results and applications are also provided.
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