7 papers
Weighted Hodge Laplacians on Manifolds with Boundary
Zhe Su, Yiying Tong, Guo-Wei Wei
The spectrum of the Hodge Laplacian on differential manifolds encodes rich topological and geometric information and thus provides a powerful tool for analyzing data on manifolds.…
Persistent Manifold Learning of Protein Properties
Xingjian Xu, Zhe Su, Guo-Wei Wei +1
Predicting how tightly two biomolecules bind remains a major challenge, in part because different interaction classes present dissimilar interfaces, from compact metal-coordinated…
A vector field induced de Rham-Hodge theory on manifolds
Zhe Su
We introduce a de Rham-Hodge framework induced by a vector field on a compact, oriented smooth manifold. Using a vector field induced bundle isomorphism on differential forms, we d…
Topological Data Analysis and Topological Deep Learning Beyond Persistent Homology -- A Review
Zhe Su, Xiang Liu, Layal Bou Hamdan +4
Topological data analysis (TDA) is a rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in c…
Manifold Topological Deep Learning for Biomedical Data
Xiang Liu, Zhe Su, Yongyi Shi +3
Recently, topological deep learning (TDL), which integrates algebraic topology with deep neural networks, has achieved tremendous success in processing point-cloud data, emerging a…
Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning
Zhe Su, Yiying Tong, Guo-Wei Wei
Recently, topological data analysis has become a trending topic in data science and engineering. However, the key technique of topological data analysis, i.e., persistent homology,…