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Title: Two-sample testing for isometry of manifolds based on the heat kernel signature (HKS) and topological data analysis
Mathematics of Data & Decisions| Speaker: | Wolfgang Polonik, UC Davis Statistics |
| Location: | 1025 PDSB |
| Start time: | Tue, May 5 2026, 3:10PM |
Description
Abstract: We discuss the construction of a two sample test for isometry of manifolds based on combining the concepts of heat kernel signature and topological data analysis. As a topological invariant, the HKS is certainly a relevant quantity when considering the construction of two-sample tests for isometry of manifolds. Two important questions need to be addressed: Having available a random sample from a manifold, how can one find an estimate of the HKS for which we are able to derive useful results about its asymptotic distribution? How to compare two HKSs defined on two different domains (manifolds)? To address the latter question, we will use ideas from topological data analysis.
The talk will introduce the necessary basics on the HKS, graph Laplacians and persistent homology, state and discuss relevant theoretical results, and present some numerical studies illustrating the performance of the proposed statistical test.
This is joint work with Eunseong Bae, UC Davis.