Topology-Preserving Dimensionality Reduction via Interleaving Optimization

Author name not available (Why is that?)

Publication date: 31 January 2022

Abstract: Dimensionality reduction techniques are powerful tools for data preprocessing and visualization which typically come with few guarantees concerning the topological correctness of an embedding. The interleaving distance between the persistent homology of Vietoris-Rips filtrations can be used to identify a scale at which topological features such as clusters or holes in an embedding and original data set are in correspondence. We show how optimization seeking to minimize the interleaving distance can be incorporated into dimensionality reduction algorithms, and explicitly demonstrate its use in finding an optimal linear projection. We demonstrate the utility of this framework to data visualization.

Has companion code repository: https://github.com/comptop/interleaving-dr

This page was built for publication: Topology-Preserving Dimensionality Reduction via Interleaving Optimization

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6389676)