Sampling from the space of persistence diagrams
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Joshua W. Slater (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Thomas Weighill
Abstract: The efficacy of using persistent homology as a tool to understand “the shape of data” has been demonstrated in a variety of different machine learning problem domains. Like many other unsupervised techniques within machine learning, the quintessential persistent homology pipeline is one-directional; data goes in, we use persistent homology to compute information about topological invariant that are present with that data, and a succinct summarization of this information, a persistence diagram, comes out. In this work, we investigate the opposite direction of this pipeline. Using Random Walk Metropolis (RWM), we explore spaces of grayscale images and weighted graphs whose persistence diagrams approximates a given target persistence diagram, presenting sampling schemes that make this process tractable. Following an overview of relevant terminology and results, we show that our methods may be used to generate images and weighted graphs whose underlying persistence diagrams closely approximate a given target.
Sampling from the space of persistence diagrams
PDF (Portable Document Format)
6962 KB
Created on 5/1/2024
Views: 4
Additional Information
- Publication
- Thesis
- Language: English
- Date: 2024
- Keywords
- Applied Mathematics, Persistent Homology