Display Accessibility Tools

Accessibility Tools

Grayscale

Highlight Links

Change Contrast

Increase Text Size

Increase Letter Spacing

Readability Bar

Dyslexia Friendly Font

Increase Cursor Size

Dissertation Defense of CMSE Danielle Barnes

Department of Computational Mathematics, Science & Engineering

Michigan State University

Dissertation Defense Notice

Danielle Barnes

 

April 4, 2024, 11:00am

428 S. Shaw Lane, Room 1502

East Lansing, MI 48824

https://msu.zoom.us/j/98193422573

Meeting ID: 981 9342 2573

Passcode: barnes

 

Topological Data Analysis Drive Feature Generation in Machine Learning Models

 

Abstract:

Topological data analysis (TDA) is an emerging field in data science, with origins in algebraic topology. I focus on two main disciplines of topological data analysis, mapper and persistent homology. Mapper is an algorithm to construct a graph that is similar to a Reeb graph, allowing for the abstraction of shape from data. Persistent homology is way to measure features in a dataset, and returns a set of points (a persistence diagram) that represents the structure of the dataset. While both mapper and persistent homology are effective tools in their own right, a significant area of research includes using features created from these topological tools in machine learning algorithms. In this dissertation, I focus on advancing both theoretical and computational methods that allow the use of topological data analysis in machine learning algorithms. I have developed an extension to the mapper algorithm, named predictive mapper, that uses the eigenvectors of the graph Laplacian of the geometric realization of a mapper graph as a basis, allowing features to be created from mapper for use in machine learning. I have also contributed to teaspoon, an open source package for topological signal processing by including new datasets and expanded functionality for featurization methods. Lastly, I have started the development of ceREEBerus, a python package for working with Reeb graphs while implementing a standardized software development framework for the Munch Lab.

Committee Members:

Dr. Elizabeth Munch (Chair)

Dr. Jose Perea

Dr. H. Metin Atkulga

Dr. Brian O’Shea