Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
8-2021
Committee Chair or Co-Chairs
Jeff Knisley
Committee Members
Michele Joyner, Nicole Lewis
Abstract
The interdisciplinary field of machine learning studies algorithms in which functionality is dependent on data sets. This data is often treated as a matrix, and a variety of mathematical methods have been developed to glean information from this data structure such as matrix decomposition. The Laplacian matrix, for example, is commonly used to reconstruct networks, and the eigenpairs of this matrix are used in matrix decomposition. Moreover, concepts such as SVD matrix factorization are closely connected to manifold learning, a subfield of machine learning that assumes the observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. Since many data sets have natural higher dimensions, tensor methods are being developed to deal with big data more efficiently. This thesis builds on these ideas by exploring how matrix methods can be extended to data presented as tensors rather than simply as ordinary vectors.
Document Type
Thesis - unrestricted
Recommended Citation
Sanders, Scott, "Manifold Learning with Tensorial Network Laplacians" (2021). Electronic Theses and Dissertations. Paper 3965. https://dc.etsu.edu/etd/3965
Copyright
Copyright by the authors.