Degree Name

MS (Master of Science)

Program

Mathematical Sciences

Date of Award

12-2017

Committee Chair or Co-Chairs

Jeff R. Knisley

Committee Members

Ariel Cintron-Arias , Christina Nicole Lewis

Abstract

High-dimensional data sets can be difficult to visualize and analyze, while data in low-dimensional space tend to be more accessible. In order to aid visualization of the underlying structure of a dataset, the dimension of the dataset is reduced. The simplest approach to accomplish this task of dimensionality reduction is by a random projection of the data. Even though this approach allows some degree of visualization of the underlying structure, it is possible to lose more interesting underlying structure within the data. In order to address this concern, various supervised and unsupervised linear dimensionality reduction algorithms have been designed, such as Principal Component Analysis and Linear Discriminant Analysis. These methods can be powerful, but often miss important non-linear structure in the data. In this thesis, manifold learning approaches to dimensionality reduction are developed. These approaches combine both linear and non-linear methods of dimension reduction.

Document Type

Thesis - Open Access

Copyright

Theophilus Siameh

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