The purpose of this thesis is to study the empirical measure of the t-distributed stochastic neighbor embedding algorithm (t-SNE) when the input is given by n independent, identically distributed inputs.We show that this sequence of measures converges to an equilibrium measure, which can be described as the solution of a variational problem. To provide context for this result, we also provide an overview of a variety unsupervised machine learning algorithms and review the currently known rigorous results about t-SNE.Further, we empirically explore properties of the equilibrium measure and discuss a variety of naturally arising open questions.

Creator

• Fletcher, Daniel

DOI

• https://doi.org/10.21985/n2-gvdv-4h63

Subject

• Mathematics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:16523
• etdadmin_upload_983853

Keyword

• Probability
• Unsupervised Machine Learning

Date created

• 2023-01-01

Resource type

• Dissertation

Rights statement

• In Copyright