Keywords

machine learning, hyperbolic geometry, rna sequencing, applied math

Abstract

This thesis explores the application of hyperbolic geometry to deep variational autoencoders (VAEs) for learning low-dimensional latent representations of data. Hyperbolic geometry has gained increasing attention in machine learning due to its potential to embed hierarchical data structures in continuous, differentiable manifolds. We extend previous work investi- gating the Poincaré ball model of hyperbolic geometry and its integration into VAEs. By evaluating hyperbolic VAEs on the MNIST handwritten digit dataset and a single-cell RNA sequencing dataset of metastatic melanoma, we assess whether the inductive bias and math- ematical properties of hyperbolic spaces result in improved data representations compared to standard Euclidean VAEs, especially for single-cell RNA sequencing data. Our findings demonstrate the potential advantages of leveraging hyperbolic geometry for representation learning, while also highlighting some challenges. This work contributes to the growing field of geometric deep learning and provides insights for future research on non-Euclidean approaches to representation learning.

Completion Date

2024

Semester

Summer

Committee Chair

Teng Zhang, PhD

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Format

application/pdf

Identifier

DP0028506

URL

https://purls.library.ucf.edu/go/DP0028506

Language

English

Release Date

8-15-2025

Length of Campus-only Access

1 year

Access Status

Masters Thesis (Campus-only Access)

Campus Location

Orlando (Main) Campus

Accessibility Status

Meets minimum standards for ETDs/HUTs

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Restricted to the UCF community until 8-15-2025; it will then be open access.

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