Date of Award

Spring 5-1-2024

Document Type

Thesis (Master's)

Department or Program

Engineering Sciences

First Advisor

Peter Chin

Abstract

This research delves into the transformative potential of Geometric Multi-Resolution Analysis (GMRA) as a robust tool for dimensionality reduction and data analysis in the context of high-dimensional graphs. Statistical techniques for classification have historically been tailored for scenarios wherein the number of observations significantly exceeds the number of features, a paradigm characteristic of low-dimensional datasets. However, recent advancements in technologies have ushered in a transformative era in data collection practices across diverse domains, resulting in the acquisition of extensive feature measurements. As a result of this shift, datasets have transitioned into a high-dimensional realm wherein the number of features significantly exceeds the number of observations, rendering classical statistical techniques such as least squares ill-suited. Analyzing such high dimensional datasets presents challenges owing to the intricacies of the dataset complexity and the wealth of information encapsulated within each data point. GMRA offers a promising solution by identifying the intrinsic low-dimensional structure within high-dimensional data spaces. High-dimensional datasets often exhibit redundancy, where many individual features can be expressed through a combination of other features, thereby indicating an exploitable property suggesting that such high-dimensional datasets possess an intrinsic, underlying lower-dimensional structure [1]. This research aims to enhance the breadth and depth of the understanding and capabilities of the GMRA algorithm across datasets structured as graphs.

Download

Share

COinS