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"Leveraging Geometric Multi-Resolution Analysis in Signal, Image, and Network Learning"

Abstract

Classical 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 immediate challenges owing to the intricacies of the dataset complexity and the wealth of information encapsulated within each data point. Fortunately, 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. An analysis of dimensionality reduction techniques, specifically leveraging Geometric Multi-Resolution Analysis (GMRA) reveals an intrinsic low-dimensional structure across various types of datasets, including signals, images, and graphs and networks. Employing Geometric Multi-Resolution Analysis (GMRA) showcases the effective computation of low-dimensional representations within high-dimensional data spaces, thus offering concise yet informative depictions of the original datasets.

Thesis Committee

• Professor Chin (Chair)
• Professor Vaze
• Professor Raymond

Contact

For more information, contact Thayer Registrar at thayer.registrar@dartmouth.edu.