Date of Award

Spring 2023

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Coifman, Ronald

Abstract

Extracting the common information amongst a collection of datasets has become a majortopic of research called Sensor Fusion. Instead, we explore a collection of methods for extracting the information which differentiates between collections of datasets. We focus on methods for differentating the perspectives of datasets using diffusion operators. We formulate a minimax problem for optimizing the relative smoothness of functions between collections of graphs, and prove a minimax theorem for generalized eigenvalues to compute the solution. We further investigate methods for extracting control variables from multidimensional time-series, motivated by a differentiation problem in stroke detection.

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