Senior Thesis

Department of Mathematics
Harvey Mudd College

David Uminsky

Harvey Mudd College Mathematics 2003

mugshot
Thesis: Generalized Spectral Analysis for Large Sets of Approval Voting Data

Thesis Advisor: Prof. Michael Orrison
Second Reader: Prof. Francais Su


Generalized Spectral Analysis for Large Sets of Approval Voting Data

Generalized Spectral analysis of approval voting data uses representation theory and the symmetry of the data to project the approval voting data into orthogonal and interpretable subspaces. Unfortunately, as the number of voters grows, the data space becomes prohibitively large to compute the decomposition of the data vector. To attack these large data sets we develop a method to partition the data set into equivalence classes, in order to drastically reduce the size of the space while retaining the necessary characteristics of the data set. We also make progress on the needed statistical tools to explain the results of the spectral analysis. The standard spectral analysis will be demonstrated, and our partitioning technique is applied to U.S. Senate roll call data.



Other Work:


Iteration of an Even-Odd Splitting Map Can Make Integration Easier
  Pi Mu Epsilon Journal , Fall 2001, WPI.