Matrix Distances With their Application to Finding Directional Deviations from normality in High-Dimensional Data

Open Access
Author:
Hui, Guodong
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
December 18, 2007
Committee Members:
  • Bruce G Lindsay, Committee Chair
  • Thomas P Hettmansperger, Committee Member
  • Runze Li, Committee Member
  • Jesse Louis Barlow, Committee Member
Keywords:
  • non-normal direction
  • quadratic distance
  • eigenanalysis
  • Fisher information
  • projection pursuit
  • mixture model
Abstract:
Projection pursuit is a technique locating projections from high- to low-dimensional space that reveal interesting non-linear features of a data set, such as clustering and outliers. The two key components of projection pursuit are the measure of interesting features(projection index) and its algorithm. In this thesis, two projection matrix indices based on Fisher information matrix are presented. Both matrix indices are easily estimated by the kernel method. The eigenanalysis of the estimated matrix index provides all solution projections. The asymptotic distribution of the estimated index is studied using the Von-Mises expansion and kernel-based quadratic distance theory. The application to simulated data and real data sets shows that our algorithm successfully reveals interesting features in fairly high dimensions with a practical sample size.