Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Operational Sciences

First Advisor

Kenneth W. Bauer, Jr., PhD.


Linear approaches for multivariate data analysis are popular due to their lower complexity, reduced computational time, and easier interpretation. In many cases, linear approaches produce adequate results; however, non-linear methods may generate more robust transformations, features, and decision boundaries. Of course, these nonlinear methods present their own unique challenges that often inhibit their use. In this research, improvements to existing non-linear techniques are investigated for the purposes of providing better, timely class separation and improved anomaly detection on various multivariate datasets, culminating in application to anomaly detection in hyperspectral imagery. Primarily, kernel-based methods are investigated, with some consideration towards other methods. Improvements to existing linear-based algorithms are also explored. Here, it is assumed that classes in the data have minimal overlap in the originating space or can be made to have minimal overlap in a transformed space, and that class information is unknown a priori. Further, improvements are demonstrated for global anomaly detection on a variety of hyperspectral imagery, utilizing fusion of spatial and spectral information, factor analysis, clustering, and screening. Additionally, new approaches for n-dimensional visualization of data and decision boundaries are developed.

AFIT Designator


DTIC Accession Number