Title page for ETD etd-10252001-104137

Type of Document Master's Thesis
Author McGraw, John M.
Author's Email Address jmcgraw@icam.vt.edu
URN etd-10252001-104137
Title An Investigation into Classification of High Dimensional Frequency Data
Degree Master of Science
Department Statistics
Advisory Committee
Advisor Name Title
Smith, Eric P. Committee Chair
Burns, John A. Committee Member
Woodall, William H. Committee Member
  • Multivariate Normal
  • Frequency Response
  • Confidence Interval
  • Data Analysis
  • Correlation
  • Maximum Likelihood
Date of Defense 2001-10-23
Availability unrestricted
We desire an algorithm to classify a physical object in

``real-time" using an easily portable probing device. The probe excites

a given object at frequencies from 100 MHz up to 800 MHz at intervals

of 0.5 MHz. Thus the data used for classification is the

1400-component vector of these frequency responses.

The Interdisciplinary Center for Applied Mathematics (ICAM) was asked to

help develop an algorithm and executable computer code for the probing

device to use in its classification analysis. Due to these and other

requirements, all work had to be done in Matlab. Hence a significant portion

of the effort was spent in writing and testing applicable Matlab code which

incorporated the various statistical techniques implemented.

We offer three approaches to classification: maximum log-likelihood

estimates, correlation coefficients, and confidence bands. Related work

included considering ways to recover and exploit certain symmetry

characteristics of the objects (using the response data). Present

investigations are not entirely conclusive, but the correlation

coefficient classifier seems to produce reasonable and consistent results.

All three methods currently require the evaluation of the full

1400-component vector. It has been suggested that unknown portions of

the vectors may include extraneous and misleading information, or

information common to all classes. Identifying and removing the respective

components may be beneficial to classification regardless of method. Another

advantage of dimension reduction should be a strengthening of mean and

covariance estimates.

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