| Summary: | Methodologies for data reduction, modeling, and classification of grouped
response curves are explored. In particular, the thesis focuses on the analysis of
a collection of highly correlated, highly dimensional response-curve data of
spectral reflectance curves of wood surface features.
In the analysis, questions about the application of cross-validation
estimation of discriminant function error rates for data that has been previously
transformed by principal component analysis arise. Performing cross-validation
requires re-calculating the principal component transformation and discriminant
functions of the training sets, a very lengthy process. A more efficient approach
of carrying out the cross-validation calculations, plus the alternative of
estimating error rates without the re-calculation of the principal component
decomposition, are studied to address questions about the cross-validation
procedure.
If populations are assumed to have common covariance structures, the
pooled covariance matrix can be decomposed for the principal component
transformation. The leave-one-out cross-validation procedure results in a rank-one
update in the pooled covariance matrix for each observation left out.
Algorithms have been developed for calculating the updated eigenstructure
under rank-one updates and they can be applied to the orthogonal
decomposition of the pooled covariance matrix. Use of these algorithms results
in much faster computation of error rates, especially when the number of
variables is large.
The bias and variance of an estimator that performs leave-one-out cross-validation
directly on the principal component scores (without re-computation
of the principal component transformation for each observation) is also
investigated. === Graduation date: 1993
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