Modern data collection methods are now frequently returning observations that should
be viewed as the result of digitized recording or sampling from stochastic processes rather
than vectors of finite length. In spite of great demands, only a few classification methodologies
for such data have been suggested and supporting theory is quite limited. The focus of
this dissertation is on discrimination and classification in this infinite dimensional setting.
The methodology and theory we develop are based on the abstract canonical correlation
concept of Eubank and Hsing (2005), and motivated by the fact that Fisher's discriminant
analysis method is intimately tied to canonical correlation analysis. Specifically, we have
developed a theoretical framework for discrimination and classification of sample paths
from stochastic processes through use of the Loeve-Parzen isomorphism that connects a
second order process to the reproducing kernel Hilbert space generated by its covariance
kernel. This approach provides a seamless transition between the finite and infinite dimensional
settings and lends itself well to computation via smoothing and regularization. In
addition, we have developed a new computational procedure and illustrated it with simulated
data and Canadian weather data.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/5832 |
| Date | 17 September 2007 |
| Creators | Shin, Hyejin |
| Contributors | Eubank, Randall L., Parzen, Emanuel |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 595968 bytes, electronic, application/pdf, born digital |
Page generated in 0.0021 seconds