Functional Data Analysis on Spectroscopic Data
Cox, Dennis D.
Doctor of Philosophy
Cervical cancer is a very common type of cancer that is highly curable if treated early. We are investigating spectroscopic devices that make in-vivo cervical tissue measurements to detect pre-cancerous and cancerous lesions. This dissertation is focused on new methods and algorithms to improve the performance of the device, treating the spectroscopic measurements as functional data. The first project is to calibrate the device measurements using correction factors from a log additive model, based on results from a carefully designed experiment. The second project is a peak finding algorithm using local polynomial regression to get accurate peak location and height estimates of one of the standards (Rhodamine B) measurements from the experiment. We propose a plug-in bandwidth selection method to estimate curve peak location and height. Simulation results and asymptotic properties are presented. The third project is based on patient measurements, particularly when the diseased and non-diseased cases are highly unbalanced. A marginalized corruption methodology is introduced to improve the classification results. Performance of several classification methods is compared.
Functional Data; Log additive model; Local polynomial regression