On Functional Sure Independence Screening (fSIS) and Dynamic Spectral Featuring Extraction for Neuroscience Data
Type of DegreePhD Dissertation
Mathematics and Statistics
Restriction TypeAuburn University Users
MetadataShow full item record
This dissertation is composed of two parts. The first part introduces a methodology for high-dimensional functional variable screening and selection--the functional sure independent screening (fSIS). The fSIS method is an extension of the Sure Independent Screening (SIS) and grouped Sure Independent Screening (gSIS) to functional data analysis. Extensive simulation studies and analysis of a real data application show that our proposed approach outperforms other approaches. The second part presents a novel dynamic spectral featuring extraction method for neuroscience data---the EnergySpectrum. This feature extracting approach is based on the time-frequency analysis of neuroscience data. In a Electroencephalography (EEG) data classification problem, the EnergySpecturm-based features are compared with power-spectral-density-based features as well as Riemaniann geometry-based features to classify EEG epochs for each participant into its lab condition. With cross-validation studies, we show that the EnergySpecturm features achieve better or equivalent classification accuracy compared with other features. Further, we also include a functional connectivity analysis study using Zebrafish Calcium imaging data. The study shows that our methods work well with clustering questions.