High dimensional classification for spatially dependent data with application to neuroimaging

The methods developed in this thesis are motivated by how to use structure Magnetic resonance imaging (MRI) data to predict Alzheimer’s disease (AD) or to discriminate between healthy subjects and AD patients. Imaging data is a typical example of spatially dependent data where the correlation between data points collected at various voxels (pixels) can be described by proximity. Also, it is high dimensional data since the number of voxels is extremely high comparing to the number of subjects.The first piece of work considers use longitudinal volumetric MRI data of five regions of interest (ROIs), which are known to be vulnerable to Alzheimer’s disease (AD) for prediction. A longitudinal data prediction method based on functional data analysis is applied for identifying when an early prediction can reasonably be made and determining whether one ROI is superior with regard to predicting progression to AD over others. By adopting statistically validated procedures, we compared the prediction performance based on individual ROIs as well as their combinations. For all the models, the results show that the overall one year, two years, three years in advance prediction accuracy is above 80%. MCI converter subjects can be correctly detected as early as two years prior to conversion.The second piece of work considers use voxel level MRI data for classification of AD patients and healthy subjects. A supervised learning method based on the linear discriminant analysis (LDA) was developed for high dimensional spatially dependent data. The theory shows that the method proposed can achieve consistent parameter estimation, consistent features selection, and asymptotically optimal misclassification rate. The extensive simulation study showed a significant improvement in classification performance under spatial dependence. We applied the proposed method to voxel level MRI data for classification. The classification performance is superior compared to other comparable methods.