Applications of Statistical Analysis Techniques for Neuroimaging Data: Randomized Singular Value Decomposition for Partial Least Squares Analysis and Thin Plate Splines for Spatial Normalization

2008 iv This dissertation applies two statistical analysis techniques for neuroimaging data. The first aim of this dissertation is to apply randomized singular value decomposition for the approximation of the top singular vectors of the singular value decomposition of a large matrix. Randomized singular value decomposition is an algorithm that approximates the top k singular vectors of a matrix given a subset of its rows or columns. Several statistical applications, such as partial least squares, require the computation of the singular value decomposition of a matrix. Statistical packages have built in functions that can compute the singular value decomposition of a matrix. In many applications, however, computing the SVD of a matrix is not possible because computer memory requirements associated with matrix allocation is high, limiting its use in high-dimensional settings. Neuroimaging studies can generate measurements for hundreds of thousands of voxels from an image. Therefore, performing partial least squares analysis on these datasets is not possible using statistical packages. Simulation studies showed that the randomized singular value decomposition method provides a good approximation of the top singular vectors and therefore a good approximation of the partial least squares summary scores. This method is significant for public health since it allows researchers to perform statistical analysis at a voxel level with only a sample of a large dataset. The second aim is to apply a thin plate spline method for spatial normalization of structural magnetic resonance images. Spatial normalization is the process of standardizing v images of different subjects into the same anatomical space. The idea behind this procedure is to match each data volume from a subject to a template, so that specific anatomic structures will occupy the same voxels. Spatial normalization is a critical step in the analysis of brain imaging data since it produces the " raw " data for subsequent statistical analyses. Figure 14 Summary Scores for PIB for voxel-based analysis (two slices) from functional image Figure 33 Magnetic Resonance Image for a healthy control subject (coronal, sagittal and axial views). xiii Figure 34 Coronal (top), sagittal (middle) and axial views (bottom). (A) Standard template in SPM, (B) Atlas from the standard template in SPM, (C) Results for the interpolation TPS. xiv ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my committee chair, Dr. Lisa Weissfeld, for her guidance, patience, and support throughout the process of preparing my dissertation. I would also like to …