| Cortical alignment is an essential link in the processing chain for establishing neurological relationships across multiple subjects. This thesis addresses multi-subject cortical alignment using functional magnetic resonance imaging (fMRI) data. Starting from a correlation-based alignment metric, we derive hyperalignment, a previously-established method that has demonstrated significant improvement over anatomical alignment through the use of a common, synchronous stimulus. We then introduce a regularized form of hyperalignment, revealing qualitative connections with canonical correlation analysis (CCA) and further improving hyperalignment.;Extending hyperalignment beyond inter-subject correlations, we then investigate hyperalignment via intra-subject correlations, yielding a functional connectivity hyperalignment (FCH) problem. Weakened by severe identifiability issues from a lack of synchrony, FCH grossly underperforms. We show, however, that with a small injection of synchrony, FCH can match the performance levels of anatomical alignment. Next, we address the scalability of hyperalignment, where we focus on an efficient means of hyperaligning the entire cortex. Reformulating the hyperalignment problem in terms of a voxel-derived feature set, which generally increases dimensionality, we form a kernelized hyperalignment procedure. Using positive definite kernels as generalized measures of similarity, kernel hyperalignment proves robust and competitive.;Beyond alignment, this thesis presents two supervised learning methods fit for fMRI data analysis. The first is linear regression with the Pairwise Elastic Net (PEN), a regularization term that can encode local and sparse groupings of the linear weights. We use PEN for binary classification with support vector machines (SVM) in the fMRI setting, demonstrating its ability to automatically select a sparse set of spatially-grouped voxels. The second method is VIBoost, a boosting-like algorithm emanating from variational inference. The VIBoost algorithm can generate a binary classifier along with meaningful statistics about the label noise. Such statistics are vital when there is a lack of ground truth, as in the case of fMRI data. |
