A better, more optimized processing pipeline for functional connectivity (FC) data will likely accelerate practical advances within the field of neuroimaging. When using correlation-based measures of FC, researchers have recently employed a few data-driven methods to maximize its predictive power. In this study, we apply a few of these post-processing methods in both task, twin, and subject identification problems. First, we employ PCA reconstruction of the original dataset, which has been successfully used to maximize subject-level identifiability. We show there is dataset-dependent optimal PCA reconstruction for task and twin identification. Next, we analyze FCs in their native geometry using tangent space projection with various mean covariance reference matrices. We demonstrate that the tangent projection of the original FCs can drastically increase subject and twin identification rates. For example, the identification rate of 106 MZ twin pairs increased from 0.487 of the original FCs to 0.943 after tangent projection with the logarithmic Euclidean reference matrix. We also use Schaefer’s variable parcellation sizes to show that increasing parcellation granularity in general increases twin and subject identification rates. Finally, we show that our custom convolutional neural network classifier achieves an average task identification rate of 0.986, surpassing state-of-the-art results. These post-processing methods are promising for future research in functional connectome predictive modeling and, if optimized further, can likely be extended into clinical applications.

在本碩士論文中, 我們闡述了投射有限群表現, 以及其形變理論。 我們亦特別研究這些表示在 GL_1 和 GL_2 之形變, 並且給了可表示化 的判定準則。 最後, 我們解釋相對應的泛形變環之扎里斯基切空間與 群餘調之關連, 並計算了 GL_1 的泛形變表現。 / In this master thesis, we give an exposition of the deformation theory of representations for GL_1 and GL_2, respectively, of certain profinite groups. We give rigidity conditions of the fixed representation and verify several conditions for the representability. Finally, we interpret the Zariski tangent spaces of respective universal deformation rings as certain group cohomology and calculate the universal deformation for GL_1.