Browsing by Subject "Laplacian matrix"

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    Brain Connectivity-Informed Regularization Methods for Regression
    (Springer, 2017-12-06) Karas, Marta; Brzyski, Damian; Dzemidzic, Mario; Goñi, Joaquín; Kareken, David A.; Randolph, Timothy W.; Harezlak, Jaroslaw; Neurology, School of Medicine
    One of the challenging problems in brain imaging research is a principled incorporation of information from different imaging modalities. Frequently, each modality is analyzed separately using, for instance, dimensionality reduction techniques, which result in a loss of mutual information. We propose a novel regularization method to estimate the association between the brain structure features and a scalar outcome within the linear regression framework. Our regularization technique provides a principled approach to use external information from the structural brain connectivity and inform the estimation of the regression coefficients. Our proposal extends the classical Tikhonov regularization framework by defining a penalty term based on the structural connectivity-derived Laplacian matrix. Here, we address both theoretical and computational issues. The approach is first illustrated using simulated data and compared with other penalized regression methods. We then apply our regularization method to study the associations between the alcoholism phenotypes and brain cortical thickness using a diffusion imaging derived measure of structural connectivity. Using the proposed methodology in 148 young male subjects with a risk for alcoholism, we found a negative associations between cortical thickness and drinks per drinking day in bilateral caudal anterior cingulate cortex, left lateral OFC, and left precentral gyrus.
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    Connectivity‐informed adaptive regularization for generalized outcomes
    (Wiley, 2021-02) Brzyski, Damian; Karas, Marta; Ances, Beau M.; Dzemidzic, Mario; Goñi, Joaquín; Randolph, Timothy W.; Harezlak, Jaroslaw; Neurology, School of Medicine
    One of the challenging problems in neuroimaging is the principled incorporation of information from different imaging modalities. Data from each modality are frequently analyzed separately using, for instance, dimensionality reduction techniques, which result in a loss of mutual information. We propose a novel regularization method, generalized ridgified Partially Empirical Eigenvectors for Regression (griPEER), to estimate associations between the brain structure features and a scalar outcome within the generalized linear regression framework. griPEER improves the regression coefficient estimation by providing a principled approach to use external information from the structural brain connectivity. Specifically, we incorporate a penalty term, derived from the structural connectivity Laplacian matrix, in the penalized generalized linear regression. In this work, we address both theoretical and computational issues and demonstrate the robustness of our method despite incomplete information about the structural brain connectivity. In addition, we also provide a significance testing procedure for performing inference on the estimated coefficients. Finally, griPEER is evaluated both in extensive simulation studies and using clinical data to classify HIV+ and HIV− individuals.