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Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures...
In a brain network, weak and nonsignificant edge weights between nodes signal spurious connections and are often thresh-olded out of the network. The traditional practice of thresholding edge weights at an arbitrary value can be problematic. Network filtration provides an alternative by summarizing the changes in the network topology with respect to a broad range of thresholds. A well established...
General linear modeling (GLM) is one of the most commonly used approaches to perform voxel based analyses (VBA) for hypotheses testing in neuroimaging. In this paper we tie support vector machine based regression (SVR) and classical significance testing to provide the benefits of max margin estimation in the GLM setting. Using Welch-Satterthwaite approximations, we compute degrees of freedom (df)...
The tensor-based morphometry (TBM) has been widely used in characterizing tissue volume difference between populations at voxel level. We present a novel computational framework for investigating the white matter connectivity using TBM. Unlike other diffusion tensor imaging (DTI) based white matter connectivity studies, we do not use DTI but only T1-weighted magnetic resonance imaging (MRI). To construct...
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