We derive an efficient method to perform clustering of nodes in Gaussian graphical models directly from sample data. Nodes are clustered based on the similarity of their network neighborhoods, with edge weights defined by partial correlations. In the limited-data scenario,
On the Computation and Applications of Large Dense Partial Correlation Networks
While sparse inverse covariance matrices are very popular for modeling network connectivity, the value of the dense solution is often overlooked. In fact the L2-regularized solution has deep connections to a number of important applications to spectral graph theory, dimensionality
Spectral Resolution Clustering for Brain Parcellation
We take an image science perspective on the problem of determining brain network connectivity given functional activity. But adapting the concept of image resolution to this problem, we provide a new perspective on network partitioning for individual brain parcellation. The
A regularized clustering approach to brain parcellation from functional MRI data
We consider a data-driven approach for the subdivision of an individual subject’s functional Magnetic Resonance Imaging (fMRI) scan into regions of interest, i.e., brain parcellation. The approach is based on a computational technique for calculating resolution from inverse problem theory,
A robust sparse-modeling framework for estimating schizophrenia biomarkers from fMRI
Our goal is to identify the brain regions most relevant to mental illness using neuroimaging. State of the art machine learning methods commonly suffer from repeatability difficulties in this application, particularly when using large and heterogeneous populations for samples. We
Fast and robust estimation of ophthalmic wavefront aberrations
Rapidly rising levels of myopia, particularly in the developing world, have led to an increased need for inexpensive and automated approaches to optometry. A simple and robust technique is provided for estimating major ophthalmic aberrations using a gradient-based wavefront sensor.
Computational estimation of resolution in reconstruction techniques utilizing sparsity, total variation, and nonnegativity
Techniques which exploit properties such as sparsity and total variation have provided the ability to reconstruct images that surpass the conventional limits of imaging. This leads to difficulties in assessing the result, as conventional metrics for resolution are no longer
Imposing uniqueness to achieve sparsity
In this paper we take a novel approach to the regularization of underdetermined linear systems. Typically, a prior distribution is imposed on the unknown to hopefully force a sparse solution, which often relies on uniqueness of the regularized solution (something
Element-wise uniqueness, prior knowledge, and data-dependent resolution
Techniques for finding regularized solutions to underdetermined linear systems can be viewed as imposing prior knowledge on the unknown vector. The success of modern techniques, which can impose priors such as sparsity and non-negativity, is the result of advances in
Bounding pixels in computational imaging
We consider computational imaging problems where we have an insufficient number of measurements to uniquely reconstruct the object, resulting in an ill-posed inverse problem. Rather than deal with this via the usual regularization approach, which presumes additional information which may