2016/12/11 by Nicolas Honnorat, Christos Davatzikos, Honnorat, Nicolas +1
Medicine · Neuroscience · #Advanced MRI Techniques and Applications #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Functional Brain Connectivity Studies #Methodology (stat.ME) #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1612.03428
openalex publication_date 2016/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The introduction of graph theory in neuroimaging has pro- vided invaluable tools for the study of brain connectivity. These methods require the definition of a graph, which is typically derived by estimating the effective connectivity between brain regions through the optimization of an ill-posed inverse problem. Considerable efforts have been devoted to the development of methods extracting sparse connectivity graphs. The present paper aims at highlighting the benefits of an alternative ap- proach. We investigate low-rank L2 regularized matrices recently intro- duced under the denomination of Riccati regularized precision matrices. We demonstrate their benefits for the analysis of cortical thickness map and for the extraction of functional biomarkers from resting state fMRI scans. In addition, we explain how speed and result quality can be further improved with random projections. The promising results obtained using the Human Connectome Project dataset as well as the numerous possi- ble extensions and applications suggest that Riccati precision matrices might usefully complement current sparse approaches.