Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE

Unified Geostatistical Modeling for Data Fusion and Spatial Heteroskedasticity with R Package ramps

This article illustrates usage of the ramps R package, which implements the reparameterized and marginalized posterior sampling (RAMPS) algorithm for complex Bayesian geostatistical models. The RAMPS methodology allows joint modeling of areal and point-source data arising from the same underlying spatial process. A reparametrization of variance parameters facilitates slice sampling based on simplexes, which can be useful in general when multiple variances are present. Prediction at arbitrary points can be made, which is critical in applications where maps are needed. Our implementation takes advantage of sparse matrix operations in the Matrix package and can provide substantial savings in computing time for large datasets. A user-friendly interface, similar to the nlme mixed effects models package, enables users to analyze datasets with little programming effort. Support is provided for numerous spatial and spatiotemporal correlation structures, user-defined correlation structures, and non-spatial random effects. The package features are illustrated via a synthetic dataset of spatially correlated observation distributed across the state of Iowa, USA.