Statistical Network Analysis for Functional MRI: Summary Networks and Group Comparisons

Comparing weighted networks in neuroscience is hard, because the topological properties of a given network are necessarily dependent on the number of edges of that network. This problem arises in the analysis of both weighted and unweighted networks. The term density is often used in this context, in order to refer to the mean edge weight of a weighted network, or to the number of edges in an unweighted one. Comparing families of networks is therefore statistically difficult because differences in topology are necessarily associated with differences in density. In this review paper, we consider this problem from two different perspectives, which include (i) the construction of summary networks, such as how to compute and visualize the mean network from a sample of network-valued data points; and (ii) how to test for topological differences, when two families of networks also exhibit significant differences in density. In the first instance, we show that the issue of summarizing a family of networks can be conducted by adopting a mass-univariate approach, which produces a statistical parametric network (SPN). In the second part of this review, we then highlight the inherent problems associated with the comparison of topological functions of families of networks that differ in density. In particular, we show that a wide range of topological summaries, such as global efficiency and network modularity are highly sensitive to differences in density. Moreover, these problems are not restricted to unweighted metrics, as we demonstrate that the same issues remain present when considering the weighted versions of these metrics. We conclude by encouraging caution, when reporting such statistical comparisons, and by emphasizing the importance of constructing summary networks.Comment: 16 pages, 5 figure

Evaluating Graph Signal Processing for Neuroimaging Through Classification and Dimensionality Reduction

Graph Signal Processing (GSP) is a promising framework to analyze multi-dimensional neuroimaging datasets, while taking into account both the spatial and functional dependencies between brain signals. In the present work, we apply dimensionality reduction techniques based on graph representations of the brain to decode brain activity from real and simulated fMRI datasets. We introduce seven graphs obtained from a) geometric structure and/or b) functional connectivity between brain areas at rest, and compare them when performing dimension reduction for classification. We show that mixed graphs using both a) and b) offer the best performance. We also show that graph sampling methods perform better than classical dimension reduction including Principal Component Analysis (PCA) and Independent Component Analysis (ICA).Comment: 5 pages, GlobalSIP 201

Local Difference Measures between Complex Networks for Dynamical System Model Evaluation

Acknowledgments We thank Reik V. Donner for inspiring suggestions that initialized the work presented herein. Jan H. Feldhoff is credited for providing us with the STARS simulation data and for his contributions to fruitful discussions. Comments by the anonymous reviewers are gratefully acknowledged as they led to substantial improvements of the manuscript.Peer reviewedPublisher PD