Abstract
Characterizing the variability of resting-state functional brain connectivity across subjects and/or over time has recently attracted much attention. Principal component analysis (PCA) serves as a fundamental statistical technique for such analyses. However, performing PCA on high-dimensional connectivity matrices yields complicated “eigenconnectivity” patterns, for which systematic interpretation is a challenging issue. Here, we overcome this issue with a novel constrained PCA method for connectivity matrices by extending the idea of the previously proposed orthogonal connectivity factorization method. Our new method, modular connectivity factorization (MCF), explicitly introduces the modularity of brain networks as a parametric constraint on eigenconnectivity matrices. In particular, MCF analyzes the variability in both intra- and inter-module connectivities, simultaneously finding network modules in a principled, data-driven manner. The parametric constraint provides a compact module-based visualization scheme with which the result can be intuitively interpreted. We develop an optimization algorithm to solve the constrained PCA problem and validate our method in simulation studies and with a resting-state functional connectivity MRI dataset of 986 subjects. The results show that the proposed MCF method successfully reveals the underlying modular eigenconnectivity patterns in more general situations and is a promising alternative to existing methods.
Highlights
Characterizing the variability of the brain’s functional network organization is of fundamental importance in basic neuroscience as well as clinical researches
In the second column with a relatively weak variability within modules (c = 0.2), Principal component analysis (PCA) and modular connectivity factorization (MCF) produced almost the same pattern as true B, while the patterns obtained by PCA are relatively noisy compared to those by MCF; as intended, orthogonal connectivity factorization (OCF) mostly recovered the off-diagonal blocks of true B
PCA is a fundamental method to characterize the variability of functional connectivity matrices [8], it has a severe limitation in visualization and interpretation of complicated eigenconnectivity patterns
Summary
Characterizing the variability of the brain’s functional network organization is of fundamental importance in basic neuroscience as well as clinical researches. Functional connectivity [1] is usually measured as pairwise covariances or correlations of neural signals, typically for 5-10 minutes of resting state, and the connectivities among many brain regions are summarized as what is called the (functional) connectivity matrix. The inter-subject variability of this matrix, PLOS ONE | DOI:10.1371/journal.pone.0168180. Characterizing Variability of Modular Brain Connectivity with Constrained PCA and Technology Agency (JST), and KAKENHI 25730155, 15H02759 from Japan Society for the Promotion of Science (JSPS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript
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