title: Characterizing Variability of Modular Brain Connectivity with Constrained Principal Component Analysis.
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.
authors.affiliation: Brain Information Communication Research Laboratory Group, Advanced Telecommunications Research Institute International (ATR), Kyoto, Japan.|RIKEN Center for Advanced Integrated Intelligence Research, Japan.
authors.forename: Jun-Ichiro
authors.initials: JI
authors.lastname: Hirayama
authors.affiliation: Department of Computer Science/HIIT, University of Helsinki, Helsinki, Finland.|Gatsby Computational Neuroscience Unit, University College London, London, United Kingdom.
authors.forename: Aapo
authors.initials: A
authors.lastname: Hyvärinen
authors.affiliation: Department of Diagnostic Radiology, Oulu University Hospital, Oulu, Finland.
authors.forename: Vesa
authors.initials: V
authors.lastname: Kiviniemi
authors.affiliation: Brain Information Communication Research Laboratory Group, Advanced Telecommunications Research Institute International (ATR), Kyoto, Japan.|RIKEN Center for Advanced Integrated Intelligence Research, Japan.
authors.forename: Motoaki
authors.initials: M
authors.lastname: Kawanabe
authors.affiliation: Brain Information Communication Research Laboratory Group, Advanced Telecommunications Research Institute International (ATR), Kyoto, Japan.|RIKEN Center for Advanced Integrated Intelligence Research, Japan.
authors.forename: Okito
authors.initials: O
authors.lastname: Yamashita
mesh_terms: D000465:Algorithms; D001921:Brain / Q000000981:diagnostic imaging / Q000502:physiology*; D001931:Brain Mapping; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008279:Magnetic Resonance Imaging; D009415:Nerve Net; D025341:Principal Component Analysis