University of Oulu

Citation: Hirayama J-i, Hyvärinen A, Kiviniemi V, Kawanabe M, Yamashita O (2016) Characterizing Variability of Modular Brain Connectivity with Constrained Principal Component Analysis. PLoS ONE 11(12): e0168180. doi:10.1371/journal.pone.0168180

Characterizing variability of modular brain connectivity with constrained principal component analysis

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Author: Hirayama, Jun-ichiro1,2; Hyvärinen, Aapo3,4; Kiviniem, Vesa5;
Organizations: 1Brain Information Communication Research Laboratory Group, Advanced Telecommunications Research Institute International (ATR), Kyoto, Japan
2RIKEN Center for Advanced Integrated Intelligence Research, Japan
3Department of Computer Science/HIIT, University of Helsinki, Helsinki, Finland
4Gatsby Computational Neuroscience Unit, University College London, London, United Kingdom
5Department of Diagnostic Radiology, Oulu University Hospital, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 2.5 MB)
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Language: English
Published: Public Library of Science, 2016
Publish Date: 2017-03-06


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 modulebased 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.

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Series: PLoS ONE
ISSN: 1932-6203
ISSN-E: 1932-6203
ISSN-L: 1932-6203
Volume: 11
Issue: 12
Article number: e0168180
DOI: 10.1371/journal.pone.0168180
Type of Publication: A1 Journal article – refereed
Field of Science: 217 Medical engineering
3126 Surgery, anesthesiology, intensive care, radiology
Funding: AH was funded by the Academy of Finland Centre-of-Excellence in Inverse Problems.
Dataset Reference: Data are available from the USC Multimodal Connectivity Database (, tag:1000_Functional_Connectomes), tag:1000_Functional_Connectomes
Copyright information: © 2016 Hirayama et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.