Inferring functional connectivity in fMRI using minimum partial correlation

  • Lei Nie
  • Xian Yang
  • Paul M. Matthews
  • Zhi-Wei Xu
  • Yi-Ke GuoEmail author
Open Access
Research Article


Functional connectivity has emerged as a promising approach to study the functional organisation of the brain and to define features for prediction of brain state. The most widely used method for inferring functional connectivity is Pearson-s correlation, but it cannot differentiate direct and indirect effects. This disadvantage is often avoided by computing the partial correlation between two regions controlling all other regions, but this method suffers from Berkson-s paradox. Some advanced methods, such as regularised inverse covariance, have been applied. However, these methods usually depend on some parameters. Here we propose use of minimum partial correlation as a parameter-free measure for the skeleton of functional connectivity in functional magnetic resonance imaging (fMRI). The minimum partial correlation between two regions is the minimum of absolute values of partial correlations by controlling all possible subsets of other regions. Theoretically, there is a direct effect between two regions if and only if their minimum partial correlation is non-zero under faithfulness and Gaussian assumptions. The elastic PC-algorithm is designed to efficiently approximate minimum partial correlation within a computational time budget. The simulation study shows that the proposed method outperforms others in most cases and its application is illustrated using a resting-state fMRI dataset from the human connectome project.


Functional connectivity functional magnetic resonance imaging (fMRI) network modelling partial correlation PC-algorithm resting-state networks 



Data were provided by the human connectome project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil, 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research, and by the McDonnell Center for Systems Neuroscience at Washington University. Paul M. Matthews gratefully acknowledges support from the Imperial College NIHR Biomedical Research Centre and personal support from the Edmond Safra Foundation and Lily Safra.


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Authors and Affiliations

  1. 1.Department of ComputingImperial College LondonLondonUK
  2. 2.Department of MedicineImperial College LondonLondonUK
  3. 3.Institute of Computing TechnologyChinese Academy of SciencesBeijingChina
  4. 4.School of Computer Engineering and ScienceShanghai UniversityShanghaiChina

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