Minimum partial correlation: An accurate and parameter-free measure of functional connectivity in fMRI

Abstract

Functional connectivity, a data-driven modelling of spontaneous fluctuations in activity in spatially segregated brain regions, has emerged as a promising approach to generate hypotheses and features for prediction. The most widely used method for inferring functional connectivity is full correlation, but it cannot differentiate direct and indirect effects. This disadvantage is often avoided by fully partial correlation, but this method suffers from Berkson’s paradox. Some advanced methods, such as regularised inverse covariance and Bayes nets, have been applied. However, the connectivity inferred by these methods usually depends on crucial parameters. This paper suggests minimum partial correlation as a parameter-free measure of functional connectivity in fMRI. An algorithm, called elastic PC-algorithm, is designed to approximately calculate minimum partial correlation. Our experimental results show that the proposed method is more accurate than full correlation, fully partial correlation, regularised inverse covariance, network deconvolution algorithm and global silencing algorithm in most cases.