  A recent interest in resting state functional magnetic resonance imaging
(rsfMRI) lies in subdividing the human brain into anatomically and functionally
distinct regions of interest. For example, brain parcellation is often used for
defining the network nodes in connectivity studies. While inference has
traditionally been performed on group-level data, there is a growing interest
in parcellating single subject data. However, this is difficult due to the low
signal-to-noise ratio of rsfMRI data, combined with typically short scan
lengths. A large number of brain parcellation approaches employ clustering,
which begins with a measure of similarity or distance between voxels. The goal
of this work is to improve the reproducibility of single-subject parcellation
using shrinkage estimators of such measures, allowing the noisy
subject-specific estimator to "borrow strength" in a principled manner from a
larger population of subjects. We present several empirical Bayes shrinkage
estimators and outline methods for shrinkage when multiple scans are not
available for each subject. We perform shrinkage on raw intervoxel correlation
estimates and use both raw and shrinkage estimates to produce parcellations by
performing clustering on the voxels. Our proposed method is agnostic to the
choice of clustering method and can be used as a pre-processing step for any
clustering algorithm. Using two datasets---a simulated dataset where the true
parcellation is known and is subject-specific and a test-retest dataset
consisting of two 7-minute rsfMRI scans from 20 subjects---we show that
parcellations produced from shrinkage correlation estimates have higher
reliability and validity than those produced from raw estimates. Application to
test-retest data shows that using shrinkage estimators increases the
reproducibility of subject-specific parcellations of the motor cortex by up to
30%.
