Assessment of cluster homogeneity in fMRI data using Kendall's coefficient of concordance

In fMRI both model-led and exploratory data-driven methods are used to identify groups of voxels according to their correlation either with an external reference or with some similarity measure. Here we present a technique to assess intragroup homogeneity using Kendall's coefficient of concordance W once groups have been identified. We show that the time-courses belonging to the group may be ranked according to their contribution to the overall concordance and describe an algorithm for group purification. We suggest the use of W as a cluster validation index in exploratory data analysis approaches, such as fuzzy or hard clustering, principal component analysis, independent component analysis and Kohonen maps.