The ROI comprised 419 voxels, each one being 4 × 4 × 4 mm in size. We computed the whole-brain RSFC associated with each of the 419 voxels within the ventrolateral ROI, using the same methods described above. We then computed the similarity between every possible pairing of the 419 RSFC maps, using eta squared (η2). The η2 statistic was
recently applied to RSFC data for this purpose by Cohen et al. (2008), and varies between 0 (no similarity) and 1 (identical). Cohen et al. suggested that η2 provides a better measure of similarity JQ1 manufacturer between two images than spatial correlation, because it can take into account differences in scaling and offset between two images, while correlation is unaffected by these factors. We computed a 419 × 419 η2 matrix describing the similarity between each pair of the 419 RSFC maps for every participant (36 in total). We used the spectral clustering toolbox written for Matlab by Verma and Meila (available at http://www.stat.washington.edu/spectral/) http://www.selleckchem.com/products/PLX-4032.html to partition the left ventrolateral frontal ROI into K clusters, where K ranged from 2 to 10. Specifically, we used the Meila–Shi (multicut) algorithm (Meila & Shi, 2001), which performs a generalized Eigen decomposition of the normalized Lagrangian of similarity matrix A (here, the 419 × 419 matrix
of η2 values), then applies the k-means clustering algorithm to partition the data on the basis of K highest eigenvectors. The eigenvectors of the similarity matrix provide information about the data’s structure. By performing partitional clustering (with k-means)
on the basis of these eigenvectors, spectral clustering makes use of this information (the data’s spectrum) to form clusters of voxels that maximize intra-cluster similarity (here, η2) and minimize inter-cluster similarity. For comparison, we also partitioned the data using standard hierarchical clustering, as implemented in the Matlab Statistics toolbox. Hierarchical clustering is an agglomerative method, which starts by treating each data point as a singleton cluster, then, as K decreases, successively merges previously established selleck chemicals clusters (visualized as a dendrogram or tree). Here, we formed clusters of voxels on the basis of average linkage, i.e. the unweighted average of the distances (1−η2) between all pairs of voxels, where one member of the pair is assigned to one cluster and the other member is assigned to a different cluster. At each iteration, K clusters are formed by merging the two clusters (from the K + 1 solution) exhibiting the smallest average distances. In order to determine the optimal K for the ventrolateral ROI, we used a split-half comparison procedure. First, we randomly assigned each of the 36 participants to one of two groups of 18 participants.