An alternative approach to cluster validation is to perform clustering on an individual subject level and to examine the stability with which pairs of voxels are assigned to the same cluster, across individuals (e.g. Steinley, 2008). We applied the spectral clustering algorithm to each individual subject’s η2 matrix, to identify cluster solutions for the range K = 2:12 at the single-subject level. For each subject (s), and each K, we constructed an adjacency matrix, where if
voxels i and j are assigned to the same cluster k, and 0 otherwise. For each K, we then computed a consensus matrix, To discern the most stable pattern of cluster assignment across subjects, we applied the spectral clustering algorithm to the 12 resultant Proteasome inhibitor consensus matrices. For each K’s consensus matrix we identified the cluster solution, using the same K, and compared the quality of the cluster assignments using the modified silhouette metric (where the silhouette was calculated on the basis of the mean within- vs. between-cluster consensus values, rather than the η2 values). Finally, we assessed the
similarity between the solutions reached on the basis of the consensus matrices to those reached on the basis of the group-average of the single-subject η2 matrices, using the VI metric. The clustering validation methods suggested that the most favorable clustering solution was that produced by the spectral clustering algorithm for K = 4 Selleck Enzalutamide (see Results). To verify the distinctions among the regions of ventrolateral frontal cortex
suggested by this clustering solution, we created four spherical seed PFKL ROIs of diameter 8 mm, centered on the centers-of-mass of each of the clusters of the group-average K = 4 spectral clustering solution. We computed the group-level RSFC for each of the seeds, and performed direct comparisons between seeds in the same manner as for the manually selected ventrolateral prefrontal seeds (Z > 2.3; cluster significance P < 0.05, corrected). The ROI placed in BA 44 exhibited robust positive correlations with the pars triangularis (BA 45) and pars orbitalis (area 47/12) of the inferior frontal gyrus, as well as with the inferior premotor region (BA 6). In addition, there were positive correlations with the pre-supplementary motor area, the paracingulate region (BA 32) and the adjacent medial frontal cortex (BAs 8, 9) (Fig. 1). There were also correlations with the caudal dorsolateral frontal cortex (BA 
and the rostral part of dorsal BA 6. In the parietal cortex, correlations were primarily restricted to the ventral part of the posterior supramarginal gyrus and the adjacent angular gyrus.
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