Clustering cortical searchlights based on shared representational geometry

Complex representational spaces are thought to be encoded in distributed patterns of cortical activity. Here, on fMRI and simulated data, we examine several data-driven methods for identifying clusters of locally distributed response patterns with shared representational geometry. This differs from cortical clustering methods relying on functional connectivity or univariate contrasts in that the data consist of the representational geometry in surface-based searchlights defined by pairwise distances between response vectors. This approach was only recently introduced and has not been rigorously explored. Finally, we examine the effect of applying hyperalignment on the cluster solutions. Two datasets were used: a) a simulated dataset intended to mimic noisy spatial maps of 10 subjects with six different clusters each defined by a distinct known similarity structure; and b) an fMRI dataset collected while 12 participants viewed brief video clips of animals behaving. For the fMRI data, representational similarity analysis was applied to locally distributed response patterns using a surface-based searchlight approach. To reduce computational demands we considered searchlights only from the posterior half of the left hemisphere. We applied a battery of clustering algorithms to both datasets: k-means clustering, Gaussian mixture models with several covariance structures, Ward clustering (both structurally constrained and unconstrained), and the pvclust algorithm. We evaluated the stability of the cluster solutions across participants using a split-half resampling technique at k = 2 to 10. For the simulated data, we applied clustering algorithms to the full dataset (averaged across simulated subjects, n = 10) and compared cluster solutions to the ground truth (true k = 7) using the adjusted Rand index (ARI) at k = 2 to 10. With the exception of structurally constrained hierarchical clustering and pvclust, all of the algorithms were applied in the similarity space and unconstrained anatomically. For the simulated data, the stability analysis identified the true k as the most stable solution with relatively high accuracy only for the constrained Ward clustering with unconstrained version degrading significantly. All other clustering methods (k-means, and mixture models) favored a smaller number of clusters if decision was based on stability, and otherwise also produced reasonable, but worse, results if all data was provided at once and k_true was known. pvclust provided solutions with 2 to 4 clusters when target p-value was varied. When applied to fMRI data, k-means, mixture models, and hierarchical clustering were most stable again at relatively low k but hierarchical clustering stability plateaued suggesting further investigation of higher numbers of k, while pvclust yielded numerous smaller clusters. Note that hyperalignment yielded solutions with greater stability, albeit at fewer numbers of clusters. Algorithms were then reapplied to the full fMRI dataset (hyperaligned, averaged across participants) at their most stable k. Clustering of the cortical surface based on representational geometry reveals well-established functional boundaries. Although clustering algorithms produced varying solutions, results are consistent with previous reports that methods such as k-means favor smaller number of clusters and underestimate their number in simulation, with hierarchical clustering providing more realistic results. Pvclust automatically performs statistical assessment per cluster and, although conservative for simulated data, discovered large number of clusters when applied to fMRI data. Hyperalignment improves the fidelity of all the clustering solutions, supporting again its generic applicability.