Clustering-based inter-regional correlation estimation

A novel non-parametric estimator of the correlation between grouped measurements of a quantity is proposed in the presence of noise. The main motivation is functional brain network construction from fMRI data, where brain regions correspond to groups of spatial units, and correlation between region pairs defines the network. The challenge resides in the fact that both noise and intra-regional correlation lead to inconsistent inter-regional correlation estimation using classical approaches. While some existing methods handle either one of these issues, no non-parametric approaches tackle both simultaneously. To address this problem, a trade-off between two procedures is proposed: correlating regional averages, which is not robust to intra-regional correlation; and averaging pairwise inter-regional correlations, which is not robust to noise. To that end, the data is projected onto a space where Euclidean distance is used as a proxy for sample correlation. Hierarchical clustering is then leveraged to gather together highly correlated variables within each region prior to inter-regional correlation estimation. The convergence of the proposed estimator is analyzed, and the proposed approach is empirically shown to surpass several other popular methods in terms of quality. Illustrations on real-world datasets that further demonstrate its effectiveness are provided.