The Incremental Cluster Threshold-Free Cluster Enhancement Algorithm for Functional Connectivity Analysis

Threshold-free cluster enhancement (TFCE) is one of the most used statistical inference methods in neuroimaging, but its computational cost limits some of its applications. The current implementations recompute clusters at each threshold step, creating computation costs that poorly scale with precision increases. Furthermore, as larger samples and reduced noise increase maximum t-statistics, computational burden grows correspondingly. As the field moves towards finer parcellations, the number of FC edges grows quadratically with the number of ROIs, making TFCE computationally infeasible at the scales increasingly demanded by the field. We present Incremental Cluster TFCE (IC-TFCE), an algorithm that produces numerically equivalent results to standard TFCE while decoupling runtime from discretization precision. The IC-TFCE builds clusters incrementally from previous threshold steps rather than recomputing them, stores TFCE results on a region of interest (ROI) based structure instead of a functional connectivity (FC) edge structure for improved speed, and can be applied to voxel data through a novel graph transformation described and validated herein. This algorithm achieves a measured 3-93x speedup for FC TFCE depending on the precision parameter $dh$, making TFCE analyses with fine parcellations of 1000 or more ROIs computationally tractable for the first time. Finally, we validate correctness through mathematical proof and numerical comparison. The efficiency provided by IC-TFCE allowed a large-scale empirical power analysis across $dh$ values to guide practitioners in parameter selection for their analyses.