The accurate identification of individuals from functional connectomes (FCs) is central to individualized neuro/psychiatric assessment. Traditional metrics (Pearson and Euclidean) fail to capture the non-Euclidean geometry of FCs, and geodesic metrics (affine-invariant and Log-Euclidean) require task- and scale-specific regularization and degrade in high-dimensional settings. To address these challenges, we propose the Alpha-Z Bures-Wasserstein divergence, a geometry-aware divergence for FC comparison that operates effectively without meticulous parameter tuning. Across Human Connectome Project tasks, scan lengths, and spatial resolutions, we benchmark Alpha-Z against classical and state-of-the-art manifold-based distances and quantify how varying regularization influences geodesic performance. Alpha-Z yields consistently higher identification rates, with pronounced advantages in rank-deficient regimes, and preserves performance across parcellations and conditions. We further verify generalization across resting-state and task fMRI under multiple parcellation schemes. These results position Alpha-Z as a reliable, robust, and scalable framework for functional connectivity analysis, improving sensitivity to cognitive and behavioral patterns and offering strong potential for individualized clinical neuroscience.
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