Alpha-Z divergence unveils further distinct phenotypic traits of human brain connectivity fingerprint

The accurate identification of individuals from functional connectomes (FCs) is critical for advancing individualized assessments in neuropsychiatric research. Traditional methods, such as Pearson's correlation, have limitations in capturing the complex, non-Euclidean geometry of FC data, leading to suboptimal performance in identification performance. Recent developments have introduced geodesic distance as a more robust metric; however, its performance is highly sensitive to regularization choices, which vary by spatial scale and task condition. To address these challenges, we propose a novel divergence-based distance metric, the Alpha-Z Bures-Wasserstein divergence, which provides a more flexible and geometry-aware framework for FC comparison. Unlike prior methods, our approach does not require meticulous parameter tuning and maintains strong identification performance across multiple task conditions and spatial resolutions. We evaluate our approach against both traditional (e.g., Euclidean, Pearson) and state-of-the-art manifold-based distances (e.g., affine-invariant, log-Euclidean, Bures-Wasserstein), and systematically investigate how varying regularization strengths affect geodesic distance performance on the Human Connectome Project dataset. Our results show that the proposed method significantly improves identification rates over traditional and geodesic distances, particularly when optimized regularization is applied, and especially in high-dimensional settings where matrix rank deficiencies degrade existing metrics. We further validate its generalizability across resting-state and task-based fMRI, using multiple parcellation schemes. These findings suggest that the new divergence provides a more reliable and generalizable framework for functional connectivity analysis, offering enhanced sensitivity in linking FC patterns to cognitive and behavioral outcomes.