Topological Signatures of Brain Dynamics: Persistent Homology Reveals Individuality and Brain-Behavior Links

Yue Wang¹Junxing Xian^2*Yuanyuan Chen^1*YAN YAN^3,4*

• ¹Tianjin University, Tianjin, Tianjin, China
• ²Beijing Normal University, Beijing, China
• ³Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences (CAS), Shenzhen, Guangdong Province, China
• ⁴Wenzhou Institute of Technology, Wenzhou, Zhejiang Province, China

Understanding individual differences in brain dynamics is a central goal in neuroscience. While conventional time-series features capture local signal properties, they often miss the deeper structure embedded in the brain's complex activity patterns. Here, we introduce persistent homology—a method from topological data analysis—to extract structural topological features from resting-state fMRI time series. By identifying topological patterns such as connected components and loops in time-delay embedded trajectories, we capture global dynamic properties beyond the reach of conventional methods. Topological features exhibit high test-retest reliability and enable accurate individual identification across sessions. In classification tasks, they outperform commonly used temporal features in predicting gender. Canonical correlation analysis further reveals a significant brain-behavior mode linking network-level topological patterns to a continuum of cognitive strengths and behavioral risk. Regression analyses across behavioral domains show that persistent homology features better predict higher-order traits such as cognition, emotion, and personality, while traditional features perform slightly better in domains like sensory. These findings suggest that persistent homology provides a robust and informative framework for modeling individual differences in brain function, offering new avenues for personalized neuroimaging analysis.