SMA-EL:A Minimal 1-cycle Construction Algorithm with Simplicial Maps Annotation and Edge Loss for Emotional Brain Networks Analysis

The brain patterns of emotional perception remain a pivotal research domain in affective neuroscience. Modeling the brain as a complex network has become a crucial approach to understanding its functions. However, traditional brain network research based on graph theory primarily focuses on dyadic interactions between brain regions, which cannot effectively characterize the information exchange process among multiple brain regions during emotional cognitive processes. To address these limitations, we shift our perspective from graph theory to the topological data analysis (TDA) of minimal 1-cycles. The 1 cycles or loops within a network represent the fundamental high order interactions in complex networks and serve as essential pathways for information transmission and integration among the distributed networks of brain regions. By focusing on cycle structures in affective brain networks, we propose a novel SMA-EL method based on the collaborative optimization of the Minimal 1-Cycle with Simplicial Maps Annotation (SMA-M1C) method and linear programming, which balances computational efficiency and method performance to reconstruct the optimal cycles in the brain network. This method is applied to the analysis of emotional brain networks in response to positive and negative emotions induced by naturalistic viewing. Comprehensive experiments demonstrate that the 1-cycle structures of the brain's functional patterns exhibit differences at both individual and group levels, aligning with prior research. Furthermore, the 1 cycles we proposed can serve as a biological marker for emotion recognition. These findings may provide new insights into the organization patterns of functional brain networks under diverse emotional states.