Mapper-Based Topological EEG Modeling for Task Representation in Robot-Assisted Surgery

Robot-assisted surgery (RAS) requires objective and interpretable frameworks for task representation and analysis. Although electroencephalography (EEG) has been increasingly used to capture neural correlates of surgical behavior, most existing methods rely on point-wise classification or low-dimensional geometric embeddings, offering limited insight into the organization of task-related neural representations. To address this limitation, a Mapper-based topological EEG modeling framework is introduced to characterize task-related neural state spaces during robot-assisted surgical tasks. Using EEG recordings from an RAS dataset covering both coarse- and fine-grained surgical tasks, phase-locking value (PLV) connectivity features are extracted across canonical frequency bands, and Mapper is used to model the organization and transitions of task-related neural states. Persistent homology and BrainNetCNN are also incorporated as additional structural and global modeling approaches for a more balanced comparison. Within-subject analyses show that the proposed framework consistently captures coherent and separable task-related structures, with frequency-dependent neural topology enhancing task discrimination, particularly in higher-frequency bands. In six-class task modeling, an average accuracy of 94.78% is achieved. Comparative evaluation against embedding- and clustering-based baselines shows that Mapper provides stronger structural consistency and clearer task-related organization. In cross-subject settings, however, substantial inter-subject variability remains, indicating that task-related neural topology is strongly individualized. These results indicate that Mapper-based topological modeling provides an interpretable foundation for task representation and personalized EEG-based analysis in RAS. This framework may further inform future individualized monitoring of task execution and training analysis in robot-assisted surgery.