Study on the effectiveness of brain dynamic network clustering with standardized distances in space-time constraints

In order to solve the problem that the traditional clustering method in dynamic functional connection (DFC) analysis is sensitive to data distribution and ignores the continuity of time series, this paper proposes an improved clustering effectiveness evaluation framework based on spatiotemporal characteristics. Firstly, the Standardized Corrected Distance (NCD) was designed to replace the Euclidean measure, and the distance weight was dynamically adjusted by the standard deviation of the feature dimension to solve the problem of BOLD signal scale difference in multiple brain regions. Secondly, the penalty term for state transition between sliding windows was introduced to construct the spatiotemporal joint optimization objective function to constrain the physiological rationality of state switching in the brain network. The reconstruction of the evaluation function is further integrated to improve the stability of the optimal clustering number selection. In the SimTB simulation data test, the accuracy of the proposed method in the three-classification and five-classification tasks reaches $84 \%$ and $80 \%$, which is improved compared with the traditional method, and the variance of state dwell time variation is reduced. Empirical studies based on ASD autism dataset show that the accuracy of health and disease classification is higher when the optimal cluster number $\text{k}=4$. This method provides a more reliable dynamic connectivity quantification tool for the study of brain disease heterogeneity, and shows potential application value in the analysis of dynamic functional connectivity in the diagnosis of brain diseases.