拓扑数据分析在复杂脑网络分析中的应用

针对复杂脑网络分析中网络结构变化阈值选择中没有公认的标准确定合适阈值这一问题，基于拓扑分析中的持续同调性理论，本文提出一种多尺度大脑网络建模分析方法，该方法在大脑全尺度距离范围之内，通过不断增加阈值，运用Rips过滤算法捕获网络的动态持续拓扑特征，并用条形码和持续图对拓扑特征可视化，最后通过计算持续图之间的Bottleneck距离和Wasserstein距离分析持续特征的稳定性。实验结果表明，该方法能更准确地提取大脑网络的拓扑结构特征并提高诊断分类的准确性。

Application of Topological Data Analysis in Complex Brain Network Analysis

Aiming at the problem that there is no accepted standard determine appropriate threshold in brain network analysis，based on the topology data analysis of Persistent Homology(PH) theory，a multi-scale brain network modeling analysis method is proposed，in which Rips filtering algorithm is used to capture the dynamic persistence topological features by increasing threshold in the range of the whole scale distances，and the persistence topological features were visualized by barcodes and persistence diagrams，finally the stability of persistence topological features were analyzed through calculating the Bottleneck distances and Wasserstein distances between persistence diagrams.Experimental results show that this method can more accurately extract the topological features of brain networks and improve the accuracy of diagnosis and classification.