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Abstract：
Topological data analysis (TDA) is increasingly recognized as a promising tool in the field of neuroscience, unveiling the underlying topological patterns within brain signals. However, most TDA related methods treat brain signals as if they were static, i.e., they ignore potential non-stationarities and irregularities in the statistical properties of the signals. In this study, we develop a novel fractal dimension-based testing approach that takes into account the dynamic topological properties of brain signals. By representing EEG brain signals as a sequence of Vietoris-Rips filtrations, our approach accommodates the inherent non-stationarities and irregularities of the signals. The application of our novel fractal dimension-based testing approach in analyzing dynamic topological patterns in EEG signals during an epileptic seizure episode exposes noteworthy alterations in total persistence across 0, 1, and 2-dimensional homology. These findings imply a more intricate influence of seizures on brain signals, extending beyond mere amplitude changes.
摘要：
拓扑数据分析（TDA）在神经科学领域越来越被认为是一种有前途的工具，揭示大脑信号中潜在的拓扑模式。然而,大多数与TDA相关的方法将大脑信号视为静态信号，即，它们忽略了信号统计特性中潜在的非平稳性和不规则性。在这项研究中,我们开发了一种新颖的基于分形维数的测试方法，该方法考虑了大脑信号的动态拓扑特性。通过将EEG大脑信号表示为Vietoris-Rips过滤序列，我们的方法适应了信号固有的非平稳性和不规则性。我们新颖的基于分形维数的测试方法在分析癫痫发作期间EEG信号的动态拓扑模式中的应用揭示了0、1和2维同源性的总持久性的显着变化。这些发现暗示了癫痫对大脑信号的更复杂的影响，超越单纯的振幅变化。
