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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.
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This content will become publicly available on July 14, 2026
Topological Time Frequency Analysis of Functional Brain Signals
We present a novel topological framework for analyzing functional brain signals using time-frequency analysis. By integrating persistent homology with time-frequency representations, we capture multi-scale topological features that characterize the dynamic behavior of brain activity. This approach identifies 0D (connected components) and 1D (loops) topological structures in the signal's time-frequency domain, enabling robust extraction of features invariant to noise and temporal misalignments. The proposed method is demonstrated on resting-state functional magnetic resonance imaging (fMRI) data, showcasing its ability to discern critical topological patterns and provide insights into functional connectivity. This topological approach opens new avenues for analyzing complex brain signals, offering potential applications in neuroscience and clinical diagnostics.
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- Award ID(s):
- 2010778
- PAR ID:
- 10657095
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- Annual International Conference of the IEEE Engineering in Medicine and Biology Society
- ISSN:
- 2694-0604
- Page Range / eLocation ID:
- 1 to 5
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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