Dynamic topological data analysis: a novel fractal dimension-based testing framework with application to brain...

Area of Science:

• Neuroscience
• Complex Systems
• Data Science

Background:

• Topological Data Analysis (TDA) is emerging in neuroscience for brain signal pattern discovery.
• Existing TDA methods often overlook the dynamic, non-stationary nature of brain signals.
• This limitation hinders a comprehensive understanding of complex neurological processes.

Purpose of the Study:

• To develop a novel fractal dimension-based testing approach for analyzing dynamic topological properties of brain signals.
• To address the limitations of static TDA methods in neuroscience.
• To investigate alterations in brain signal topology during epileptic seizures.

Main Methods:

• Representing electroencephalogram (EEG) brain signals as a sequence of Vietoris-Rips filtrations.
• Employing a fractal dimension-based testing approach to capture signal non-stationarities.
• Analyzing topological patterns across 0, 1, and 2-dimensional homology.

Main Results:

• The novel approach successfully captured dynamic topological properties in EEG signals.
• Noteworthy alterations in total persistence were observed during an epileptic seizure episode.
• These changes occurred across multiple homology dimensions (0D, 1D, 2D).

Conclusions:

• The fractal dimension-based TDA method effectively reveals dynamic topological changes in brain signals.
• Epileptic seizures induce complex topological alterations in brain activity, not just amplitude changes.
• This approach offers a more nuanced understanding of neurological event dynamics.