This material presents Python tutorials on Dynamic TDA. To make the tutorials as friendly as possible, we base them on the Scikit-TDA project. More specifically, we will use the Ripser and Persim libraries as the backbone of our code.
The main topics of the tutorials are as follows:
- Persistence homology (PH)
- Time delay (TDE) and sliding window (SWE) embeddings for time series data
- Persistence diagrams (PDs)
- Wasserstein distance computations between PDs
- Persistence landscapes (PLs)
- Application to Epileptic Seizure EEG data set
- Higuchi Fractal dimension-based testing
These TDA tutorials are user friendly and aim to illustrate the key concepts behind Dynamic-TDA. It includes multiple examples with simulated data sets.
I would like to acknowldege Dr. Beth Malow, from the Department of Neurology at Vanderbilt University (formerly with the Department of Neurology at University of Michigan) for sharing the Epileptic Seizure EEG data set with us. You need to acknowldege Dr. Beth Malow and cite the following papers if you plan to use this data set in your own research projects.
- Ombao, H., Raz, J., von Sachs, R. and Malow, B. (2001). Automatic Statistical Analysis of Bivariate Non-Stationary Time Series, J Amer Stat Assoc, 96, 543-560.