Topological Data Analysis for Time Series

We used the PTB-XL dataset available here: https://www.physionet.org/content/ptb-xl/1.0.3/#files-panel

To run, navigate to the parent directory and pass with the arguments: fig, ax = main(data, t, max_edge_length, min_dimension, max_dimension) then to display the figure, just call plt.show().

Code in driver can be easily modified to save plots as objects or images or return additional information such as Betti Numbers or stars etc.

For inputs:

1. data is the matrix as a numpy array or pandas dataframe

2. t is a 1-D array with length of that of the the columns of data. For time series, this will be an array of timestamps.

3. max_edge_length is the maximum filtration or "alpha" value

4. min_dimension is the lower bound for the dimension of homological features
to be returned and produced in the barcode graph

5. max_dimension is the upper bound for the dimension of homological features to be returned and produced in the barcode graph

The pipeline is structured as follows:

1. input data is received as a matrix in the form of a numpy array or pandas dataframe

2. a pairwise distance matrix is computed from the data with respect to the first Wasserstein distance

3. a simplex tree object is computed from the distance matrix

4. a persistence barcode plot is generated and returned from the simplex tree object



This pipeline was originally used as part of my M.S. project, but the applications are not limited to ECG data.