2.4.2. Distances

This module provides algorithms to compute pairwise distances between persistence diagrams. The bottleneck distance and wasserstein distance are available.

teaspoon.TDA.Distance.bottleneckDist(pts0: ndarray, pts1: ndarray, matching=True, plot=True)

Compute the bottleneck distance between the diagrams pts0, pts1 using the persim package: https://persim.scikit-tda.org/en/latest/index.html

Parameters:

• pts0 (array of shape (n_top_features, 2)) – The first persistence diagram

• pts1 (array of shape (n_top_features, 2)) – The second persistence diagram

• matching (boolean, True returns matched array)

• plot (boolean, True provides plot of matching points. Matching must be true for plot to return.)

Returns:

distance – The bottleneck distance between diagrams pts0 and pts1

Return type:

float

teaspoon.TDA.Distance.wassersteinDist(pts0: ndarray, pts1: ndarray, p: int = 2, q: int = 2, y_axis: AnyStr = 'death') → float

Compute the Persistant p-Wasserstein distance between the diagrams pts0, pts1 using optimal transport.

Parameters:

• pts0 (array of shape (n_top_features, 2)) – The first persistence diagram

• pts1 (array of shape (n_top_features, 2)) – The second persistence diagram

• y_axis (optional, default="death") –

  What the y-axis of the diagram represents. Should be one of

  • "lifetime"

  • "death"

• p (int, optional (default=2)) – The p in the p-Wasserstein distance to compute

• q (1, 2 or np.inf, optional (default = 2)) – The q for the internal distance between the points, L_q. Uses L_infty (Chebyshev) distance if q = np.inf. Currently not implemented for other q.

Returns:

distance – The p-Wasserstein distance between diagrams pts0 and pts1

Return type:

float

Further information can be found in the Distance Notebook.