API Reference

persim.bottleneck(dgm1, dgm2, matching=False)[source]

Perform the Bottleneck distance matching between persistence diagrams. Assumes first two columns of S and T are the coordinates of the persistence points, but allows for other coordinate columns (which are ignored in diagonal matching)

Parameters:
dgm1: Mx(>=2)

array of birth/death pairs for PD 1

dgm2: Nx(>=2)

array of birth/death paris for PD 2

matching: bool, default False

if True, return matching information

Returns:
d: float

bottleneck distance between dgm1 and dgm2

matching: tuples of matched indices

if input matching=True, then return matching

D: (N+M)x(N+M) cross-similarity matrix

if input matching=True, then return D

persim.sliced_wasserstein(PD1, PD2, M=50)[source]

Implementation of Sliced Wasserstein distance as described in Sliced Wasserstein Kernel for Persistence Diagrams by Mathieu Carriere, Marco Cuturi, Steve Oudot (https://arxiv.org/abs/1706.03358)

Parameters:
PD1: np.array size (m,2)

Persistence diagram

PD2: np.array size (n,2)

Persistence diagram

M: int, default is 50

Iterations to run approximation.

Returns:
sw: float

Sliced Wasserstein distance between PD1 and PD2

persim.heat(dgm1, dgm2, sigma=0.4)[source]

Return the pseudo-metric between two diagrams based on the continuous heat kernel as described in “A Stable Multi-Scale Kernel for Topological Machine Learning” by Jan Reininghaus, Stefan Huber, Ulrich Bauer, and Roland Kwitt (CVPR 2015)

Parameters:
dgm1: np.array (m,2)

A persistence diagram

dgm2: np.array (n,2)

A persistence diagram

sigma: float

Heat diffusion parameter (larger sigma makes blurrier)

Returns
——–
dist: float

heat kernel distance between dgm1 and dgm2

class persim.PersImage(pixels=(20, 20), spread=None, specs=None, kernel_type='gaussian', weighting_type='linear', verbose=True)[source]

Initialize a persistence image generator.

Parameters:
pixels : pair of ints like (int, int)

Tuple representing number of pixels in return image along x and y axis.

spread : float

Standard deviation of gaussian kernel

specs : dict

Parameters for shape of image with respect to diagram domain. This is used if you would like images to have a particular range.

kernel_type : string or …

TODO: Implement this feature. Determine which type of kernel used in the convolution, or pass in custom kernel. Currently only implements Gaussian.

weighting_type : string or …

TODO: Implement this feature. Determine which type of weighting function used, or pass in custom weighting function. Currently only implements linear weighting.

transform(diagrams)[source]

Convert diagram or list of diagrams to a persistence image.

Parameters:
diagrams : list of or singleton diagram, list of pairs. [(birth, death)]

Persistence diagrams to be converted to persistence images. It is assumed they are in (birth, death) format. Can input a list of diagrams or a single diagram.