persim 0.0.5

Python implementation persistent images representation of persistence diagrams.

Persim

Persim is a Python implementation of Persistence Images as first introduced in https://arxiv.org/abs/1507.06217.

It is designed to interface with Ripser, though any persistence diagram should work fine.

Setup

Currently, the only option is to install the library from source:

pip install persim

Usage

First, construct a diagram. In this example, we will use Ripser.

import numpy as np
from ripser import Rips
from sklearn import datasets

data = np.concatenate([150 * np.random.random((300,2)), 
                       10 + 10 * datasets.make_circles(n_samples=100)[0],
                       100 + 20 * datasets.make_circles(n_samples=100)[0]])

rips = Rips()
dgm = rips.fit_transform(data)
diagram = dgm[1] # Just diagram for H1

Then from this diagram, we construct the persistence image

from persim import PersImage

pim = PersImage()
img = pim.transform(diagram)
pim.show(img)

TODO

• Implement a variety of weighting and kernel functions.

References:

Persistence Images were first introduced in Adams et al, 2017. Much of this work, an examples contained herein are inspired by the work of Obayashi and Hiraoka, 2017. Choices of weightings and general methods are often derived from Kusano, Fukumizu, and Yasuaki Hiraoka, 2016.