Bottleneck distance user manual

Definition

Author:François Godi
Introduced in:GUDHI 2.0.0
Copyright:GPL v3
Requires:CGAL \(\geq\) 4.8.0
   
_images/perturb_pd.png

Bottleneck distance is the length of the longest edge

Bottleneck distance measures the similarity between two persistence diagrams. It’s the shortest distance b for which there exists a perfect matching between the points of the two diagrams (+ all the diagonal points) such that any couple of matched points are at distance at most b.
Bottleneck distance user manual  

Function

gudhi.bottleneck_distance()

This function returns the point corresponding to a given vertex.

Parameters:
  • diagram_1 (vector[pair[double, double]]) – The first diagram.
  • diagram_2 (vector[pair[double, double]]) – The second diagram.
  • e (float) –

    If e is 0, this uses an expensive algorithm to compute the exact distance. If e is not 0, it asks for an additive e-approximation, and currently also allows a small multiplicative error (the last 2 or 3 bits of the mantissa may be wrong). This version of the algorithm takes advantage of the limited precision of double and is usually a lot faster to compute, whatever the value of e.

    Thus, by default, e is the smallest positive double.

Return type:

float

Returns:

the bottleneck distance.

Basic example

This example computes the bottleneck distance from 2 persistence diagrams:

import gudhi

diag1 = [[2.7, 3.7],[9.6, 14.],[34.2, 34.974], [3.,float('Inf')]]
diag2 = [[2.8, 4.45],[9.5, 14.1],[3.2,float('Inf')]]

message = "Bottleneck distance approximation=" + '%.2f' % gudhi.bottleneck_distance(diag1, diag2, 0.1)
print(message)

message = "Bottleneck distance exact value=" + '%.2f' % gudhi.bottleneck_distance(diag1, diag2, 0)
print(message)

The output is:

Bottleneck distance approximation=0.81
Bottleneck distance exact value=0.75