Ball Mapper

This code reimplements Algorithms 1 and 3 from P. Dlotko, "Ball mapper: A shape summary for topological data analysis," arXiv:1901.07410v1 [math.AT]. We require MATLAB R2015b and the Statistics and Machine Learning Toolbox.

The following functions are included:

Function	Description
ballmapper	Ball mapper
colorballmapper	Color ball mapper

ballmapper is a faithful implementation of Algorithms 1 and 3 in [1], whereas colorballmapper adds the node coloring scheme from [2]. Here is an example of the Fisher iris data with ballmapper:

load fisheriris
plot(ballmapper(meas,0.5))

One more time but with colorballmapper:

y = cellfun(@(s) strcmp(s,'versicolor')+strcmp(s,'virginica')*2,species);
[G,C] = colorballmapper(meas,y,0.5);
h = plot(G);
h.NodeCData = C;
colormap jet

Here the cell function assigns 0 to 'setosa', 1 to 'versicolor' and 2 to 'virginica' (the enumeration is arbitrary). The jet colormap is used to mimic the coloring scheme in [2], but this is optional.

My code is not optimized for speed. As a rule of thumb, do not use this code if you have more than 10,000 data points.

Tak-Shing Chan

19 August 2019

References

[1] P. Dlotko, "Ball mapper: A shape summary for topological data analysis," arXiv:1901.07410v1 [math.AT].

[2] G. Singh, F. Memoli, and G. Carlsson, "Topological methods for the analysis of high dimensional data sets and 3D object recognition," in Proc. Eurographics Symp. Point-Based Graphics, 2007, pp. 91-100.