Mapper Python Implementation

A few posts ago I wrote about the mapper construction by Carlsson-Memoli-Singh and want to follow up on that a little.

I wrote a straightforward implementation of the construction in Python. It can be found here

•  github.com/mirkoklukas/tda-mapper-py. 

Below you find an example how to use it.

Example Usage

from tdamapper.clusterfunctions import VietorisRipsClustering
from tdamapper import mapper
from tdamapper.referenceMap import create_functional_cover, coordinate_projection
import json

# Example data set
with open("./example/dataset.json") as f:
    data = json.load(f);
    data = [ tuple(p) for p in data ]

# Gather the mapper input
VR = VietorisRipsClustering(epsilon = 0.6) 
zAxis = coordinate_projection(axis=2, domain=data)
funcCover = create_functional_cover(endpoints=range(-12,12), overlap=0.5)

# Run the alogrithm
result = mapper(VR, zAxis, funcCover)

Below you see a visualization of the mapper result. The graph is colored by the values of zAxis , the projection on the z-axis. The size of the nodes reflects the size of the associated clusters.

The take away should be that there are actually two separate branches growing out of a bigger cluster. You shouldn't focus too much on the fact that the two branches cross each other. Although it reflects the reality of the situation pretty well, it is rather a bi-product of the fact that the data set lives in so few dimensions.

Mapper result.

And indeed (what a terrible example it would have been if that was not the case) looking at a 3d plot of the original dataset we see that this reflects the shape pretty well.

Original data set.