A straightforward implementation of the mapper construction by Carlsson-Memoli-Singh. I wrote a little blog post about it at http://blog.mirkoklukas.com/
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.
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.