I am trying to visualize a large multidimensional data set with the help of the Python Mapper (open source software package using the Mapper-Algorithm, a method of Topological Data Analysis).
With the Python Mapper one is able to construct deterministically a network (consisting of clusters, flares and loops) based on two parameter choices.
I would like to measure the robustness / stability of my network given the two parameter choices:
- robustness of the network's shape (shape can be measured by the betti numbers)
- robustness of the node's attribute (for example median value of all datapoints in the node)
I was thinking of testing the robustness with some sort of cross validation or bootstrapping. However, I am not sure how to do it.
Would you have any idea how to measure the robustness or could you link me to some literature?
