How to extract connected components from persistence diagram?

Question

From the given point cloud (Fig. 1), I use Scipy-TDA to extract persistence diagram (Fig. 2). What I’m interested in is to extract 3 circles. For example, I’d like to know 3 center points and labels for each point. I’m quite newbie to topological data analysis. Anyone to help me or guide the process?

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Edit: To show a challenging case, my data is like the following where 12 ellipses should be clustered.

data analysis

Edit: To show a challenging case, my data is like the following where 12 ellipses should be clustered.

Abdullah Ali Sivas · Answer

If you can represent your data as a sparse graph you can use; https://docs.scipy.org/doc/scipy-0.19.0/reference/generated/scipy.sparse.csgraph.connected_components.html

For the cases you are asking about, I would define a parameter $varepsilon$ such that for two nodes $p, q$ are connected via an edge $e$ if $d(p,q)<varepsilon$ -with $d(cdot,cdot)$ is some distance function-.

I have done a similar project, albeit not for topological data analysis, in MATLAB and this approach worked well there. Both MATLAB and SciPy have great graph theory tools.

How to extract connected components from persistence diagram?

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