Persistent Homology of High dimensional data I'm new to Python (and to coding in general), so this question may be trivial. I need to compute persistent homology for a high dimensional dataset ( d ~ 1000) embedded in a vector space, but I'm having some troubles:
First, I don't even know if it's possible having such a high dimensional dataset, so the first question is, can it be done? Note that I only need the barcode diagram for H0 and H1.
Second, if it can be done, how should I do it and which function/library should I use? I have looked online but haven't found much. 
Any suggestion is accepted, since I really have no idea on how to procede.   Having something I can just copy and paste would be amazing. :D
Thank you very much!
 A: Whether estimating H0 and H1 is possible depends on more than just the dimensionality. It also depends on your sample size, which simplicial complex you are using (e.g Vietoris-Rips vs Čech), and what computing resources you have available. It also depends on the structure of the data (i.e. the actual arangement of points in $\mathbb{R}^n)$.
If you are concerned with scalability, I recommend using Vietoris-Rips (VR) complexes rather than Čech complexes because it requires checking fewer conditions. While VR is also somewhat courser, it is related to the Čech complex.
As I understand it, Cross Validated isn't really meant for software recommendations. For what it is worth, scikit-tda has worked well for my own projects. The docs have a working example you can modify to your project. You can readily adjust the code to take the results of fit_transform in order to plot barcodes instead of persistence diagrams, but they are equivalent visualizations for most purposes. Sometimes persistence diagrams are favorable for thinking about the bottleneck distance between diagrams. Beyond that, perhaps look at the table of software packages here.
