As I understand it, your code goes through and adds a simplex of the Delaunay triangulation if all of the edges of that simplex are under a certain threshold. This does not quite match the definition of an alpha complex; what you have is really like a hybrid between the alpha complex and the Vietoris Rips complex. The intersection of the Voronoi balls doesn’t quite behave like this.

Let’s take an example of an equilateral triangle of side length 1. Your code would add all of the edges and the triangle at the same scale of 1 (radius 1/2). But the triangle is actually added slightly later than the edges, because the Voronoi balls meet at the circumcenter, which occurs at a ball radius of 1/sqrt(3) > 1/2

The figure at this link below shows this scenario (where I’m using the scale as the radius instead of the diameter, as your code is doing)

http://www.ctralie.com/Other/AlphaEquilateral.svg

To see more info, GUDHI has some nice pseudocode

http://gudhi.gforge.inria.fr/doc/latest/group__alpha__complex.html

I’ve also been casually working on another Python implementation here with fewer dependencies, which is more in the spirit of yours:

https://github.com/scikit-tda/cechmate/blob/master/cechmate/filtrations/alpha.py

As for references, I’d also highly recommend “The Union of Balls and Its Dual Shape” by Herbert Edelsbrunner.

Best,

Chris Tralie

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]]>learned lot of things from it regarding blogging.

thanks.

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]]>Thanks a lot !!

I know how to do the network analysis, and I am thinking whether I can use the result of DT matrix to get the network analysis

The problem I have is how to check the whole result of the DT matrix, since the code “get_token_occurences” and “get_doc_frequency” can only get the single one.

Thank you very much

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]]>The featured image (or the feature at the top) is more than the DT matrix. It is more about the network analysis or graph theory, where one explored the relationship between words. It is quite another domain knowledge.

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]]>I also have a question about modeling the result. The code you showed can just get the single word result, but how to check all results and make a network analysis like the picture at the top.

Thanks

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