Re: How to know which points form some bar code

Dmitriy Morozov
 

It's not possible to pick a unique 1-cycle; there are many cycles in a homology class. But it's possible to extract one of them, the one that the matrix reduction chose as a representative. Each column in the reduced matrix represents such a cycle, so you could pick the one that corresponds to the point of the persistence diagram you are interested in. From the documentation:

 >>> m = d.homology_persistence(f)
 >>> for i,c in enumerate(m):
 ...     print(i, c)
 0
 1
 2 1*0 + 1*1
 3
 4 1*1 + 1*3
 5

The 1*1 + 1*3 is one such cycle. You could iterate over it, and use the indices (1 and 3 in this case) to access the corresponding simplices in the filtration.

Dmitriy 

On Tue, Jul 24, 2018 at 11:08 AM, Hongyuan <zhanghon@...> wrote:

Hi,

 

For a bar code, is it possible to know which points form this bar code? For example, if I use a distance matrix to create a filtration and then a reduced matrix, then I generate the bar code graph for the first dimension. If I have a bar code that lasts for an interval [a, b) in the first dimension, could I know which data points form this loop (a 1-dimensional bar code represents a loop)? Could I know the indices of the points in the distance matrix?

 

Thank you,

 

Hongyuan


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