A library for exploring persistent homology
This paper, which is available as a shortened preprint on my personal webiste, deals with—among other things—analysing time-varying data & their topology.
This analysis relied on several statistics of persistence diagrams:
The tool persistence_diagram_statistics was developed for the purpose
of calculating these statistics and reporting them. We require a set of
persistence diagrams for demonstrating its use. Luckily, Aleph contains
several persistence diagrams as a part of its test suite,
which we may use. Having obtained them, we call the tool like this:
$ ./persistence_diagram_statistics --invalid inf Iris_dimension_*.txt
* Loading 'Iris_dimension_0.txt'...finished
* Loading 'Iris_dimension_1.txt'...finished
* Loading 'Iris_dimension_2.txt'...finished
file,power,total_persistence,total_persistence_normalized,infinity_norm,average_persistence
* Filtering all persistence pairs that contain 'inf'...
'Iris_dimension_0.txt',2,12.02,0.0858571,0.556776,0.273387
* Filtering all persistence pairs that contain 'inf'...
'Iris_dimension_1.txt',2,0.0622947,0.00222481,0.104886,0.0379867
* Filtering all persistence pairs that contain 'inf'...
'Iris_dimension_2.txt',2,0.000452442,0.000226221,0.019248,0.0141505
The output is a CSV file (written to STDOUT initially) with the required information in each column. The output format may change for versions of the software, though, but the header helps us find the desired value for each diagram easily.
Please refer to the forthcoming paper for more information. For more details about the underlying theory and data, please visit the paper code repository on GitHub.