TDA-HC

This repository contains all data and code for the experiments for the paper "A New Non-archimedan Metric on Persistent Homology" by myself and Atabey Kaygun.

Programming Language Versions We Used:

• Python 3.7.8

  • Numpy 1.18.5
  • Scipy 1.5.4
  • Pandas 1.0.4
  • Matplotlib 3.2.1
  • GUDHI 3.2.0

• SageMath 9.1 Shell

• R 3.6.3

  • TDA 1.6.9
  • vegan 2.5.6
  • repr 1.1.0
  • dendextend 1.13.4

1_Data2Diagram_GUDHI_Dionysus.R

This code is for obtaining topological features (intervals) of point clouds by using different algorithm such as GUDHI and Dionysus2

• On terminal, type

Rscript 1_Data2Diagram_GUDHI_Dionysus.R

2_Barcodes_GUDHI_Dionysus.py

This code is for visualizing the output of persistent homology as intervals. The output consists of barcodes created by two different libraries on the same data.

• On terminal, type

python 2_Barcodes_GUDHI_Dionysus.py

3_Data2Rips_Gudhi.py

Here, we obtain the filtered Vietoris Rips complex by using GUDHI library.

• On terminal, type

python 3_Data2Rips_Gudhi.py

4_Rips2Homological_Distance.sage

This code calculates the homological distance matrix.

• On SageMath shell, type

sage 4_Rips2Homological_Distance.sage 24 0 0 0.30 0.01

• sample size = 24
• degree of homology = 0
• epsilon start = 0
• epsilon end = 0.30
• epsilon step = 0.01

5_Compare_Dendrogram.R

Here, this code compares the two dendrograms one from the hierarchical clustering and one from the zeroth persistent homology. The output is the result of the Mantel Test.

• On terminal, type

Rscript 5_Compare_Dendrogram.R