HERMES

HERMES is a software package for simultaneous topological data analysis (persistent Betti numbers) and geometric data analysis (persistent eigenvalues). It is realized through persistent spectral graph theory. In the present release, we consider an implementation in alpha complex and Vietories-Rips complex.

Requirements

• cmake 3.1 or higher
• gcc 7.5.0
• GNU Make 4.1
• MATLAB
• CGAL 4.14

Install, Build, and Run

You can intall HERMES from the development repository:

 git clone https://github.com/wangru25/HERMES.git 

Or directly download the software package from here

How to build the job:

 mkdir build 

 cd build 

 cmake .. 

 make 

How to run:

 ./Snapshot InputData Filtration Num P Complex

• InputData: The point cloud data is allowed
• Filtration: The filtration parameters. Note: For alpha complex, the input filtration Filtration_alpha is actually radius^2. For Vietoris–Rips complex, the input filtration Filtration_rips is 2*radius, which match with the other open-source packages such as Ripser, Gudhi, and Diode.
• Num: The number of eigenvalues that will be calculated
• P: The persistent value, which describes the increasement of radius.
• Complex: Two choices, 1) Alpha complex 2) Vietoris–Rips complex

For Vietoris-Pis complex:

 cd examples

 ./../build/Snapshot Test_C60.xyz filtration.txt 100 0.5 r 

For alpha complex:

 cd examples

 ./../build/Snapshot Test_C60.xyz filtration.txt 100 0.5  

The output files:

• HERMES/examples/snapshots_vertex.txt: The spectra of the 0th-order persistent Laplacian. Each line presents harmonic or non-harmonic eigenvalues at a specific filtration value.
• HERMES/examples/snapshots_edge.txt: The spectra of the 1st-order persistent Laplacian. Each line presents harmonic or non-harmonic eigenvalues at a specific filtration value.
• HERMES/examples/snapshots_facet.txt: The spectra of the 2nd-order persistent Laplacian. Each line presents harmonic or non-harmonic eigenvalues at a specific filtration value.

References

1. R. Wang, R. Zhao, E. Ribando-Gros, J. Chen, Y. Tong, and G.-W. Wei. Hermes: Persistent spectral graph software, 2020.
2. R. Wang, D. D. Nguyen, and G.-W. Wei. Persistent spectral graph. International Journal for Numerical Methods in Biomedical Engineering, page e3376, 2020.