/coalescent_embedding

MATLAB code for performing the coalescent embedding

Primary LanguageMATLAB

Coalescent embedding

Reference

A. Muscoloni, J. M. Thomas, S. Ciucci, G. Bianconi, and C. V. Cannistraci, "Machine learning meets complex networks via coalescent embedding in the hyperbolic space", Nature Communications, 8:1615, 2017. https://www.nature.com/articles/s41467-017-01825-5

Folders description

  • coemb_svds_eigs
    It contains the main function for performing the coalescent embedding: coalescent_embedding.m. The dimension reduction techniques exploits the MATLAB function eigs and the function lansvd from the PROPACK library, which have a time complexity of O(kN^2). Since in our case k=2 or k=3, it is practically O(N^2). The other files are support functions for computing the edge betweenness centrality (from the MatlabBGL library) or for computing the SVD (from the PROPACK library). The subfolder mex_all_platforms contains the MEX files for different platforms.

    The support functions of the MatlabBGL library have been downloaded at:
    http://mathworks.com/matlabcentral/fileexchange/10922-matlabbgl
    The support functions of the PROPACK library have been downloaded at:
    https://github.com/mavenlin/PropackMatlab4Windows
    https://github.com/epfl-lts2/unlocbox/tree/master/test_bench/private

  • coemb_svd_eig
    It contains the main function for performing the coalescent embedding: coalescent_embedding.m. The dimension reduction techniques exploits the MATLAB built-in functions svd and eig, which have a time complexity of O(N^3). The other files are support functions for computing the edge betweenness centrality (from the MatlabBGL library). The subfolder mex_all_platforms contains the MEX files for different platforms.

  • visualization_and_evaluation

    • plot_embedding.m: plot the embedding given the network and the coordinates.
    • angular_alignment.m: align two embeddings of the same network, useful for a comparison of the plots.
    • greedy_routing.m: evaluate the greedy routing given the network and the coordinates.
    • compare_embedding.m: evaluate the comparison of two embeddings computing HD-correlation and C-score.
    • angular_separation_index: evaluate the separation of groups over the circle circumference or sphere surface (for details please see the README within the subfolder).

  • usage_example
    It contains a script RUN_EXAMPLE.m with two usage examples, all the functions needed for the embedding, visualization and evaluation (described at the previous points) and two example networks (opsahl_11.mat and PSO_network.mat).

    1. Example 1
      • 2D embedding of PSO network using RA1-LE-EA
      • evaluate comparison of embedding with original coordinates
      • plot comparison of embedding with original coordinates
    2. Example 2
      • 3D embedding of opsahl-11 network using RA1-ISO
      • evaluation of 3D greedy routing
      • 3D plot colored by ground-truth communities

  • edgelist_to_matrix
    It contains the function create_matrix.m for creating an adjacency matrix starting from an edge list, an example of edge list (opsahl_11.txt) and a script RUN.m with an usage example of the function.

Contact

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