graphKKE: graph Kernel Koopman Embedding.

Code for the paper Melnyk K., Klus S., Montavon G., Conrad T. "GraphKKE: Graph Kernel Koopman Embedding for Human Microbiome Analysis", https://arxiv.org/abs/2008.05903.

Repository Structure

• graphkke/algorithm: consists of the main function for the grapphKKE method;
• graphkke/graph: consists of the class Graph and of C++ implemenatation of WL kernel with multithreading. The Python interface is created from a C++ source code that is wrapped with SWIG (http://www.swig.org);
• graphkke/generate_graphs: consists of functions and classes for generating the benchmark graphs with metastable behavior;
• examples: consists of experiments with the benchmark data and real-world datasets, and also a script for generating benchmark data;
• data: contains OTU tables and constructed adjacency matrices. Microbiome data is coming from [1] and [2].

Install

• The package uses setuptools, which is a common way of installing python modules. To install:
  • To install in your home directory, use:

    $ git clone https://github.com/k-melnyk/graphKKE.git
    $ cd graphKKE
    
    $ python setup.py build
    $ python setup.py install
    
    NOTE:
    In the Anaconda package, in the file "anaconda3\Lib\site-packages\graphkke-0.1.1-py3.8-win-amd64.egg\graphkke\graph\GraphLib_c.py" do the following:
    #if __package__ or "." in __name__:
    #from . import _GraphLib_c
    #else:
    import _GraphLib_c
    

Examples

• You need first convert your array of adjacency matrices adj_matrix or adjacency lists adj_list into graph data type, where node_labels is a list of node labels for each time-point.

  from graphkke.algorithm import m_graphkke
  import graphkke.algorithm.kernels as kernels
  import graphkke.graph.graph as gl
  
  graphs = []
  
  for ind, graph in enumerate(adj_matrix):
      graph = gl.Graph(graph)
      graph.add_node_labels(node_labels[ind])
  
      graphs.append(graph)

  Or adjacency lists:

  graphs = []
  
  for ind, graph in enumerate(adj_list):
      graph = gl.Graph(graph, num_nodes)
      graph.add_node_labels(node_labels[ind])
  
      graphs.append(graph)

• For running graphKKE:

  # Hyperparameters of graphKKE
  epsilon = 0.5
  operator = 'K'
  num_iterations = 5
  k = kernels.WlKernel(num_iterations)
  
  # Run graphKKE method
  m_graphkke.graphkke(graphs, k, tau=1, epsilon=epsilon, outdir=outdir)

• In order to run WL kernel:

  import graphkke.graph.graph as gl
  
  kernel = gl.wl_subtree_kernel(graph, n_iterations)

References

[0] Shervashidze N. et al. "Weisfeiler-Lehman GraphKernels". In: Journal of Machine Learning Research 12 (2011), pp. 2539–2561.

 @article{WL,
   title={Weisfeiler-Lehman Graph Kernels.},
   author={Shervashidze N. and Schweitzer P. and Jan van Leeuwen E. and Mehlhorn K. and Borgwardt K.},
   journal={Journal of Machine Learning Research},
   year={2011},
   volume={12},
   pages={2539-2561}
 }

[1] Hsiao A. et al. "Members of the human gut mi-crobiota involved in recovery from Vibrio choleraeinfection". In:Nature 515 (Jan. 2014), pp. 423–426.

@article{CholeraInfOriginal,
 author = {Hsiao A. and Shamsir Ahmed AM. and Subramanian S. and Griffin NW. and Drewry LL. and Petri WA. and Haque R. and Ahmed T. and Gordon JI.},
 year = {2014},
 month = {01},
 title = {Members of the human gut microbiota involved in recovery from Vibrio cholerae infection},
 volume = {515},
 pages={423-426},
 journal = {Nature},
 doi = {10.1038/nature13738}
 }

[2] Caporaso J. et al. "Moving pictures of the humanmicrobiome". In: Genome biology 12. May 2011, R50.

@article{MovingPicture,
 author = {Caporaso J. and Lauber C. and Costello E. and Berg-Lyons D. and González A. and Stombaugh J. and Knights D and Gajer P. and Ravel J. and Fierer N. and Gordon J. and Knight R.},
 year = {2011},
 month = {05},
 pages = {R50},
 title = {Moving pictures of the human microbiome},
 volume = {12},
 journal = {Genome biology},
 doi = {10.1186/gb-2011-12-5-r50}
 }

[3] Klus S. et al. "A kernel-based approach to molecular conformation analysis". In: Journal of Chemistry Physics 149. 2018.

@article{KlusMolecularAnalysis,
title={A kernel-based approach to molecular conformation analysis},
author={Klus S. and Bittracher A. and Schuster I. and Schütte C.},
journal={Journal of Chemical Physics},
year={2018},
volume={149},
doi={10.1063/1.5063533}
}