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Selecting features as (network) nodes.


This work is still ongoing, and some parts have not been experimentally validated nor (for obvious reasons) peer-reviewed yet.


The goal of this project is to provide a tool for various flavors of network-guided feature selection with graph cuts. This tool is meant for feature selection on data with the following characteristics:

  • a relevance score, which characterizes the importance of each feature, is available. The underlying premise is that the relevance of a set of features is the sum of the relevances of that set. Some examples of relevance scores include Pearson's correlation and SKAT (Wu et al., 2011);
  • a network (graph) is given over the features. In this network, nodes (vertices) represent features, while links (edges) connect two features that "work together" or "should tend to be selected together". The network can be weighted.

In this context, feature selection is done by finding the set of features that maximizing an objective function that is the sum of

  • the relevance of the selected features;
  • a regularization term that (1) encourages sparsity (few features are selected) and (2) encourages the selected features to be connected to each other in the network.

The resulting optimization problem can be rewritten as a minimum cut problem. We solve it using a version of the Shekhostov implementation (Shekhovtsov & Hlavac, 2011) of the Goldberg-Tarjan-Cherkassky algorithm (Cherkassky et al., 1995.)

This approach was first described in Azencott et al. (2013).

There are also several multi-task variants of this, in which one attempts to solve the same problem on multiple related tasks simultaneously. The features aren't necessarily the same for all tasks (although a large overlap is required for the approach to make sense) and the networks can also be task specific.

The first of these multitask approaches was described in Sugiyama et al. (2014).

These approaches have been developed with biomarker discovery in mind. In this case, the features are SNPs or other biomarkers (genes, epigenetic markers...) and we make use of biological networks.

Technical details are available under paper/tech_notes.pdf (to be compiled from paper/tech_notes.tex)


This work was initiated at the Centre for Computational Biology (CBIO) of MINES ParisTech and Institut Curie by Chloé-Agathe Azencott. Jean-Daniel Granet and Killian Poulaud worked on previous, private versions of this code. Please contact Chloé-Agathe Azencott at for all inquiries.



cd code


Modifications to

  • You might need to replace -I/usr/include/python2.7 with the path to your Python.h (Python development header).
  • On some architectures, or if you have an older version of gcc, you will need to add the flag -D__USE_XOPEN2K8 to the g++ line. This is linked to gcc's fixinclude mechanism, and usually manifests itself as errors regarding the type name __locale_t.
  • If you're getting undefined reference to 'clock_gettime' and 'clock_settime' errors, you might need to add the flag -lrt to the g++ line.

On the CBIO SGE cluster, use ./

cd code


For testing (doctest) the core optimization module run by code/

cd code
python -t -v


Core optimization

The core optimization (for given regularization parameters) is run by code/ See code/ for usage.

Single task example:

 python --num_tasks 1 --networks ../data/simu_01/ \
       --node_weights ../data/simu_01/simu_01.scores_0.txt -l 0.001 -e 0.02 --output runtime.txt

Multitask example:

 python --num_tasks 2 --networks ../data/simu_01/ \
       --node_weights ../data/simu_01/simu_01.scores_0.txt ../data/simu_01/simu_01.scores_1.txt \
       --covariance_matrix ../data/simu_01/simu_01.task_similarities.txt -l 0.001 -e 0.02 -m 0.01

The user can either provide a covariance or a precision matrix between tasks. The covariance matrix encodes a notion of similarity between the tasks. The precision matrix is its inverse, and its off-diagonal entries can be interpreted as the normalized opposite of the partial correlation between the corresponding tasks. The methods only makes it possible to account for positive or non-existant partial correlations, meaning that positive off-diagonal entries of the precision matrix, if any, will be thresholded to 0.

If no covariance nor precision matrix is given, a precision matrix with (<number of tasks>-1+epsilon) on the diagonal and -1 off the diagonal is used and the value of eta is adjusted to match the formulation of MultiSConES by Sugiyama et al. (2014).

Data generation

Simulate simple data :

code/ generates synthetic data for experiments:

  • a modular network (modules of MOD_SIZE features fully connected) over the features;
  • a genotype (SNP) matrix X of random integers between 0 and 2;
  • a covariance matrix Omega of similarities between tasks;
  • for each task, NUM_CAUSAL_EACH causal features (SNPs) randomly chosen among the first NUM_CAUSAL_TOTAL features, with corresponding weights, generated so as to respect the covariance structure given by Omega (inverse of the precision matrix);
  • the corresponding k phenotypes and vectors of node weights (computed as Pearson's correlation).


cd code
python -k 3 -m 1000 -n 50 ../data/simu_synth_01 simu_01 --verbose

The number of nodes MOD_SIZE = 15 in each module, the total number of features possibly causal NUM_CAUSAL_TOTAL = 30 among which are chosen NUM_CAUSAL_EACH = 20 causal features for each task are hardcoded in code/

Simulate gwas :

Network generation :

code/ generate the SNPs network using a .map file (Example : data/synthetic_gwas/, a .sif file (Example : data/synthetic_gwas/hugo_ppi.sif), a list of gene (Example : data/synthetic_gwas/mart_export.txt) and a window value. Example : ''' python code/ data/synthetic_gwas/hugo_ppi.sif data/synthetic_gwas/ data/synthetic_gwas/mart_export.txt 10 snp_network.dimacs '''

In, for some reasons, you want to modify code/, we provide a bunch of file in data/synthetic_gwas/tests_snp_network_from_gene_network to test some situations describded in data/synthetic_gwas/tests_snp_network_from_gene_network/tested_cases.svg.

  • data/synthetic_gwas/acsn_names.gmt
  • data/synthetic_gwas/acsn_ppi_ver2.txt
  • and data/synthetic_gwas/icogs_snplist.csv are initial files downloaded from the Internet. They are described in data/synthetic_gwas/README.txt.

In order to have the files in the right format from these initial files to use code/, we provide some scripts :

  • code/ :

    • Input :
      • .txt file
    • Output :
      • .sif file
    • Example :
    python code/ data/synthetic_gwas/acsn_ppi_ver2.txt data/synthetic_gwas/acsn_ppi_ver2.sif
  • code/ :

    • Inputs :
      • .sif file
      • .gmt file (Example : data/synthetic_gwas/acsn_names.gmt)
    • Output :
      • .sif file
    • Example :
    python code/ data/synthetic_gwas/acsn_ppi_ver2.sif data/synthetic_gwas/acsn_names.gmt data/synthetic_gwas/hugo_ppi.sif
  • code/ :

    • Input:
      • .csv file
    • Output :
      • .map file
    • Example :
    python code/ data/synthetic_gwas/icogs_snp_list.csv data/synthetic_gwas/

For a visualisation about the workflow, see data/synthetic_gwas/workflow_snp-network-from-real-dat.svg

Data visualisation

For a visualisation of dimacs networks (do not use to big networks), use : code\show-dimacs.R.

Example :

cd code
Rscript show-dimacs.R ../data/simu_01/ 0.00000000001

The script save the visualisation under <path>.pdf, so you can open it later.

Synthetic data experiments -- TO BE COMPLETED

For a visualisation of the validation pipeline, see code/validation-pipeline.svg.

code/ contains methods and classes needed for evaluation (determining cross-validation sets, computing performance, etc.)

code/ runs experiments on synthetic data.

code/ contains methods needed for plot. To have an overview of what is possible to do with this script, just run :

cd code

It will output :

  • horizontal_boxplot.png
  • vertical_boxplot.png
  • vertical_barplot.png

code/ uses output of code/ to produce results

  • For each fold :
    • Fit a ridge regression model between finally selected features genotype of train set and their phenotype
    • Predict phenotype of test set using this model with finally selected features genotype of test set
  • Output values of each criterion for each fold of each plot
  • Output summary
  • Boxplot results

Example :

cd code
python -k 3 -m 200 -n 100 -r 10 -f 10 -s 10 \
             ../data/simu_synth_01 ../results/simu_synth_01 simu_01 --verbose
python -k 3 -m 200 -n 100 -r 10 -f 10 -s 10 \
             ../data/simu_synth_01 ../results/simu_synth_01 simu_01 --verbose

Usage on SGE cluster

Some nodes of the SGE cluster of CBIO has problems using PyTables, so generate data before running experimentation and ensure DATA_GEN flag of is False. Moreover, ensure SEQ_MODE flag is False and set a tmp_dir .

TODO : Find a way to get tmp_dir automatically. will use a qsub job for each fold.

Runtime experiment (on SGE cluster only)

Once, optimal parameters are chosen for each algo at each fold. Then, a runtime experiement can be run. Ensure TIME_EXP flag at the begining of is True and run

The script won't search for optimal parameters, but take those chosen previously.

Qsub jobs concerning features selection using all the training set of the fold and opt param are run on nodes from 15 to 24 which have the same spec. So timing can be compared.

numSNP experiment

code/ launches with different values of num_features, but with num_tasks , num_samples, num_repeats, num_folds, and num_subsamples fixed.

Usage :

Open the script, change values of variables that are in var to modify section and run the script.

Example :

cd code
chmod u+x
Usage on SGE cluster

There are several user of the cluster. Thus, it is important to not launch to much as the same time.

code/ waits for your number of running jobs to be lesser than 100 before running another

Usage :

Open the script, change values of variables that are in var to modify section and run the script.

Example :

cd code
chmod u+x

Some nodes of the SGE cluster of CBIO has problems using PyTables, so generate data before running experimentation. For this purpose, you can use code/

Usage :

Open the script, change values of variables that are in var to modify section and run the script.

Example :

cd code
chmod u+x

numTask experiment

code/ generate data and launches with different values of num_tasks, but with num_features , num_samples, num_repeats, num_folds, and num_subsamples fixed.

Usage :

Open the script, change values of variables that are in var to modify section and run the script.

Example :

cd code
chmod u+x

File formats

Relevance scores

Each line is the (floating point) relevance score of the corresponding node (in the same order as for the network file).

Example: data/simu_multitask_01.scores_0.txt.


Networks built over features are given as "DIMACS for maxmimum flow" files. For details about this format see DIMACS maximum flow problems.

Network files begin with a header of the form:

p max number_of_nodes number_of_edges

and each arc is listed as

a node_a node_b edge_weight


  • An undirected edge must be listed twice, first as a node_a node_b edge_weight, then as a node_b node_a edge_weight.
  • Because of the maxflow implementation, edges must be ordered by increasing values of node_a and then of node_b.
  • Node indices start at 1.

Example: data/ Note that edge weights can be given as floats.

We use this format because it is the one that gt_maxflow (Shekhovtsov & Hlavac, 2011) understands.

Covariance (similarity) between tasks

number_of_tasks x number_of_tasks symmetric matrix (space-separated columns).

Example: data/simu_multitask_01.task_similarities.txt.

Output of code/

Commented lines give the parameter values. Then each line corresponds to one tasks, and is a space-separated list of node indices, starting at 1.

Output of code/

For each algo (sfan, msfan_np, msfan):

  • <resu_dir>/<simu_id>.<algo>.maxRSS : maxRSS used during feature selection using all training set and optimal parameters. One value per line, one line per fold, all repeats mixed.

  • <resu_dir>/<simu_id>.<algo>.timing : Timing infos when runing feature selection using all training set and optimal paramters :

    Task (<task_idx>) computation time : <value>
    Task average computation time: <value>
    Standard deviation computation time: <value>
    Network building time: <value>
    gt_maxflow computation time: <value>

    for each fold.

If using SGE cluster :

  • <resu_dir>/SGE-output/<num_SNP>r<repeat_idx>f<fold_idx>.o: Hold prints.

    TODO : Find a way to output log and stderr as well

For each repeat :

For each fold :
  • <resu_dir>/<repeat_idx>/<simu_id>.<algo>.fold_<fold_idx>.parameters : list of optimal parameters retain for the fold
  • <resu_dir>/<repeat_idx>/<simu_id>.<algo>.fold_<fold_idx>.selected_features : space separated list of features one line per task
  • <resu_dir>/<repeat_idx>/<simu_id>.<algo>.fold_<fold_idx>.ss.maxRSS : One value of max RSS per line, one line per subsample
  • <resu_dir>/<repeat_idx>/<simu_id>.<algo>.fold_<fold_idx>.ss.process_time : One value of max RSS per line, one line per subsample
For each measure (pvv, tpr) :

<resu_dir>/<repeat_idx>/<simu_id>.<algo>.fold_<fold_idx>.<measure> : space-separated list of value measure

  • <resu_dir>/<repeat_idx>/<simu_id>.<algo>.fold_<fold_idx>.ppv
  • <resu_dir>/<repeat_idx>/<simu_id>.<algo>.fold_<fold_idx>.tpr

Output of code/

Results are saved in following files :

  • <resu_dir>/<simu_id>.table.<measure>.tex : Average/standard deviation values for: consistency index, RMSE, PPV and TPR, as LaTeX table.

For each algo (sfan, msfan_np, msfan):

  • <resu_dir>/<simu_id>.<algo>.rmse : List of final RMSEs one line per repeat for each repeat, one value per task
  • <resu_dir>/<simu_id>.<algo>.consistency : List of final Consistency Indices one line per repeat for each repeat, one value per task

Analysis files :

To see what these files look like, see results/analysis-files.svg.

For each classification measure (accuracy (acc), Mathieu coefficient (mcc), Prositive Predictive Value (ppv) and True Positive Value (tpr) )

a file named <resu_dir>/<simu_id>.<algo>.<measure> : Space-separated lists of PPVs (one value per task and per fold), each line corresponds to one repeat.

  • <resu_dir>/<simu_id>.<algo>.acc
  • <resu_dir>/<simu_id>.<algo>.mcc
  • <resu_dir>/<simu_id>.<algo>.ppv
  • <resu_dir>/<simu_id>.<algo>.tpr
For each repeat, fold and task :
  • <resu_dir>/<repeat_idx>/<simu_id>.<algo>.fold_<fold_idx>.task_<task_idx>.predicted : phenotype prediction of the test set using a ridge-regression trained with the selected features only. One value per line, one line per sample

Charts :

For each measure (ci, mcc, ppv, tpr, rmse, acc), a chart named <simu_id>..png : one boxplot per algorithm, grouped per task, with error bars.

  • <resu_dir>/<simu_id>.ci.png
  • <resu_dir>/<simu_id>.rmse.png
  • <resu_dir>/<simu_id>.acc.png
  • <resu_dir>/<simu_id>.mcc.png
  • <resu_dir>/<simu_id>.ppv.png
  • <resu_dir>/<simu_id>.tpr.png


Azencott, C.-A., Grimm, D., Sugiyama, M., Kawahara, Y., and Borgwardt, K.M. (2013). Efficient network-guided multi-locus association mapping with graph cuts. Bioinformatics 29, i171–i179.

Cherkassky, Boris V., and Andrew V. Goldberg. “On Implementing Push-Relabel Method for the Maximum Flow Problem.” In Integer Programming and Combinatorial Optimization, edited by Egon Balas and Jens Clausen, 920:157–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995.

Shekhovtsov A. and Hlavac V. (2011). A Distributed Mincut/Maxflow Algorithm Combining Path Augmentation and Push-Relabel. EMMCVPR 2011 / Technical Report CTU--CMP--2011--03.

Sugiyama, M., Azencott, C., Grimm, D., Kawahara, Y., and Borgwardt, K. (2014). Multi-Task Feature Selection on Multiple Networks via Maximum Flows. In Proceedings of the 2014 SIAM International Conference on Data Mining, pp. 199–207.

Wu, M.C., Lee, S., Cai, T., Li, Y., Boehnke, M., and Lin, X. (2011). Rare-Variant Association Testing for Sequencing Data with the Sequence Kernel Association Test. The American Journal of Human Genetics 89, 82–93.