The goal in the graph-fused lasso (GFL) is to find a solution to the following convex optimization problem:

where l is a smooth, convex loss function. The problem assumes you are given a graph structure of edges and nodes, where each node corresponds to a variable and edges between nodes correspond to constraints on the first differences between the variables. The objective function then seeks to find a solution to the above problem that minimizes the loss function over the vertices plus the sum of the first differences defined by the set of edges E.

The solution implemented here is based on the graph-theoretic trail decomposition and ADMM algorithm implemented in [1]. The code relies on a slightly modified version of a linear-time dynamic programming solution to the 1-d (i.e. chain) GFL [2].

The python wrapper requires numpy, scipy, and networkx to be able to run everything.

The package can be installed via Pip:

pip install pygfl

or directly from source:

python setup.py build
python setup.py install

Note that the installation has not been tested on anything other than Mac OS X and Ubuntu. The underlying solver is implemented in pure C and should be cross-platform compatible.

There are two steps in running the GFL solver (once installed). First, you need to decompose your graph into a set of trails then you need to run the C-based GFL solver.

Suppose you have a graph file like the one in example/edges.csv, where each edge is specified on a new line, with a comma separating vertices:

0,1
1,2
3,4
2,4
5,4
6,0
3,6
...

You can then decompose this graph by running the command line maketrails script:

trails file --infile example/edges.csv --savet example/trails.csv

This will create a file in example/trails.csv containing a set of distinct, non-overlapping trails which minimally decomposes the original graph. Next you need to run the solver.

Given a set of trails in example/trails.csv and a vector of observations in example/data.csv, you can run the graphfl script to execute the GFL solver:

graphfl example/data.csv example/edges.csv --trails example/trails.csv --o example/smoothed.csv

This will run a solution path to auto-tune the value of the penalty parameter (the λ in equation 1). The results will be saved in example/smoothed.csv. The results should look something like the image at the top of the readme.

To compile the C solver as a standalone library, you just need to run the make file from the cpp directory:

make all

Then you will need to make sure that you have the cpp/lib directory in your LD_LIBRARY_PATH:

export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/my/path/to/gfl/cpp/lib/

Note the above instructions are for *nix users.

This library / package is distributed under the GNU Lesser General Public License, version 3. Note that a subset of code from [2] was modified and is included in the C source.

[1] W. Tansey and J. G. Scott. "A Fast and Flexible Algorithm for the Graph-Fused Lasso," arXiv:1505.06475, May 2015.

[2] glmgen