danielgribel / assortativesbm

Source code of AC-DC-SBM, from "Assortative-Constrained Stochastic Block Models" (Gribel, Vidal and Gendreau, 2020)

AC-DC-SBM

Assortative-Constrained Stochastic Block Models

Run

To run the AC-DC-SBM algorithm in Julia, try the following command:

> julia AC_DCSBM.jl 'dataset_name' seed nb_runs

Example

> julia AC_DCSBM.jl 'A-4-05-02-101' 1234 100

Data format

Graph file. The graph file is a 3-column and m-row file, where m is the number of edges in the graph. Each column is separated by a single space, and each line correponds to one edge in the graph. In a row, the first value is the number of the first sample, the second value is the number of the second sample, and the third value is the weigth of the edge:

a1	b1	w1
a2	b2	w2
...	...	...
am	bm	wm

Important: Graph files must have the .link extension. Some graphs are provided within the folder /data in this repository.

Label file. The label file contains the ground-truth community of each sample of the dataset, and is a N-row file, where N is the number of samples. Each line presents the label of the i-th sample:

y₁

y₂

...

y_N

Important: Labels files must have the .label extension. Some labels are provided within the folder /data in this repository.

assortativesbm's Issues

Optimization errors with k > 7~ and poor scaling with k

Testing on empirical networks I noticed that past around 7 communities the constrained optimization will fail sometimes,

 Warning: Problem status NUMERICAL_ERROR; solution may be inaccurate.

Also that the optimization succeeded is never checked. I think spurious solutions can be accepted. Tweaking it to just ignore those cases in eval_relocate is easy enough

solve!(problem, ECOS.Optimizer(verbose=false))

# println("Optval = ", -problem.optval)
return problem.status, -problem.optval

problem_status, sbm_cost = solve_convex(sol.data, m_, kappa_, omega)

if sbm_cost < sol.ll && problem_status == Convex.MOI.OPTIMAL

I'm not sure if there is some ECOS setting that can be tweaked to solve these problematic cases or not. Around the same number of communities (7~) (and above) the algorithm slows down considerably. When I flip the CONSTRAINED flag the algorithm doesn't slow down noticeably at the same point. I wonder now if these optimization errors can be worked around will the algorithm scale more closely with the unconstrained case?

Thanks for any thoughts