The most persistent soft-clique in a set of sampled graphs
Novi Quadrianto, Chao Chen and Christoph Lampert
In: ICML 2012, 26 Jun - 1 Jul 2012, Edinburgh, Scotland, UK.
When searching for characteristic subpatterns in
potentially noisy graph data, it appears self-evident
that having multiple observations would be better than
having just one.
However, it turns out that the inconsistencies
introduced when different graph instances have
different edge sets pose a serious challenge.
In this work we address this challenge for the problem
of finding maximum weighted cliques.
We introduce the concept of most persistent soft-clique.
This is subset of vertices, that 1) is almost fully or at
least densely connected, 2) occurs in all or almost all
graph instances, and 3) has the maximum weight.
We present a measure of clique-ness, that essentially
counts the number of edge missing to make a subset of vertices
into a clique. With this measure, we show that the problem of finding the most
persistent soft-clique problem can be cast either as:
a) a max-min two person game optimization problem, or b) a min-min
soft margin optimization problem.
Both formulations lead to the same solution when using a partial
Lagrangian method to solve the optimization problems.
By experiments on synthetic data and on real social network
data we show that the proposed method is able to reliably find
soft cliques in graph data, even if that is distorted by
random noise or unreliable observations.