The most persistent soft clique in a set of sampled graphs Conference Paper

Author(s): Quadrianto, Novi; Lampert, Christoph; Chen, Chao
Title: The most persistent soft clique in a set of sampled graphs
Affiliation IST Austria
Abstract: 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.
Keywords: Optimization problems; Edge-sets; Graph data; Lagrangian methods; Max-min; Random noise; Social Networks; Soft margins; Sub-patterns; Synthetic data; Two person game
Conference Title: ICML: International Conference on Machine Learning
Conference Dates: June 26 - July 1, 2012
Conference Location: Edinburgh, Scotland, UK
Publisher: Omnipress  
Date Published: 2012-06-01
Start Page: 583
End Page: 590
Open access: yes (repository)
IST Austria Authors
  1. Christoph Lampert
    87 Lampert
  2. Chao Chen
    14 Chen
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