抽样图集中最持久的软团
The Most Persistent Soft-Clique in a Set of Sampled Graphs
摘要：
当在潜在的噪声图形数据中搜索特征子模式时，具有多个观察结果比只有一个观察结果更好，这似乎是不言而喻的。然而，事实证明，当不同的图实例具有不同的边集时引入的不一致性构成了严重的挑战。在这项工作中，我们解决这个挑战的问题，找到最大加权集团。我们引入了最持久软团的概念。这是顶点的子集，1）几乎完全或至少密集连接，2）出现在所有或几乎所有图实例中，并且3）具有最大权重。我们提出了一个衡量团，本质上是计数的边缘丢失，使一个子集的顶点成团的数量。有了这个措施，我们发现，找到最持久的软集团问题可以铸造的问题：a）一个最大-最小两人博弈优化问题，或b）一个最小-最小软边际优化问题。当使用部分拉格朗日方法来解决优化问题时，这两种制剂导致相同的解决方案。通过对合成数据和真实社交网络数据的实验，我们表明所提出的方法能够可靠地找到图数据中的软团，即使是由随机噪声或不可靠的观察扭曲。
英文摘要：
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.
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