Inductive Correlation Clustering with Graph Neural Networks

Correlation Clustering (CC) is a natural formulation of clustering in combinatorial optimization, which uses a graph representation of the input and does not require a pre-specified number of clusters. Given $n$ objects and a pairwise similarity function, the goal is to cluster the objects so that similar objects are put in the same cluster and dissimilar objects are put in different clusters. Despite its versatility, existing CC algorithms suffer from significant scalability issues and are inherently transductive: i.e., the algorithm must be executed from scratch for any new problem instance. In this work, we bridge this gap by leveraging Graph Neural Networks (GNNs) to solve Inductive Correlation Clustering, a novel generalization of the CC problem designed to handle unseen graph instances. By learning to exploit common structural patterns and node features during training, our framework generalizes to new graphs drawn from the same distribution with minimal computational overhead with respect to standard algorithms. We demonstrate the effectiveness and scalability of our approach through extensive experiments. Our framework not only excels in the inductive setting, e.g., lowering the inference time up to $5$ order of magnitude, while maintaining an approximation ratio within $~10\%$ of the best baseline solution, but also achieves competitive results on standard (transductive) CC benchmarks. Finally, we showcase a practical application of our framework as a learnable pooling mechanism for graph classification. Our results indicate that our method serves as an efficient pooling layer, enhancing the ability of GNNs to capture hierarchical structural information in networks.

Contrastive Learning and Correlation Clustering for Sequences of Network Telescope Data

Understanding activities of Internet scanners is challenging; it often requires identifying relationships between sources, a task for which semantic annotations are scarce. This work investigates whether semantically meaningful pairwise relationships between sequences of network flow records can be estimated by contrastive learning, without pretraining and without annotations. To this end, we propose a transformer model that embeds minimally preprocessed sequences of network flow records and train it using contrastive learning. With the similarities obtained from this model, we state a correlation clustering problem and solve it locally. Experimentally, we show: Learned similarities are higher on average for sequences originating from the same source than for sequences originating from different sources, and this property generalizes to unseen sequences of unseen sources. Moreover, correlation clustering yields clusters consistent with scanner labels. The complete source code of the algorithms and for reproducing the experiments is publicly available.