Correlation Clustering Algorithms in Graph Structures

Correlation clustering is a framework for partitioning the nodes of a graph according to pairwise similarity and dissimilarity labels on edges. Rather than fixing the number of clusters in advance, this paradigm identifies an optimal grouping that maximises agreement—positive edges within clusters and negative edges between clusters—and minimises disagreement. The problem is inherently combinatorial and is known to be NP-hard in general, prompting the development of a variety of exact and approximate methods. Approaches range from integer-program formulations and convex relaxations (linear and semidefinite), to spectral techniques and greedy heuristics, often combined with sophisticated rounding or neighbourhood-growing steps. Recent efforts have addressed large-scale and dynamic data, the incorporation of higher-order network motifs, and uncertainty in edge information. These advances enable applications in social network analysis, bioinformatics, image segmentation and beyond, where relations are naturally encoded by signed graphs.

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Correlation Clustering Algorithms in Graph Structures publication trend

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Technical terms

Correlation clustering: A method for grouping graph vertices based on labelled edges indicating similarity (positive) or dissimilarity (negative).

NP-hard: A classification of decision problems for which no polynomial-time algorithm is known and such that a polynomial-time solution to any NP-hard problem would solve all problems in NP.

Combinatorial Multi-Armed Bandit (CMAB): A reinforcement-learning framework that selects combinations of actions (arms) and observes rewards, applied here to estimate unknown edge weights.

Data-stream model: A computational setting where input arrives as a sequence of updates, requiring algorithms that use limited memory and make few passes.

Motif: A small, recurring subgraph pattern whose presence or absence informs higher-order network structure.

Hypergraph: A generalisation of a graph in which edges (hyperedges) can connect any number of vertices, modelling group interactions.

References

1. A combinatorial multi-armed bandit approach to correlation clustering. Data Mining and Knowledge Discovery (2023).
2. Correlation Clustering in Data Streams. Algorithmica (2021).
3. Motif and Hypergraph Correlation Clustering. IEEE Transactions on Information Theory (2019).