Quantum-Assisted Correlation Clustering

TL;DR

This work tackles correlation clustering on signed graphs, an NP-hard problem, by reframing it as maximizing intra-cluster edge weights and solving bipartitions with a quantum annealing–based QUBO. By adapting the GCS-Q solver for coalition structure generation to a divisive hierarchical clustering setting, the method can operate without a predefined number of clusters and accommodate negative edges. Empirical results on synthetic graphs with varying cluster-size imbalance and real hyperspectral data show robust performance and higher modularity compared to classical baselines, with competitive or superior NMI across diverse regimes. The findings illustrate the promise of hybrid quantum-classical optimization for scalable, structure-aware clustering in graph-based unsupervised learning and motivate future work on gate-based quantum solvers and larger-scale, sparse graphs.

Abstract

This work introduces a hybrid quantum-classical method to correlation clustering, a graph-based unsupervised learning task that seeks to partition the nodes in a graph based on pairwise agreement and disagreement. In particular, we adapt GCS-Q, a quantum-assisted solver originally designed for coalition structure generation, to maximize intra-cluster agreement in signed graphs through recursive divisive partitioning. The proposed method encodes each bipartitioning step as a quadratic unconstrained binary optimization problem, solved via quantum annealing. This integration of quantum optimization within a hierarchical clustering framework enables handling of graphs with arbitrary correlation structures, including negative edges, without relying on metric assumptions or a predefined number of clusters. Empirical evaluations on synthetic signed graphs and real-world hyperspectral imaging data demonstrate that, when adapted for correlation clustering, GCS-Q outperforms classical algorithms in robustness and clustering quality on real-world data and in scenarios with cluster size imbalance. Our results highlight the promise of hybrid quantum-classical optimization for advancing scalable and structurally-aware clustering techniques in graph-based unsupervised learning.

Figures (4)

• Figure 1: The ground truth clusters and the outputs of various algorithms for a balanced graph with 10 nodes and edge weights in the range $[-1, 1]$ representing correlations. Red dashed edges highlight inconsistent assignments: a red edge between nodes in the same cluster indicates a negative correlation, while a red edge between nodes in different clusters indicates a positive correlation. In other words, red dashed lines mark violations of clustering agreement. All other edges are shown in grey, either because they are neutral or consistent with the clustering. These inconsistencies are usually minimized by GCS-Q and are more frequent in classical methods.
• Figure 2: Correlation matrices of three synthetic signed graphs used in our experiments. The examples correspond to a setting with $5$ clusters. Warmer colors indicate strong positive correlations (intra-cluster), while cooler tones represent negative correlations (inter-cluster). The corresponding Gini index and Cluster Size Ratio for each matrix are reported in Table \ref{['tab:Gini']}.
• Figure 3: NMI scores across synthetic signed graphs with increasing cluster size disparity.
• Figure 4: Modularity scores for clustering hyperspectral bands across four real-world remote sensing datasets. GCS-Q consistently achieves superior modularity, indicating more coherent grouping of highly correlated spectral bands.