Normalized cut co-clustering with out-of-sample extension

Co-clustering is a critical data mining technology in various real-world applications, where anchor-based methods reveal the dual relationships between samples and anchors. Due to the information loss caused by relaxation and post-processing, classical anchor-based methods suffer from potential performance degradation. To overcome this disadvantage, we propose a Normalized Cut Co-Clustering (${\mathrm{NC}}^3$) model, which assigns clusters for samples and anchors by alternatively updating the discrete label matrices. Different from traditional anchor-based co-clustering methods, our model solves the original discrete normalized cut problem on the bipartite graph directly. To address the discrete cut problem, an iterative coordinate ascent algorithm is presented, which can speed up the clustering process. Through optimization on the label matrices of samples and anchors, the clusters can be obtained without relaxation–discretization operation. Furthermore, the proposed ${\mathrm{NC}}^3$ model can tackle the out-of-sample clustering issue based on labels of anchors. Through extensive experiments, we validate the effectiveness of our model, achieving competitive results compared to state-of-the-art approaches.