Integrating Dual Graph Constraints into Sparse Non-Negative Tucker Decomposition for Enhanced Co-Clustering

Collaborative clustering is an ensemble technique that enhances clustering performance by simultaneously and synergistically processing multiple data dimensions or tasks. This is an active research area in artificial intelligence, machine learning, and data mining. A common approach to co-clustering is based on non-negative matrix factorization (NMF). While widely used, NMF-based co-clustering is limited by its bilinear nature and fails to capture the multilinear structure of data. With the objective of enhancing the effectiveness of non-negative Tucker decomposition (NTD) in image clustering tasks, in this paper, we propose a dual-graph constrained sparse non-negative Tucker decomposition NTD (GDSNTD) model for co-clustering. It integrates graph regularization, the Frobenius norm, and an $l_1$ norm constraint to simultaneously optimize the objective function. The GDSNTD mode, featuring graph regularization on both factor matrices, more effectively discovers meaningful latent structures in high-order data. The addition of the $l_1$ regularization constraint on the factor matrices may help identify the most critical original features, and the use of the Frobenius norm may produce a more highly stable and accurate solution to the optimization problem. Then, the convergence of the proposed method is proven, and the detailed derivation is provided. Finally, experimental results on public datasets demonstrate that the proposed model outperforms state-of-the-art methods in image clustering, achieving superior scores in accuracy and Normalized Mutual Information.