Multi-view and Multi-order Graph Clustering via Constrained l_1,2-norm

The graph-based multi-view clustering algorithms achieve decent clustering performance by consensus graph learning of the first-order graphs from different views. However, the first-order graphs are often sparse, lacking essential must-link information, which leads to suboptimal consensus graph. While high-order graphs can address this issue, a two-step strategy involving the selection of a fixed number of high-order graphs followed by their fusion may result in information loss or redundancy, restricting the exploration of high-order information. To address these challenges, we propose Multi-view and Multi-order Graph Clustering via Constrained l_1,2-norm (MoMvGC), which mitigates the impact of graph sparsity on multi-view clustering. By innovatively designing constrained l_1,2-norm, the model ingeniously integrates the selection of multi-order graphs and corresponding weight learning into a unified framework. Furthermore, MoMvGC not only enable sparse selection of multi-order graphs but also simultaneous selection of views. Afterwards, we design an efficient alternative optimization algorithm to solve the optimization problems in MoMvGC. The proposed model achieves state-of-the-art clustering performance on nine real-world datasets, with particularly notable improvements observed on the MSRC dataset, where the clustering accuracy is increased by 5.24% compared to the best baseline. Comprehensive experiments demonstrate the effectiveness and superiority of our model. The code is available at https://github.com/haonanxin/MoMvGC_code.