High-order enhanced multi-view subspace clustering via dual norm and manifold constraints

Multi-view subspace clustering (MSC) algorithms are an important component of multi-view clustering research. The problem with current MSC studies is that they often struggle to simultaneously achieve a subspace representation (SR) that preserves inter-class sparsity and intra-class consistency, while enhancing the block-diagonal property of SR. Moreover, these approaches often fall short in their ability to delve deep into the underlying manifold structure within the data. Based on this, a new high-order enhanced MSC via dual norm and manifold constraints (HEMSCDM) is proposed. This method utilizes the Frobenius norm constraint and a novel sparse constraint to obtain SR with intra-class consistency and inter-class sparsity while further enhancing the block diagonal structure of SR. To extract the common data in multi-view data, this study adopts the concept of tensor and apply low-rank (LR) constraint to the tensor to eliminate irrelevant information. Additionally, the constructed method employs manifold constraint to explore the manifold information in the data to obtain more essential information, thereby enhancing the model's learning ability. For the HEMSCDM, we developed an efficient solution algorithm and analyzed its convergence. Experiments on various multi-view datasets ultimately demonstrate the enhanced clustering power of our model, even outperforming cutting-edge multi-view clustering power.