Tensorized multi-dimensional multi-view clustering based on nonnegative matrix factorization

With the growing availability of multi-view data, numerous multi-view clustering (MVC) algorithms have been developed to effectively group samples across different views. Although existing methods have achieved notable progress, most still suffer from several limitations. (1) A majority of approaches are constrained by the computational and storage overhead of affinity matrix construction, which prevents them from scaling to large datasets. (2) Although nonnegative matrix factorization (NMF) methods perform well on large-scale data, they usually assume a dimension-fixed shared coefficient matrix across all views along with view-specific basis matrices, which constrains the model's performance. (3) Matrix-based approaches are also prone to noise and feature redundancy when handling high-dimensional data, leading to reduced robustness and clustering accuracy. To solve these problems, we propose a novel tensorized multi-dimensional multi-view clustering based on nonnegative matrix factorization (TMMVC). Specifically, we first adopt NMF to map each view into embedding spaces of different dimensionalities, thereby obtaining their respective basis matrices, thereby capturing the structural information specific to each view more comprehensively. Subsequently, the coefficient matrices learned from these basis matrices are mapped into a shared k-dimensional subspace through view-specific rotation matrices, enabling effective alignment and fusion into a unified consensus representation. This operation significantly reduces computational overhead, then the fused representation matrix is then stacked together with the previously obtained feature mapping to form a third-order tensor, upon which a tensor Schatten-p norm regularization is imposed to capture the underlying global structure and enhance clustering accuracy and robustness. We employ the Augmented Lagrange Multiplier (ALM) method to solve the optimization problem. Experimental results on several public benchmark datasets demonstrate that TMMVC method consistently outperforms state-of-the-art MVC algorithms in terms of clustering accuracy and scalability.