Hyper-Laplacian Regularized Concept Factorization in Low-Rank Tensor Space for Multi-View Clustering

Tensor-oriented multi-view subspace clustering has achieved significant strides in assessing high-order correlations of multi-view data. Nevertheless, most of existing investigations are typically hampered by the two flaws: (1) Self-representation based tensor subspace learning usually induces high time and space complexity, and is limited in perceiving nonlinear local structure in the embedding space. (2) The tensor singular value decomposition model redistributes each singular value equally without considering the diverse importance among them. To well cope with the above issues, we propose a hyper-Laplacian regularized concept factorization (HLRCF) in low-rank tensor space for multi-view clustering. Specifically, HLRCF adopts the concept factorization to explore the latent cluster-wise representation of each view. Further, the hypergraph Laplacian regularization endows the model with the capability of extracting the nonlinear local structures in the latent space. Considering that different tensor singular values associate structural information with unequal importance, we develop a self-weighted tensor Schatten $p$-norm to constrain the tensor comprised of all cluster-wise representations. Notably, the tensor with smaller size greatly decreases the time and space complexity in the low-rank optimization. Finally, experimental results on eight benchmark datasets exhibit that HLRCF outperforms other multi-view methods, showing its superior performance.