  Tensor-oriented multi-view subspace clustering has achieved significant
strides in assessing high-order correlations and improving clustering analysis
of multi-view data. Nevertheless, most of existing investigations are typically
hampered by the two flaws. First, 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. Second, the tensor
singular value decomposition (t-SVD) model redistributes each singular value
equally without considering the diverse importance among them. To well cope
with the issues, we propose a hyper-Laplacian regularized concept factorization
(HLRCF) in low-rank tensor space for multi-view clustering. Specifically, we
adopt 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, showingcasing its superior performance.
