Nonconvex Low-Rank Tensor Multi-View Clustering via the Markov Chain Spectral Framework

As high-dimensional data analysis becomes increasingly prevalent, tensor-based subspace clustering has emerged as a significant research focus. Multi-view data integration enables a deeper understanding of underlying data structures and relationships. Nonetheless, traditional multi-view subspace models often fail to preserve local geometric structures within each view and to utilize complementary information across views. Recent work primarily relies on self-representation-based clustering, which is computationally intensive. To overcome these limitations, this study presents a novel nonconvex low-rank tensor multi-view clustering model grounded in Markov chain-based spectral clustering. Our approach incorporates Laplacian regularization to preserve local manifold structures and leverages the Hilbert-Schmidt independence criterion (HSIC) to promote diversity and harness cross-view complementarity. We also develop an efficient optimization algorithm based on the alternating direction method of multipliers (ADMM), supported by a rigorous convergence analysis. Experiments on six diverse datasets highlight the model's superior accuracy and efficiency.