Beyond SVD: Differentiable Low-Rank Matrix Factorization for Multiview Subspace Clustering

Multi-view subspace clustering (MvSC) has attracted considerable attention due to its ability to uncover underlying subspace structures from heterogeneous multiview data. However, existing methods require time-consuming SVD during each iteration, resulting in quadratic or even cubic computational complexity with respect to the number of samples and thereby limiting their scalability to large-scale datasets. To overcome these limitations, we propose a novel differentiable low-rank matrix factorization method for MvSC, which unifies multi-factor decomposition, low-rank representation learning, and structural regularization within a coherent framework. The proposed method not only characterizes the intrinsic low-rank structure through multiple factor matrices under cross-view consistency and symmetry constraints, but also transforms the factor-wise iterative optimization into differentiable learning steps, avoiding repeated SVD and enabling end-to-end learning through back propagation. The resulting block-wise optimization algorithm is further supported by a theoretical convergence analysis. Extensive experiments on multiple benchmark datasets demonstrate that our method achieves superior clustering performance while substantially reducing computational costs.