Multi-View Spectral Contrastive Learning.

Spectral clustering provides a principled framework for partitioning data through graph Laplacian optimization, yet its integration into deep multi-view learning remains fundamentally challenging due to hard orthogonality constraints, numerical instability, and the lack of principled mechanisms for fusing multiple spectral operators. In this paper, we propose Multi-View Spectral Contrastive Learning (MSCL), a theoretically grounded framework that unifies contrastive learning and spectral clustering from a spectral-operator perspective. MSCL jointly optimizes multiple view-specific spectral embeddings together with a consensus spectral embedding, and introduces a spectral contrastive regularization to align them in the spectral domain. A key component of MSCL is a differentiable Newton-Schulz orthogonalization module, which, for the first time, is introduced into deep spectral clustering to enforce hard orthogonality without explicit matrix decomposition or inversion, leading to numerically stable optimization and smooth gradient propagation. We further show that the proposed contrastive loss admits an interpretation as Laplacian smoothing on a kernel-induced similarity graph, establishing a principled connection between contrastive learning and spectral optimization. Extensive experiments on twelve benchmark datasets demonstrate that MSCL consistently outperforms state-of-the-art multi-view clustering methods, while additional analyses on orthogonalization stability and kernel choice further validate its robustness and scalability.