Hierarchical Multi-View Representation Learning via Generalized Deep Non-Negative Matrix Factorization

Multi-view clustering aims to exploit complementary information from multiple views to uncover intrinsic grouping structures in data, where effective representation learning plays a critical role. Non-negative matrix factorization (NMF) has been widely used for multi-view representation learning due to its inherent interpretability; however, most existing NMF-based methods rely on shallow architectures and are therefore insufficient for capturing hierarchical characteristics. Although recent deep NMF models introduce multi-layer structures by factorizing either feature matrices or basis matrices, their performance may degrade when the data are limited or exhibit relatively simple structures. To address these issues, this paper proposes a generalized deep non-negative matrix factorization framework for multi-view representation learning, termed GDNMF-MRL, which jointly decomposes feature and basis matrices to learn hierarchical representations. By integrating shallow linear components with deep nonlinear structures, the proposed method enhances representation capability and yields more discriminative latent subspaces. Furthermore, a one-step variant, termed OS-GDNMF-MRL, is developed to simultaneously learn latent representations and clustering assignments within a unified optimization framework, enabling direct interaction between representation learning and clustering without requiring separate post-processing. Two efficient alternating optimization algorithms with guaranteed convergence of the objective function are derived, and extensive experiments on benchmark datasets demonstrate that the proposed methods consistently outperform several state-of-the-art multi-view clustering approaches.