Discriminative Non-negative Matrix Factorization Model with Local Manifold Preservation

Non-negative matrix factorization (NMF) has been widely studied for data representation learning and dimensionality reduction. However, existing NMF-based approaches often suffer from limitations such as inadequate preservation of manifold structure and insufficient exploitation of available label information. To address these issues, this paper proposes a novel NMF-based framework that incorporates supervised information to enhance class discriminability in the learned latent space. In addition, the proposed model explicitly preserves the local geometric structure of the data during factorization, thereby improving the fidelity of the learned representation. By jointly integrating discriminative supervision and manifold preservation, the proposed approach yields more informative embeddings for downstream machine learning tasks. Extensive experiments on image classification and community detection benchmarks demonstrate that the proposed model consistently outperforms several state-of-the-art approaches.