Robust latent nonnegative matrix factorization with automatic sparse reconstruction for unsupervised feature extraction

In recent years, the combination of nonnegative matrix factorization (NMF) and manifold learning has been widely confirmed. Although these methods are successful, there are some shortcomings: 1) The traditional manifold learning methods require predefined manifold geometry, which cannot reasonably reflect intrinsic geometric properties; 2) Most previous methods only consider the robustness of models to noise and outliers, but not occlusion; 3) Many models only contain the local neighborhood structure, but not the global geometric structure. To address these issues, we propose a novel model robust latent nonnegative matrix factorization with sparse reconstruction (RLNMF-SR) to conduct complex classification tasks. Our method utilizes sparse nodes to automatically reconstruct a global-based affinity graph without manually defining the graph structure, which guarantees that our model more accurately grasps the underlying distribution of the data. In addition, by decomposing the principal component with a low-rank structure, we can not only remove redundant features and reduce the computational cost but also obtain a more compact, discriminative and interpretable low-rank representation. At the same time, low-rank restriction can also recover the row and column information of the matrix to decrease the negative effects of noise and occlusion. On the other hand, applying the L2,1-norm to perform part-based nonnegative factorization can also attain the local attribute information of the data and suppress the model's sensitivity to destruction, greatly enhancing the robustness of the RLNMF-SR. Extensive experiments indicate that our method outperforms other state-of-the-art methods, especially on low-quality image datasets.