Deep Grouped Non-Negative Matrix Factorization Method for Image Data Representation

Non-negative matrix factorization (NMF) is an unsupervised learning method that can be exploited for parts-based image representation due to non-negativity constraints. However, singer-layer NMF cannot capture the latent hierarchical structure features from images, while deep features play more important roles in the image representation and recognition tasks. To overcome the limitation of NMF, this paper proposes a novel deep grouped NMF (DGNMF) approach to learn different level attributes of the data. It is interesting that DGNMF approach automatically makes the data from distinct classes share different basis images and the feature vectors among different classes are mutually orthogonal at the same layer. Meanwhile, to preserve the local information, our DGNMF model establishes the objective function with graph regularization, and its optimization problem is solved using gradient descent method. The developed DGNMF algorithm is proved to be convergent and is finally evaluated on face datasets for classification. Compared with some state-of-the-art deep NMF variants, the results demonstrate the proposed DGNMF algorithm achieves surpassing performances using different layer features.