Rank-Adaptive Non-Negative Matrix Factorization

Dimension reduction is a challenge task in data processing, especially in high-dimensional data processing area. Non-negative matrix factorization (NMF), as a classical dimension reduction method, has a contribution to the parts-based representation for the characteristics of non-negative constraints in the NMF algorithm. In this paper, the NMF algorithm is introduced to extract local features for dimension reduction. Considering the problem of which NMF is required to define the number of the decomposition rank manually, we proposed a rank-adaptive NMF algorithm, in which the affinity propagation (AP) clustering algorithm is introduced to determine adaptively the number of the decomposition rank of NMF. Then, the rank-adaptive NMF algorithm is used to extract features for the original image. After that, a low-dimensional representation of the original image is obtained through the projection from the original images to the feature space. Finally, we used extreme learning machine (ELM) and k-nearest neighbor (KNN) as the classifier to classify those low-dimensional feature representations. The experimental results demonstrate that the decomposition rank determined by the AP clustering algorithm can reflect the characteristics of the original data. When it is combined with the classification algorithm ELM or KNN and applied to handwritten character recognition, the proposed method not only reduces the dimension of original images but also performs well in terms of classification accuracy and time consumption. A new rank-adaptive NMF algorithm is proposed based on the AP clustering algorithm and the original NMF algorithm. According to this algorithm, the low-dimensional representation of the original data can be obtained without any prior knowledge. In addition, the proposed rank-adaptive NMF algorithm combined with the ELM and KNN classification algorithms performs well.