Adaptive graph regularized nonnegative matrix factorization for data representation

As a classical data representation method, nonnegative matrix factorization (NMF) can well capture the global structure information of the observed data, and it has been successfully applied in many fields. It is generally known that the local manifold structures will have a better effect than the global structures in image recognition and clustering. The local structure information can well be preserved by the neighbor graph in the manifold learning methods. The traditional neighbor graph constructed relies heavily on the original observed data. However, the original data usually contain a lot of noise and outliers in practical application, which results in obtaining inaccurate neighbor graph, and ultimately leads to performance degradation. How to get the ideal local structure information becomes more and more important. By combing the manifold learning into NMF, we propose an adaptive graph regularized nonnegative matrix factorization (AGNMF). In AGNMF, the neighbor graph is obtained by adaptive iteration. Both the global information and the local manifold can be well captured in AGNMF, and the better data representation can be obtained. A large number of experiments on different data sets show that our AGNMF has good clustering ability.