Adaptive Graph Regularization Discriminant Nonnegative Matrix Factorization for Data Representation

Abstract

Nonnegative matrix factorization, as a classical part-based representation method, has been widely used in pattern recognition, data mining and other fields. However, the traditional nonnegative matrix factorization directly factoring decomposes the original data, and the original data often contains a lot of redundancy and noise, which seriously affect the subsequent processing of the data. In this work, we propose an adaptive graph regularization discriminant nonnegative matrix factorization (AGDNMF) for image clustering. The AGDNMF algorithm makes full use of local structure information and a small amount of label information. In AGDNMF, the local structure information can be more accurate and the label information can prevent the points with the same label from being merged into one point. These two items are combined into the objective function of NMF. In addition, we provide the update rules for the corresponding optimization functions and prove its convergence. A large number of experiments on different data sets show that the proposed algorithm has good clustering performance.