Projection concept factorization with self-representation for data clustering

In recent years, matrix factorization-based techniques have received much attention in the data analysis field since it can perform dimensionality reduction and clustering simultaneously. Despite the great success achieved by the Non-negative matrix factorization (NMF) and concept factorization (CF) methods, they suffer from the out-of-sample problem and are sensitive to the noise. Some recent studies have indicated that the similarity relationship is capable of revealing the local structure. In this paper, a similarity graph is constructed to reflect the geometric information of manifold structure, while the concept factorization is employed to capture the global structure. In addition, the projection matrix is incorporated into the concept factorization model to eliminate the noise and avoid the out-of-sample problem. An iterative algorithm is introduced to solve the model. The experimental results obtained on both human face and text data sets verify the high efficiency of the proposed method.