Neighborhood preserving concept factorization algorithm for data representation

Non-negative matrix factorization (NMF) and concept factorization (CF) have attracted great attention in pattern recognition and machine learning. However, NMF and CF do not explore the local manifold structure among the high dimensional data. In this paper, a novel semi-supervised matrix factorization method, called Neighborhood Preserving Concept Factorization (NPCF), is proposed. The NPCF algorithm exploits local manifold structure information among the data with resorting to adding neighborhood preserving regulation. This method makes full use for the local geometric structure information in concept factorization. Therefore, the NPCF algorithm has more discriminate ability than traditional concept factorization. Meanwhile, the updating rules and the convergence proof of the NPCF algorithm are provided in this paper. Experiments on benchmark data sets demonstrate this proposed approach is more effective than other algorithms.