Semi-supervised structured nonnegative matrix factorization for anchor graph embedding

Semi-supervised nonnegative matrix factorization (NMF) has been widely used in various clustering tasks due to its reliable performance. The key is how to use effectively a small amount of label information to obtain a more discriminative low-dimensional representation of data. In order to improve the clustering performance of semi-supervised NMF more effectively, this paper proposes a new semi-supervised NMF method, namely semi-supervised structured NMF for anchor graph embedding (AESSNMF). Specifically, AESSNMF uses three kinds of supervision information simultaneously, namely, pointwise constraints, pairwise constraints, and negative label information. Also, in order to handle mixed-sign data, AESSNMF uses a convex NMF form and only imposes nonnegative constraints on the coefficient matrix. AESSNMF constructs an anchor graph to embed the matrix factorization process, rather than performing the matrix factorization directly on the original data. We use the alternating iterative algorithm to optimize the objective function of AESSNMF. We also discuss the relationship between several related NMF based algorithms and AESSNMF. A large number of experimental results show that AESSNMF is superior to other related algorithms.