Sparse dual graph-regularized NMF for image co-clustering

Nonnegative matrix factorization (NMF) as fundamental technique for clustering has been receiving more and more attention. This is because it can effectively reduce high dimensional data and produce parts-based, linear image representations of nonnegative data. For practical clustering tasks, NMF ignores the geometric structures of both data manifold and feature manifold. In addition, recent research results showed that leveraging sparseness can greatly improve the ability of learning parts. Motivated by the two aspects above mentioned, we propose a novel co-clustering algorithm to enhance the clustering performance, called sparse dual graph-regularized nonnegative matrix factorization (SDGNMF). It aims for finding a parts-based, linear representation of the non-negative data and facilitating the learning tasks. SDGNMF jointly incorporates the dual graph-regularized and sparseness constraints as additional conditions to uncover the intrinsic geometrical, discriminative structures of the data space and feature space. The iterative updating scheme for the optimization problem of SDGNMF and its convergence proofs are also given in detail. Experimental results of clustering on three benchmark datasets demonstrated that SDGNMF algorithm outperforms the compared state-of-the-art methods in image co-clustering.