Dual-graph regularized concept factorization for clustering

In past decades, tremendous growths in the amount of text documents and images have become omnipresent, and it is very important to group them into clusters upon desired. Recently, matrix factorization based techniques, such as Non-negative Matrix Factorization (NMF) and Concept Factorization (CF), have yielded impressive results for clustering. However, both of them effectively see only the global Euclidean geometry, whereas the local manifold geometry is not fully considered. Recent research has shown that not only the observed data are found to lie on a nonlinear low dimensional manifold, namely data manifold, but also the features lie on a manifold, namely feature manifold. In this paper, we propose a novel algorithm, called dual-graph regularized concept factorization for clustering (GCF), which simultaneously considers the geometric structures of both the data manifold and the feature manifold. As an extension of GCF, we extend that our proposed method can also be apply to the negative dataset. Moreover, we develop the iterative updating optimization schemes for GCF, and provide the convergence proof of our optimization scheme. Experimental results on TDT2 and Reuters document datasets, COIL20 and PIE image datasets demonstrate the effectiveness of our proposed method.