Topological structure regularized nonnegative matrix factorization for image clustering

Image representation is supposed to reveal the distinguishable feature and be captured in unsupervised fashion. Recently, nonnegative matrix factorization (NMF) has been widely used in capturing the parts-based feature for image representation. Previous NMF variants for image clustering first set the reduced rank as the number of clusters to obtain image representations. Then, K-means technology is adopted for ultimate clustering. However, the setting of rank is too rigid to preserve the geometrical structure of images, leading to unsuitable representation for the following clustering. Moreover, the image representation learning and clustering procedures are conducted individually which is inefficient as well as suboptimal for image clustering. This paper incorporates the constraint of topological structure into the procedure of NMF for simultaneously accomplishing nonnegative image representation and image clustering task. The proposed topological structure regularized NMF (TNMF) makes the rank bigger than the number of clusters, allotting one image more than one coarse clusters to guarantee the geometrical structure of images. In addition, a connected graph constructed by the coefficient matrix is enforced to have the strong connected components whose number equals to the number of clusters. By checking the number of connected components of graph against the number of clusters during the learning procedure, the optimization of TNMF is accomplished using alternative update rules. Extensive experiments on the challenging face, digit, and object data sets demonstrate the effectiveness of TNMF compared with competitive NMF variants for image clustering.