Projective non-negative matrix factorization for unsupervised graph clustering

We develop an unsupervised graph clustering and image segmentation algorithm based on non-negative matrix factorization. We consider arbitrarily represented visual signals (in 2D or 3D) and use a graph embedding approach for image or point cloud segmentation. We extend a Projective Non-negative Matrix Factorization variant to include local spatial relationships over the image graph. By using properly defined region features, one can apply our method of unsupervised graph clustering for object and image segmentation. To demonstrate this, we apply our ideas on many graph based segmentation tasks such as 2D pixel and super-pixel segmentation and 3D point cloud segmentation. Finally, we show results comparable to those achieved by the only existing work in pixel based texture segmentation using Nonnegative Matrix Factorization, deploying a simple yet effective extension that is parameter free. We provide a detailed convergence proof of our spatially regularized method and various demonstrations as supplementary material. This novel work brings together graph clustering with image segmentation.