Multi-view embedding learning via robust joint nonnegative matrix factorization

Real data often are comprised of multiple modalities or different views, which provide complementary and consensus information to each other. Exploring those information is important for the multi-view data clustering and classification. Multiview embedding is an effective method for multiple view data which uncovers the common latent structure shared by different views. Previous studies assumed that each view is clean, or at least there are not contaminated by noises. However, in real tasks, it is often that every view might be suffered from noises or even some views are partially missing, which renders the traditional multi-view embedding algorithm fail to those cases. In this paper, we propose a novel multi-view embedding algorithm via robust joint nonnegative matrix factorization. We utilize the correntropy induced metric to measure the reconstruction error for each view, which are robust to the noises by assigning different weight for different entries. In order to uncover the common subspace shared by different views, we define a consensus matrix subspace to constrain the disagreement of different views. For the non-convex objective function, we formulate it into half quadratic minimization and solve it via update scheme efficiently. The experiments results show its effectiveness and robustness in multiview clustering.