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Graph-based semi-supervised learning (SSL) has attracted lots of interests in machine learning community as well as many application areas including video annotation recently. However, one of the two basic assumptions, structure assumption, which is an essential point of graph-based SSL, is not embedded into the pairwise similarity measure. Accordingly, we propose a novel graph-based SSL method for video annotation, named anisotropic manifold ranking (AniMR), based on a structure-related similarity measure. This method takes the influence of the density difference between samples into account to improve the pairwise similarity. Furthermore, we will show that AniMR can also be deduced from partial differential equation (PDE) based anisotropic diffusion. It demonstrates that the label propagation in AniMR is anisotropic, which is intrinsically different from the isotropic label propagation process in general …