  In this paper, a novel weighted nonlocal total variation (WNTV) method is
proposed. Compared to the classical nonlocal total variation methods, our
method modifies the energy functional to introduce a weight to balance between
the labeled sets and unlabeled sets. With extensive numerical examples in
semi-supervised clustering, image inpainting and image colorization, we
demonstrate that WNTV provides an effective and efficient method in many image
processing and machine learning problems.
