Large-scale user contributed images with tags are easily available on photo sharing websites. However, the noisy or incomplete correspondence between the images and tags prohibits them from being leveraged for precise image retrieval and effective management. To tackle the problem of tag refinement, we propose a method of Ranking based Multi-correlation Tensor Factorization (RMTF), to jointly model the ternary relations among user, image, and tag, and further to precisely reconstruct the user-aware image-tag associations as a result. Since the user interest or background can be explored to eliminate the ambiguity of image tags, the proposed RMTF is believed to be superior to the traditional solutions, which only focus on the binary image-tag relations. During the model estimation, we employ a ranking based optimization scheme to interpret the tagging data, in which the pair-wise qualitative difference between positive and negative examples is used, instead of the point-wise 0/1 confidence. Specifically, the positive examples are directly decided by the observed user-image-tag interrelations, while the negative ones are collected with respect to the most semantically and contextually irrelevant tags. Extensive experiments on a benchmark Flickr dataset demonstrate the effectiveness of the proposed solution for tag refinement. We also show attractive performances on two potential applications as the by-products of the ternary relation analysis.