Nowadays numerous social images have been emerging on the Web. How to precisely label these images is critical to image retrieval. However, traditional image-level tagging methods may become less effective because global image matching approaches can hardly cope with the diversity and arbitrariness of Web image content. This raises an urgent need for the fine-grained tagging schemes. In this work, we study how to establish mapping between tags and image regions, i.e. localize tags to image regions, so as to better depict and index the content of images. We propose the spatial group sparse coding (SGSC) by extending the robust encoding ability of group sparse coding with spatial correlations among training regions. We present spatial correlations in a two-dimensional image space and design group-specific spatial kernels to produce a more interpretable regularizer. Further we propose a joint version of the SGSC model which is able to simultaneously encode a group of intrinsically rela...