People often use multiple platforms to fulfill their different information needs, which has opened opportunities for research on the cross-platform recommendation. Existing cross-platform recommendation works either assume no overlapping users on different platforms or require enough overlapping users to reach a good performance. None of them pays attention to the sparse overlap problem, that is, the number of observed overlapping users of different platforms is very small. In this paper, we propose a cross-platform recommendation framework termed Adaptive Similarity Structure Regularization Through Connector (AdaSTC), which adaptively learns the user similarity structure on different platforms and further uses it to regularize the modeling process of user preference. Experiments conducted on two real-world datasets demonstrate that AdaSTC significantly outperforms the state-of-the-art methods in the sparse overlap situation.