Spatio-temporal data collected from GPS have become an important resource to study the relationships of moving objects. While previous studies focus on mining objects being together for a long time, discovering real-world relationships, such as friends or colleagues in human trajectory data, is a fundamentally different challenge. For example, it is possible that two individuals are friends but do not spend a lot of time being together every day. However, spending just one or two hours together at a location away from work on a Saturday night could be a strong indicator of friend relationship. Based on the above observations, in this paper we aim to analyze and detect semantically meaningful relationships in a supervised way. That is, with an interested relationship in mind, a user can label some object pairs with and without such relationship. From labeled pairs, we will learn what time intervals are the most important ones in order to characterize this relationship. These significant time intervals, namely T-Motifs, are then used to discover relationships hidden in the unlabeled moving object pairs. While the search for T-Motifs could be time-consuming, we design two speed-up strategies to efficiently extract T-Motifs. We use both real and synthetic datasets to demonstrate the effectiveness and efficiency of our method.