Abstract: Existing methodologies on the measurement of trajectory similarity pay little attention to the spatial temporal semantics and temporal randomness of trajectories, and as a result they likely misclassify moving objects by their social roles. This problem, this research addresses this problem from four aspects. Firstly, this research proposes the concept of spatial temporal associated semantics (STAS) which is proportion to the probability of the evens that different moving objects pass by areas with same type at a time. Secondly, this research proposes the concept of temporal entropy which quantifies the randomness of the time instances, at which one trajectory passes by the areas with same type. Thirdly, this research proposes a new similarity measure, trajectory semantic similarity (TSS), which combines STAS and temporal entropy and captures the spatial-temporal characteristics of the social roles of trajectories. Finally, this research presents an algorithm, SRDA (social roles discovering algorithm), to cluster the trajectories based on TSS, and each resulting cluster represents a different social role. The extensive experiments conducted on real data set and synthetic data set show that SRDA improves the average accuracy by 18% with linear temporal complexity, which validates the effectiveness and efficiency of SRDA.