Social media community detection is a fundamental challenge in social data analytics, in order to understand user relationships and improve social recommendations. Although the problem has been extensively investigated, the majority of research has been based on social networks with static structures. Our findings within large social networks, such as Twitter, show that only a few users have interactions or communications at fixed time intervals. Finding active communities that demonstrate constant interactions between its members comprises a reasonable perspective. Communities examined from this perspective will provide time-variant social relationships, which may greatly improve the applicability of social data analytics. In this paper, we address the problem of temporal interaction-biased community detection using a four-step process. First, we develop a partition approach using an objective function based on clique structure, to enhance the time efficiency of our methodology. Second, we develop an influence propagation model that gives greatest weight to active edges or to inactive edges in close proximity to active edges. Third, we develop expansion-driven algorithms to efficiently find the activity-biased densest community. Finally, we verify the effectiveness of the extended community metric and the efficiency of the algorithms using three real data sets and a case study conducted on Twitter dynamic data set.