Twitter as a big data social network becomes one of the most important sources for capturing the up-to-date events happening in the world. Topic derivation from Twitter is important for various applications such as situation awareness, market analysis, content filtering, and recommendations. However, tweets are short messages, which makes topic derivation challenging. Current methods employ various semantic features of tweet content but mostly overlook the interactions among tweets. In this paper, we propose a novel topic derivation method that takes into account the interactions among tweets, defined as the reciprocal activities related to people who send the tweets, as well as actions and tweet contents. In particular, topics are derived by performing a two-step matrix factorization jointly over the interactions and semantic features of the tweets. We have conducted a number of experiments on tweets collected over a period of time, showing that the proposed method consistently outperforms other advanced topic derivation methods in the literature. Our experiments also reveal that the interactions among tweets do significantly relieve the sparsity problem caused by the short-text nature of Twitter.