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This paper focuses on the problem of discovering users' topics of interest on Twitter. While previous efforts in modeling users' topics of interest on Twitter have focused on building a "bag-of-words" profile for each user based on his tweets, they overlooked the fact that Twitter users usually publish noisy posts about their lives or create conversation with their friends, which do not relate to their topics of interest. In this paper, we propose a novel framework to address this problem by introducing a modified author-topic model named twitter-user model. For each single tweet, our model uses a latent variable to indicate whether it is related to its author's interest. Experiments on a large dataset we crawled using Twitter API demonstrate that our model outperforms traditional methods in discovering user interest on Twitter.