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In this paper, we propose Factorized Adversarial Networks (FAN) to solve unsupervised domain adaptation problems for image classification tasks. Our networks map the data distribution into a latent feature space, which is factorized into a domain-specific subspace that contains domain-specific characteristics and a task-specific subspace that retains category information, for both source and target domains, respectively. Unsupervised domain adaptation is achieved by adversarial training to minimize the discrepancy between the distributions of two task-specific subspaces from source and target domains. We demonstrate that the proposed approach outperforms state-of-the-art methods on multiple benchmark datasets used in the literature for unsupervised domain adaptation. Furthermore, we collect two real-world tagging datasets that are much larger than existing benchmark datasets, and get significant improvement upon baselines, proving the practical value of our approach.