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Unsupervised domain adaptation (UDA) is to make predictions for unlabeled data on a target domain, given labeled data on a source domain whose distribution shifts from the target one. Mainstream UDA methods learn aligned features between the two domains, such that a classifier trained on the source features can be readily applied to the target ones. However, such a transferring strategy has a potential risk of damaging the intrinsic discrimination of target data. To alleviate this risk, we are motivated by the assumption of structural domain similarity, and propose to directly uncover the intrinsic target discrimination via discriminative clustering of target data. We constrain the clustering solutions using structural source regularization that hinges on our assumed structural domain similarity. Technically, we use a flexible framework of deep network based discriminative clustering that minimizes the KL divergence between predictive label distribution of the network and an introduced auxiliary one; replacing the auxiliary distribution with that formed by ground-truth labels of source data implements the structural source regularization via a simple strategy of joint network training. We term our proposed method as Structurally Regularized Deep Clustering (SRDC), where we also enhance target discrimination with clustering of intermediate network features, and enhance structural regularization with soft selection of less divergent source examples. Careful ablation studies show the efficacy of our proposed SRDC. Notably, with no explicit domain alignment, SRDC outperforms all existing methods on three UDA benchmarks.