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Multi-source domain adaptation (MDA) aims to transfer knowledge from multiple source domains to an unlabeled target domain. MDA is a challenging task due to the severe domain shift, which not only exists between target and source but also exists among diverse sources. Prior studies on MDA either estimate a mixed distribution of source domains or combine multiple single-source models, but few of them delve into the relevant information among diverse source domains. For this reason, we propose a novel MDA approach, termed Pseudo Target for MDA (PTMDA). Specifically, PTMDA maps each group of source and target domains into a group-specific subspace using adversarial learning with a metric constraint, and constructs a series of pseudo target domains correspondingly. Then we align the remainder source domains with the pseudo target domain in the subspace efficiently, which allows to exploit additional structured source information through the training on pseudo target domain and improves the performance on the real target domain. Besides, to improve the transferability of deep neural networks (DNNs), we replace the traditional batch normalization layer with an effective matching normalization layer, which enforces alignments in latent layers of DNNs and thus gains further promotion. We give theoretical analysis showing that PTMDA as a whole can reduce the target error bound and leads to a better approximation of the target risk in MDA settings. Extensive experiments demonstrate PTMDA's effectiveness on MDA tasks, as it outperforms state-of-the-art methods in most experimental settings.