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Unsupervised domain adaptation (UDA) person re-identification (ReID) faces enormous challenges due to the severe shift between the source and target domains, as well as the dramatic variations within the target domain. In this paper, to address these issues, we propose a multi-loss gap minimization learning (MGML) approach for UDA person ReID. Firstly, we introduce the part model to learn discriminative patch features and design a Patch-based Part Ignoring (PPI) loss to select reliable instances for the efficient learning of the part model. Then, given the gap that typically occurs because of the inter-domain shift and intra-domain variations, a Gap-based Minimum Camera Discrepancy (G-MCD) loss is proposed. Specifically, in terms of the inter-domain, we propose to leverage the tracklet and camera information to label each distance vector, and accordingly align pair-wise distance distributions to bridge the inter-domain gap. As for the intra-domain, to alleviate the biased search, we propose to perform the mined neighborhood for intra-camera and inter-camera separately to optimize matching results by exploring neighborhood relations more deeply. Finally, experimental results on three challenging datasets demonstrate that applying our method to unlabeled target domain outperforms current UDA methods for person ReID. [ABSTRACT FROM AUTHOR]