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Weakly supervised person re-identification (Re-ID) is appealing to handle real-world tasks by using state information that is available without manual annotation. At present, most methods perform unsupervised cross domain (UCD) learning by transferring the knowledge from the labeled source domain to the unlabeled target domain, which results in poor performance due to the severe shift. To address this problem, in this paper, we utilize the tracklet and camera information as weak supervision to propose a distribution discrepancy minimization learning (DDML) model for UCD person Re-ID. In addition to aligning data distributions from the perspective of domain adaptation learning, two losses are developed from the view of neighborhood invariance exploration to optimize matching results. Specifically, to bridge the gap between domains, we propose a camera-distribution-based (CDB) loss to align pair-wise distance distributions. Furthermore, to alleviate the biased search within the target domain, we propose a ranking-confidence-based (RCB) loss to perform the mined neighborhood for intra-camera and inter-camera separately to explore a high degree of confidence neighbor relations. Extensive experiments on three challenging datasets demonstrate that applying our method to unlabeled target domain outperforms current weakly supervised methods for person Re-ID.