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Convolutional neural networks (CNNs) have obtained high accuracy results for pedestrian re-identification in the past few years. There is always a trade-off between high accuracy and computational time in CNNs. Training CNN is always very difficult as it may take a long time to produce high accuracy results. To overcome this limitation, a novel method parallel stochastic gradient descent (PSGD) is proposed to train a five-hierarchical parallel CNNs that is designed according to pedestrian attributes. Moreover, the momentum correction and adaptive adjustment of learning rate are applied during training process and the time interval for updating parameters is inspected during optimization of parameters selection. The results of this paper prove the effectiveness of proposed PSGD that successfully decreases the training process by five times and surpasses the state-of-the-art methods of pedestrian re-identification in terms of both accuracy and time. The minimum reported running time of the proposed method is 8.7 s which is minimum among all other state-of-the-art methods. These promising results show the efficiency and performance of the proposed model. [ABSTRACT FROM AUTHOR]