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Highly accurate supervised deep learning-based classifiers for polarimetric synthetic aperture radar (PolSAR) images require large amounts of data with manual annotations. Unfortunately, the complex echo imaging mechanism results in a high labeling cost for PolSAR images. Extracting and transferring knowledge to utilize the existing labeled data to the fullest extent is a viable approach in such circumstances. To this end, we are introducing unsupervised deep adversarial domain adaptation (ADA) into PolSAR image classification for the first time. In contrast to the standard learning paradigm, in this study, the deep learning model is trained on labeled data from a source domain and unlabeled data from a related but distinct target domain. The purpose of this is to extract domain-invariant features and generalize them to the target domain. Although the feature transferability of ADA methods can be ensured through adversarial training to align the feature distributions of source and target domains, improving feature discriminability remains a crucial issue. In this paper, we propose a novel polarimetric scattering characteristics-guided adversarial network (PSCAN) for unsupervised PolSAR image classification. Compared with classical ADA methods, we designed an auxiliary task for PSCAN based on the polarimetric scattering characteristics-guided pseudo-label construction. This approach utilizes the rich information contained in the PolSAR data itself, without the need for expensive manual annotations or complex automatic labeling mechanisms. During the training of PSCAN, the auxiliary task receives category semantic information from pseudo-labels and helps promote the discriminability of the learned domain-invariant features, thereby enabling the model to have a better target prediction function. The effectiveness of the proposed method was demonstrated using data captured with different PolSAR systems in the San Francisco and Qingdao areas. Experimental results show that the proposed method can obtain satisfactory unsupervised classification results. [ABSTRACT FROM AUTHOR]