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The histopathological image classification method, based on deep learning, can be used to assist pathologists in cancer recognition in colon histopathology. The popularization of automatic and accurate histopathological image classification methods in this way is of great significance. However, smaller medical institutions with limited medical resources may lack colon histopathology image training sets with reliable labeled information; thus they may be unable to meet the needs of deep learning for many labeled training samples. Therefore, in this paper, the colon histopathological image set with rich label information from a certain medical institution is taken as the source domain; the colon histopathological image set from a smaller medical institution with limited medical resources is taken as the target domain. Considering the potential differences between histopathological images obtained by different institutions, this paper proposes a classification learning framework, namely unsupervised domain adaptation with local structure preservation for colon histopathological image classification, which can learn an adaptive classifier by performing distribution alignment and preserving intra-domain local structure to predict the labels of the colon histopathological images from institutions with lower medical resources. Extensive experiments demonstrate that the proposed framework shows significant improvement in accuracy and specificity of colon histopathological images without reliable labeled information compared to models without unsupervised domain adaptation. Specifically, in an affiliated hospital in Fuyang City, Anhui Province, the classification accuracy of benign and malignant colon histopathological images reaches 96.21%. The results of comparative experiments also show promising classification performance of our method in comparison with other unsupervised domain adaptation methods. [ABSTRACT FROM AUTHOR]