Subspace learning (SL) plays an important role in hyperspectral image (HSI) classification, since it can provide an effective solution to reduce the redundant information in the image pixels of HSIs. Previous works about SL aim to improve the accuracy of HSI recognition. Using a large number of labeled samples, related methods can train the parameters of the proposed solutions to obtain better representations of HSI pixels. However, the data instances may not be sufficient enough to learn a precise model for HSI classification in real applications. Moreover, it is well-known that it takes much time, labor and human expertise to label HSI images. To avoid the aforementioned problems, a novel SL method that includes the probability assumption called subspace learning with conditional random field (SLCRF) is developed. In SLCRF, first, the 3D convolutional autoencoder (3DCAE) is introduced to remove the redundant information in HSI pixels. In addition, the relationships are also constructed using the spectral-spatial information among the adjacent pixels. Then, the conditional random field (CRF) framework can be constructed and further embedded into the HSI SL procedure with the semi-supervised approach. Through the linearized alternating direction method termed LADMAP, the objective function of SLCRF is optimized using a defined iterative algorithm. The proposed method is comprehensively evaluated using the challenging public HSI datasets. We can achieve stateof-the-art performance using these HSI sets.
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