In recent years, representation-based methods have attracted more attention in the hyperspectral image (HSI) classification. Among them, sparse representation-based classifier (SRC) and collaborative representation-based classifier (CRC) are the two representative methods. However, SRC only focuses on sparsity but ignores the data correlation information. While CRC encourages grouping correlated variables together but lacks the ability of variable selection. As a result, SRC and CRC are incapable of producing satisfied performance. To address these issues, in this work, a correlation adaptive representation (CAR) is proposed, enabling a CAR-based classifier (CARC). Specifically, the proposed CARC is able to explore sparsity and data correlation information jointly, generating a novel representation model that is adaptive to the structure of the dictionary. To further exploit the correlation between the test samples and the training samples effectively, a distance-weighted Tikhonov regularization is integrated into the proposed CARC. Furthermore, to handle the small training sample problem in the HSI classification, a multi-feature correlation adaptive representation-based classifier (MFCARC) and MFCARC with Tikhonov regularization (MFCART) are presented to improve the classification performance by exploring the complementary information across multiple features. The experimental results show the superiority of the proposed methods over state-of-the-art algorithms.
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