Tensor Decomposition-Based Relaxed Linear Regression for Hyperspectral Image Classification

Linear regression and its variants have achieved considerable success in image classification. However, those methods still encounter two challenges when dealing with hyperspectral image (HSI) classification. On the one hand, the existing ones focus on mining the relationship between the label space and original data space during the classifier training, which is generally sensitive to noise corruptions. On the other hand, transforming the training samples into a strict binary label matrix makes the generalization ability of the classifier limited. To address these challenges, this article constructs a novel integrative model called tensor decomposition-based relaxed linear regression (TDRLR) for HSI classification. First, the model adopts tensor canonical polyadic (CP) decomposition to learn two dictionaries from spatial and spectral directions, respectively, which can help to generate a double dictionary representation for HSI data. Then, the linear regression classifier is integrated to learn a transformation that reveals the mapping relation between the double dictionary representation and label space rather than the original data for enhancing robustness. Meanwhile, a more flexible way, label relaxation (LR), is employed to enlarge the margins between different classes. More importantly, the learned double dictionary representation and classifier can be fine-tuned in tandem to enhance performance through the designed alternate iterative joint learning algorithm. Experiments conducted on four real-world HSI datasets demonstrate that the proposed method achieves significant improvements in classification performance with a small size training set, when compared with state-of-the-art HSI classification methods.