Low-rank tensor learning for classification of hyperspectral image with limited labeled samples

Previous studies have demonstrated that integrating spatial information can potentially provide significant improvements for classification of hyperspectral image (HSI). However, it remains a challenging task to classify the high-dimensional HSI with limited number of training samples. In this paper, we propose a spectral-spatial classification framework based on low-rank tensor learning (lrTL). Unlike the traditional vector/matrix-based methods, the proposed lrTL method aims at improving the classification performance by naturally treating the HSI as a third-order tensor under the umbrella of multilinear algebra. First, small local patches containing the training (or test) samples are extracted from the original HSI cube by superpixel segmentation to preserve the structural information. Second, the lrTL algorithm is proposed to present the local patch of each test sample as a linear combination of all of the training patches. Low-rank constraint is enforced on the parameter tensor to capture the global structure of the HSI. Finally, the class label of the test sample can be determined by the minimal residual between the local patch containing the test sample and its approximation from different class subdictionaries. Experimental results on three benchmark HSI datasets demonstrate the effectiveness of the lrTL in improving the classification performance especially with limited training samples.