Local Matrix Feature-Based Kernel Joint Sparse Representation for Hyperspectral Image Classification

Hyperspectral image (HSI) classification is one of the hot research topics in the field of remote sensing. The performance of HSI classification greatly depends on the effectiveness of feature learning or feature design. Traditional vector-based spectral-spatial features have shown good performance in HSI classification. However, when the number of labeled samples is limited, the performance of these vector-based features is degraded. To fully mine the discriminative features in small-sample case, a novel local matrix feature (LMF) was designed to reflect both the correlation between spectral pixels and the spectral bands in a local spatial neighborhood. In particular, the LMF is a linear combination of a local covariance matrix feature and a local correntropy matrix feature, where the former describes the correlation between spectral pixels and the latter measures the similarity between spectral bands. Based on the constructed LMFs, a simple Log-Euclidean distance-based linear kernel is introduced to measure the similarity between them, and an LMF-based kernel joint sparse representation (LMFKJSR) model is proposed for HSI classification. Due to the superior performance of region covariance and correntropy descriptors, the proposed LMFKJSR shows better results than existing vector-feature-based and matrix-feature-based support vector machine (SVM) and JSR methods on three well-known HSI data sets in the case of limited labeled samples.