A dual-layer supervised Mahalanobis kernel for the classification of hyperspectral images

To address the drawback of traditional Mahalanobis distance metric learning (DML) methods that learn the matrix without considering the weights of each class, in this paper, a novel dual-layer supervised Mahalanobis kernel is proposed for the classification of hyperspectral images. By modifying the traditional unsupervised Mahalanobis kernel, a supervised Mahalanobis matrix that can include more relativity information of different types of real materials in hyperspectral images is learned to obtain a new kernel. The proposed Mahalanobis matrix is obtained in two steps. In step one, we learn the first traditional Mahalanobis matrix with all samples to map the raw data. In step two, based on the data mapped by the first matrix, we pick several hard-to-identify classes from all the classes and learn the second Mahalanobis matrix using only these data. Finally, by combining these two matrices, we construct a new form of the Mahalanobis kernel. Simulation experiments are conducted on three real hyperspectral data sets. We use SVM as the kernel-based classifier to classify the dimensionally reduced data and compare with several methods from various aspects. The results show that the proposed methods perform better than other unsupervised or single-layer DML methods in classifying the hard-to-identify classes, especially under an extreme condition.