Discriminative multiple kernel learning for hyperspectral image classification

In this paper, we propose a discriminative multiple kernel learning (DMKL) method for spectral image classification. The core idea of the proposed method is to learn an optimal combined kernel from predefined basic kernels by maximizing separability in reproduction kernel Hilbert space. DMKL achieves the maximum separability via finding an optimal projective direction according to statistical significance, which leads to the minimum within-class scatter and maximum between-class scatter instead of a time-consuming search for the optimal kernel combination. Fisher criterion (FC) and maximum margin criterion (MMC) are used to find the optimal projective direction, thus leading to two variants of the proposed method, DMKL-FC and DMKL-MMC, respectively. After learning the projective direction, all basic kernels are projected to generate a discriminative combined kernel. Three merits are realized by DMKL. First, DMKL can achieve a substantial improvement in classification performance without strict limitation for selection of basic kernels. Second, the discriminating scales of a Gaussian kernel, the useful bands for classification, and the competitive sizes of spatial filters can be selected by ranking the corresponding weights, where the large weights correspond to the most relevant. Third, DMKL reduces the computational burden by requiring fewer support vectors. Experiments are conducted on two hyperspectral data sets and one multispectral data set. The corresponding experimental results demonstrate that the proposed algorithms can achieve the best performance with satisfactory computational efficiency for spectral image classification, compared with several state-of-the-art algorithms.