Semisupervised Hyperspectral Image Classification via Laplacian Least Squares Support Vector Machine in Sum Space and Random Sampling

Recently, the semisupervised learning for hyperspectral image classification (HIC) has attracted increasing attention. The previous semisupervised methods were usually based on reproducing kernel Hilbert spaces with a single kernel. In this paper, we propose a novel Laplacian least squares support vector machine in sum space (Lap-LSSVM-SS) for semisupervised HIC with multiscale kernels, which can simultaneously deal with the high and low frequency components of the target classification function with small and large scale kernels, respectively. Furthermore, due to its representation theorem, a noniterative algorithm based on the closed-form classification function of Lap-LSSVM-SS is provided to make a rapid semisupervised HIC possible in the multiple kernel learning framework. The proposed method can solve the multiclass problem of hyperspectral dataset directly. We further reduce the storage and computation cost of the proposed Lap-LSSVM-SS method with the random sampling strategy, i.e., Lap-LSSVM-SS-RS. We also show that the Lap-LSSVM-SS-RS method has near-optimal classification performance when the number of local Lap-LSSVM-SS machines is not too large. The experimental results on two real hyperspectral datasets demonstrate that Lap-LSSVM-SS-RS yields superior classification performance over the conventional semisupervised classifiers (e.g., LapSVM, S4VM, and BagSVMs, etc.) in challenging small training labeled samples and a large amount of unlabeled samples.