Model selection and classification with multiple kernel learning for hyperspectral images via sparsity

The goal of multiple kernel learning (MKL) is to simultaneously learn a kernel and the associated predictor in task of supervised learning. In this paper, a new sparse MKL (SMKL) algorithm is proposed to simultaneously carry out classification and kernel interpretation on hyperspectral remote sensing images. First, the multiscale Gaussian kernels are adopted as basis kernels, and learning from these basis kernels is then formulated as a problem of maximizing variance projection, which can be solved by singular value decomposition (SVD). A cardinality-based constraint is then involved to control the sparsity of the MKL and selection of the Gaussian kernel scales for improving the interpretability. This cardinality-constrained optimization can be further converted to a convex optimization. The proposed MKL algorithm can achieve a good classification performance by using a linear combination of only a few kernels. The experiments are conducted on three real hyperspectral datasets, and the results prove the effectiveness of the SMKL in terms of classification statistics and computational feasibility, by comparing it with the state-of-the-art MKL algorithms. More important, interpretability of learning model can be preliminary addressed by the proposed SMKL.