Multiple Kernel Learning via Low-Rank Nonnegative Matrix Factorization for Classification of Hyperspectral Imagery

In this paper, a novel multiple kernel learning (MKL) algorithm is proposed for the classification of hyperspectral images. The proposed MKL algorithm adopts a two-step strategy to learn a multiple kernel machine. In the first step, unsupervised learning is carried out to learn a combined kernel from the predefined base kernels. In our algorithms, low-rank nonnegative matrix factorization (NMF) is used to carry out the unsupervised learning and learn an optimal combined kernel. Furthermore, the kernel NMF (KNMF) is introduced to substitute NMF for enhancing the ability of the unsupervised learning with the predefined base kernels. In the second step, the optimal kernel is embedded into the standard optimization routine of support vector machine (SVM). In addition, we address a major challenge in hyperspectral data classification, i.e., using very few labeled samples in a high-dimensional space. Experiments are conducted on three real hyperspectral datasets, and the experimental results show that the proposed algorithms, especially for KNMF-based MKL, achieve the outstanding performance for hyperspectral image classification with few labeled samples when compared with several state-of-the-art algorithms.