Semisupervised Manifold Joint Hypergraphs for Dimensionality Reduction of Hyperspectral Image

In this letter, a new semisupervised dimensionality reduction (DR) method, termed geodesic-based manifold joint hypergraphs (GMJHs), is proposed for hyperspectral image (HSI). This method first builds a geodesic-based reconstruction model to discover the nonlinear similarity between two manifold reconstruction neighborhoods. Then, it implies the probabilistic relationship between unlabeled samples and each class via the geodesic-based reconstruction distance. With the probabilistic class relationship, a supervised hypergraph and an unsupervised hypergraph are constructed to represent the multivariate manifold relationship of samples. Finally, the supervised and unsupervised hypergraphs are jointed for learning optimal projection matrix and enhancing the intraclass compactness in low-dimensional embedding space. Experiments on two HSI data sets show that the proposed GMJH algorithm performs better performance than some state-of-the-art DR methods.