Local Constraint-Based Sparse Manifold Hypergraph Learning for Dimensionality Reduction of Hyperspectral Image

Abstract

Sparse representation-based graph embedding methods have been successfully applied to dimensionality reduction (DR) in recent years. However, these approaches usually become problematic in the presence of the hyperspectral image (HSI) that contains complex nonlinear manifold structure. Inspired by recent progress in manifold learning and hypergraph framework, a novel DR method named local constraint-based sparse manifold hypergraph learning (LC-SMHL) algorithm is proposed to discover the manifold-based sparse structure and the multivariate discriminant sparse relationship of HSI, simultaneously. The proposed method first designs a new sparse representation (SR) model named local constrained sparse manifold coding (LCSMC) by fusing local constraint and manifold reconstruction. Then, two manifold-based sparse hypergraphs are constructed with sparse coefficients and label information. Based on these hypergraphs, LC-SMHL learns an optimal projection for mapping data into low-dimensional space in which embedding features not only discover the manifold structure and sparse relationship of original data but also possess strong discriminant power for HSI classification. Experimental results on three real HSI data sets demonstrate that the proposed LC-SMHL method achieves better performance in comparison with some state-of-the-art DR methods.