Learning Dual Geometric Low-Rank Structure for Semisupervised Hyperspectral Image Classification

Most of the available graph-based semisupervised hyperspectral image classification methods adopt the cluster assumption to construct a Laplacian regularizer. However, they sometimes fail due to the existence of mixed pixels whose recorded spectra are a combination of several materials. In this paper, we propose a geometric low-rank Laplacian regularized semisupervised classifier, by exploring both the global spectral geometric structure and local spatial geometric structure of hyperspectral data. A new geometric regularized Laplacian low-rank representation (GLapLRR)-based graph is developed to evaluate spectral-spatial affinity of mixed pixels. By revealing the global low-rank and local spatial structure of images via GLapLRR, the constructed graph has the characteristics of spatial-spectral geometry description, robustness, and low sparsity, from which a more accurate classification of mixed pixels can be achieved. The proposed method is experimentally evaluated on three real hyperspectral datasets, and the results show that the proposed method outperforms its counterparts, when only a small number of labeled instances are available.