Dimensionality reduction of hyperspectral images based on sparse discriminant manifold embedding

Sparse manifold clustering and embedding (SMCE) adaptively selects neighbor points from the same manifold and approximately spans a low-dimensional affine subspace, but it does not explicitly give a projection matrix and encounters the out-of-sample problem. To overcome this drawback, we propose a new dimensionality reduction method, called sparse manifold embedding (SME), based on graph embedding and sparse representation for hyperspectral image (HSI). It utilizes the sparse coefficients of affine subspace to construct a similarity graph and preserves this sparse similarity in embedding space. Furthermore, we try to make full use of the prior label information to design a novel supervised learning method termed sparse discriminant manifold embedding (SDME). SDME not only inherits the merits of the sparsity property of affine subspace but also boosts the compactness of intra-manifold, which achieves discriminating features and further improves the classification performance of HSI. Experiments on two real hyperspectral data sets (Indian Pines and PaviaU) show the benefits of the proposed SME and SDME methods.