Sparse representation classification (SRC) is being widely applied for target detection in hyperspectral images (HSI). However, due to the problem of the curse of dimensionality and redundant information in HSI, SRC methods fail to achieve high classification performance via a large number of spectral bands. Selecting a subset of predictive features in a high-dimensional space is a challenging problem for hyperspectral image classification. In this paper, we propose a novel discriminant feature selection (DFS) method for hyperspectral image classification in the eigenspace. Firstly, our proposed DFS method selects a subset of discriminant features by solving the combination of spectral and spatial hypergraph Laplacian quadratic problem, which can preserve the intrinsic structure of the unlabeled pixels as well as both the inter-class and intra-class constraints defined on the labeled pixels in the projected low-dimensional eigenspace. Then, in order to further improve the classification performance of SRC, we exploit the well-known simultaneous orthogonal matching pursuit (SOMP) algorithm to obtain the sparse representation of the pixels by incorporating the interpixel correlation within the classical OMP by assuming that neighboring pixels usually consist of similar materials. Finally, the recovered sparse errors are directly used for determining the label of the pixels. The extracted discriminant features are compatibly used in conjunction with the established SRC methods, and can significantly improve their performance for HSI classification. Experiments conducted with the hyperspectral data sets and different experimental settings show that our proposed method increases the classification accuracy and outperforms the state-of-the-art feature selection and classification methods.