With the advanced hyperspectral sensors, it provides a possibility to discriminate the land-cover types which cannot be detect with natural photographic or multi-spectral images. Hyperspectral image classification has become one of the hottest research fields of the remote sensing area. The task of hyperspectral image classification is to assign each pixel to its truth class. The classification methods in hyperspectral image are mainly divided into two categories: pixelwise classification and spectral-spatial classification. Recent researches show that spectral-spatial classification is prone to achieving the state-of-the-art performance. However, there exists still an open issue for how to utilize the spectral and spatial information. This thesis includes five parts to introduce the proposed methods. (1) This thesis introduces a spatial hypergraph embedding model for dimension reduction. Comparing with graph model, hypergraph model can represent higher order relationships. (2) This thesis introduces two manifold-based sparse representation algorithms, which exploit the local spatial structure of the test samples in corresponding sparse representations for enforcing smoothness across neighboring samples' sparse representations. Using techniques from regularization and local invariance, two manifold-based regularization terms are incorporated into the 1 -based objective function. (3) This thesis generalizes the 1 -based sparse representation method to its tensor form, which uses a patch structure to represent original pixel. To optimize the scale of the patch structure, a multi-scale fusion framework based on the ensemble learning method is proposed to further improve classification performance. iii (4) This thesis proposes a sparse representation based on the set-to-set distance for HSI classification. Through utilizing the set-to-set distance, the spatial information is incorporated into the sparse representation-based model. (5) This thesis proposes a novel sparsity-based framework is proposed, which adopts the max pooling operation for HSI classification. Compared with the traditional sparsity-based frameworks using residual error, sparse representations in our proposed framework are utilized to generate the feature vectors using max pooling operation. The experimental results have demonstrated the effectiveness of the proposed methods