This paper proposes a spectral-spatial linear discriminant analysis (LDA) method for the hyperspectral image classification. A natural assumption is that similar samples have similar structure in the dimensionality reduced feature space. The proposed method uses a local scatter matrix from a small neighborhood as a regularizer incorporated into the objective function of LDA. Different from traditional LDA and its variants, our proposed method yields a self-adaptive projection matrix for dimension reduction, which improves the classification accuracy and avoids running out of memory. In order to consider the nonlinear case, this paper generalizes our linear version to its kernel version. Experimental results demonstrate that our proposed methods outperform several dimension reduction algorithms.