Automated classification of land cover types based on hyperspectral imagery often involves a large geographical area, but class labels are available for only small portions of the entire area. Moreover, the spectral signature of the same land cover class may vary substantially over different locations. When a classifier is trained on a specific geographical location and applied to other areas, it often performs poorly because of such spatial variation of spectral signatures. In this paper, we propose a novel framework for classification of hyperspectral data: a Gaussian-Process Maximum-Likelihood (GPML) model where the mean of each spectral band is spatially modeled using a Gaussian process. Our framework provides a practical and effective way to model spatial variations of high dimensional data such as hyperspectral images for classification problems.