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In recent years, hyperspectral imaging, also known as imaging spectroscopy, has been paid an increasing interest in geoscience and remote sensing community. Hyperspectral imagery is characterized by very rich spectral information, which enables us to recognize the materials of interest lying on the surface of the Earth more easier. We have to admit, however, that high spectral dimension inevitably brings some drawbacks, such as expensive data storage and transmission, information redundancy, etc. Therefore, to reduce the spectral dimensionality effectively and learn more discriminative spectral low-dimensional embedding, in this paper we propose a novel hyperspectral embedding approach by simultaneously considering spatial and spectral information, called spatial-spectral manifold embedding (SSME). Beyond the pixel-wise spectral embedding approaches, SSME models the spatial and spectral information jointly in a patch-based fashion. SSME not only learns the spectral embedding by using the adjacency matrix obtained by similarity measurement between spectral signatures, but also models the spatial neighbours of a target pixel in hyperspectral scene by sharing the same weights (or edges) in the process of learning embedding. Classification is explored as a potential strategy to quantitatively evaluate the performance of learned embedding representations. Classification is explored as a potential application for quantitatively evaluating the performance of these hyperspectral embedding algorithms. Extensive experiments conducted on the widely-used hyperspectral datasets demonstrate the superiority and effectiveness of the proposed SSME as compared to several state-of-the-art embedding methods.