Dimensionality reduction is one of the commonly used techniques in the field of hyperspectral image (HSI) classification. In this paper, we propose an edge-smoothing-based distribution preserving hyperspherical embedding (DPHE) framework, which can project the high-dimensional HSI data into a lower-dimensional hyperspherical coordinate system. Our proposed framework is capable of capturing the intrinsic structures and then maintain these structures in the lower-dimensional embedding space as much as possible. Especially, when we estimate the distribution of each pixel with spectral signatures, we take full advantage of both the spatial information and the intensity information. As a result, the proposed framework can detect the real object boundaries by smoothing the distributions with edge-stopping function. We also devise a coefficient normalization type of algorithm to optimize the proposed constrained framework. The experimental results on three real-life HSI data sets, i.e., Botswana Hyperion, Kennedy Space Center, and Indian Pines, show that our proposed DPHE can significantly improve the classification accuracy. For instance, the over accuracy is increased from 78% to 97% on Indian Pines data. As part of evaluation, we also present the visualization of HSI cube in the three-dimensional unit hyperspherical coordinate system.