Dimensionality reduction is a preprocessing step for hyperspectral image (HSI) classification. Principal component analysis reduces the spectral dimension and does not utilize the spatial information of an HSI. Both spatial and spectral information are used when an HSI is modeled as a tensor, that is, the noise in the spatial dimension is decreased and the dimension in a spectral dimension is reduced simultaneously. However, this model does not consider factors affecting the spectral signatures of ground objects. This means that further improving classification is very difficult. The authors propose that the spectral signatures of ground objects are the composite result of multiple factors, such as illumination, mixture, atmospheric scattering and radiation, and so on. In addition, these factors are very difficult to distinguish. Therefore, these factors are synthesized as within-class factors. Within-class factors, class factors, and pixels are selected to model a third-order tensor. Experimental results indicate that the classification accuracy of the new method is higher than that of the previous methods.