In hyperspectral image analysis, dimensionality reduction is a preprocessing step for hyperspectral image (HSI) classification. Principal component analysis (PCA) reduces the spectral dimension and does not utilize the spatial information of an HSI. To solve it, the tensor decompositions have been successfully applied to joint noise reduction in spatial and spectral dimensions of hyperspectral images, such as parallel factor analysis (PARAFAC). However, the PARAFAC method does not reduce the dimension in the spectral dimension. To improve it, two new methods were proposed in this article, that is, combine PCA and PARAFAC to reduce both the dimension in the spectral dimension and the noise in the spatial and spectral dimensions. The experimental results indicate that the new methods improve the classification compared with the PARAFAC method.