Hyperspectral imagers collect hundreds of images corresponding to different wavelength channels for the same area on the surface of the earth. Since a lot of information is redundant in neighboring bands and pixels, reducing dimensionality is necessary. Due to the high resolution in the spatial–spectral domain and complex computation, this procedure is time-consuming. Advances in leveraging special hardware, such as GPUs and MICs, show new ways of accelerating dimensionality reduction. We propose a parallel framework of fast independent component analysis (FastICA) for hyperspectral image (HSI) dimensionality reduction on heterogeneous platforms, which offers six parallel implementations on different parallel platforms. We also use specialized optimizations for each hotspot of FastICA and implement them in our framework running on a local GPU server and the Tianhe-2 supercomputer. The experimental results show that all these parallel implementations in the framework can obtain excellent performances and good scalabilities: the speed-up is up to 169 times on the GPU server and 410 times using 64 nodes on the Tianhe-2 supercomputer compared to the sequential implementation. We conclude that by using our framework, HSI dimensionality reduction can be implemented in real-time on the heterogeneous platform.