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In hyperspectral image analysis, the principal components analysis (PCA) and the maximum noise fraction (MNF) are most commonly used techniques for dimensionality reduction (DR), referred to as PCA-DR and MNF-DR, respectively. The criteria used by the PCA-DR and the MNF-DR are data variance and signal-to-noise ratio (SNR) which are designed to measure data second-order statistics. This paper presents an independent component analysis (ICA) approach to DR, to be called ICA-DR which uses mutual information as a criterion to measure data statistical independency that exceeds second-order statistics. As a result, the ICA-DR can capture information that cannot be retained or preserved by second-order statistics-based DR techniques. In order for the ICA-DR to perform effectively, the virtual dimensionality (VD) is introduced to estimate number of dimensions needed to be retained as opposed to the energy percentage that has been used by the PCA-DR and MNF-DR to determine energies contributed by signal sources and noise. Since there is no prioritization among components generated by the ICA-DR due to the use of random initial projection vectors, we further develop criteria and algorithms to measure the significance of information contained in each of ICA-generated components for component prioritization. Finally, a comparative study and analysis is conducted among the three DR techniques, PCA-DR, MNF-DR, and ICA-DR in two applications, endmember extraction and data compression where the proposed ICA-DR has been shown to provide advantages over the PCA-DR and MNF-DR.