Independent component analysis-based dimensionality reduction with applications in hyperspectral image analysis

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.