Hyperspectral Data Processing: Algorithm Design and Analysis

6.5 Dimensionality Reduction by Projection Pursuit-Based Components Analysis Transforms

The component analysis transforms discussed in Sections 6.3 and 6.4 are actually special cases of projection pursuit (PP)-based component analysis transforms to be presented in this section where projection vectors specified by various orders of statistics can be interpreted by a more general concept called projection index (PI). This section investigates the idea of representing high-order statistics-based component analysis transforms in the context of PP and further develops three approaches similar to the three ICA-based component analysis transforms in discussed in Sections 6.6.1–6.6.3 to implement the PI-based PP. The first one is to use PI as a criterion to produce components, referred to as projection index components (PIC). In light of this interpretation the PI specified by data variance makes PP become PCA with PICs reduced to PCs. On the other hand, if the PI is specified by mutual information to measure statistical independence, the resulting PP turns out to be ICA in which case PICs become independent components (ICs). While using random initial conditions is the classical PP approach, it actually results in inconsistent PICs. So, the second and third approaches are developed to mitigate this dilemma by eliminating the inconsistency caused by the use of random initial condition, which are random projection index-based projection pursuit (RPI-PI) that is similar to RICA-DR in discussed ...