Hyperspectral Data Processing: Algorithm Design and Analysis

10.6 Random ICA-Based EEA (RICA-EEA)

The idea of RICA-EEA is derived from a recent work on an independent component analysis (ICA)-based approach to DR (Wang and Chang, 2006a) where FastICA developed by Hyvarinen and Oja (1997) is used to generate independent components (ICs). Since FastICA also uses random projection vectors as its initial condition to initialize its algorithm, it also encounters the same problem as both PPI and N-FINDR do. Because the initial projection vector for each IC is randomly generated by FastICA for each run, the ICs generated by each run are also different. Nevertheless, if the information contained in an IC is significant, such an IC will always appear in each run. With this assumption, if FastICA is repeatedly implemented, the ICs that are common in all runs should be the desired ICs for endmember extraction. The detailed implementation of RICA-EEA is summarized as follows.

RICA-EEA Algorithm

1. Initialization

Assume that the number of initial endmembers is p. Set .

2. At each n, run FastICA to find p independent components, , where each independent component, can be formed as a vector denoted by . It should be noted that FastICA randomly generates ...