8

Sequential Endmember Extraction Algorithms (SQ-EEAs)

One major disadvantage of implementing a simultaneous endmember extraction algorithm (SM-EEA), as discussed in Chapter 7, is its high computational complexity and exceedingly high computing cost. This is because of the fact that an SM-EEA does not use the results produced by previous searches and a new full search must be resumed as long as previously found endmembers are not desired ones. In addition, its searching process must be conducted in an exhaustive manner for which the computation will become formidable once the number of endmembers to generate grows large. The sequential EEAs (SQ-EEAs), presented in this chapter, are the result of a need for addressing these two issues. An SQ-EEA is developed to sequentially find one endmember after another to address the first issue, where previously generated endmembers can be retained and included as part of a subsequent search for a new endmember. Because an SQ-EEA can only find one endmember at a time, its computational complexity is tremendously reduced which also resolves the second issue. The outcome of these two advantages is that an SQ-EAA may not necessarily produce an optimal solution as does an SM-EEA. Nevertheless, experiments demonstrate that the trade off is small and an SQ-EEA can perform almost equally like an SM-EEA provided that an SQ-EEA is appropriately designed to match its SM-EEA version. Interestingly, many SQ-EEAs have actually been derived from their SM-EEA counterparts in Chapter 7. Examples include vertex component analysis (Nascimento and Dias, 2005) from PPI, SQ N-FINDR (Wu et al., 2008), and simplex growing algorithm (Chang et al., 2006) from N-FINDR and unsupervised fully constrained least-squares (Heinz and Chang, 2002) from FCLS-EEA.