Hyperspectral Data Processing: Algorithm Design and Analysis

11.3 Comparative Study and Analysis Between SGA and VCA

Two major design criteria, OP and simplex volume, have been widely used to design EEAs. In Section 11.2, relationships among three popular algorithms, PPI, VCA, and ATGP, were explored from a perspective of OP. As also demonstrated in Section 11.2, simplexes formed by VCA-found endmembers did not necessarily yield maximal simplex volumes. This is because maximal OP does not imply maximal simplex volume. This fact is further confirmed and supported in the following experiments. In this section, we follow a similar treatment from a perspective of simplex volume. Despite that there are several simplex volume-based EEAs, N-FINDR remains the most popular EEA that has been used as a base to derive new EEAs. However, as discussed in Chapter 7, N-FINDR has several difficulties with practical implementation. As a matter of fact, many simplex volume-based algorithms claimed to be implemented as N-FINDR are not its original version but actually sequential versions of N-FINDR. Recently, a rather different sequential algorithm, called simplex growing algorithm (SGA) proposed by Chang et al. (2006), finds endmembers one after another by growing simplexes with the maximal volumes one vertex at a time. It can be considered as a sequential N-FINDR in the same way as VCA is considered as PPI by growing convex hulls with the maximal orthogonal projections one vertex at a time. This similarity allows us to make a fair and very interesting comparison ...