Hyperspectral Data Processing: Algorithm Design and Analysis

11.6 Conclusions

This chapter is a culmination of previous chapters in PART II and concludes endmember extraction with exploration of insights into relationships among several recently developed popular EEAs, PPI, N-FINDR, VCA, SGA, and ATGP. With appropriate interpretations VCA and SGA can be considered sequential versions of PPI and N-FINDR, respectively, with ATGP bridging the gap between PPI and VCA. On the other hand, the relationship between VCA and SGA is derived from the same idea of growing convex hulls for VCA and growing simplexes for SGA by adding a new endmember at a time as a new vertex in sequence, with the only difference that VCA follows PPI to use maximal orthogonal projection as a criterion as opposed to SGA, which follows N-FINDR to use maximal simplex volume as a criterion. This difference leads to an interesting issue: What is the best criterion to design EEAs? As investigated in this chapter it turns out that using the maximal simplex volume as a criterion is a better measure to design EEAs due to the fact that simplex volume satisfies full abundance constraints, abundance sum-to-one constraint (ASC) and abundance nonnegativity constraint (ANC), while convex hull volume only satisfies ANC. Details on this will be found in Section 33.2 and Chang (2013). Since most EEAs require dimensionality reduction (DR) to reduce data volumes, the impact of DR on endmember extraction is also investigated in this chapter. The experimental results demonstrate that high-order ...