Hyperspectral Data Processing: Algorithm Design and Analysis

11.4 Does an Endmember Set Really Yield Maximum Simplex Volume?

One of commonly used criteria for finding an endmember set is to assume that for a given number of endmembers, p, a p-vertex simplex with its vertices specified by p endmembers always yields the maximal volume. Since there are also other criteria that have been widely used for endmember extraction, an issue of interest is “does an endmember set really produce a simplex with maximal volume?” In other words, using the criterion of maximal simplex volume is a better and more effective measure than other criteria currently being used by EEAs such as OP fully constrained least squares-based spectral unmixing, etc. This section explores this issue by investigating a number of popular EEAs that are designed by different criteria. An extensive experiment-based study is also conducted for comparative analysis.

Endmember extraction has received considerable interest recently. Many EEAs have been also developed for this purpose based on different philosophies, of which three major criteria are of interest. One is convex geometry-based methods that include finding extreme points of convexity via orthogonal projection such as PPI, VCA ATGP. Another is finding a simplex with the minimal volume that embraces all data samples such as MVT, CCA, or a simplex with the maximal volume that includes as many data samples as possible such as N-FINDR. A third one is least squares error-based constrained spectral unmixing methods such as iterative ...