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 maximum volume. Since there are also other criteria which have been widely used for endmember extraction, the issue of interest is "does an endmember set really produce a simplex with maximum volume?" In other words, using the criterion of a simplex with maximum volume is a better and more effective measure than other criteria currently being used by endmember extraction such as orthogonal projection-based pixel purity index (PPI), fully constrained least squares-based spectral unmixing, etc. This paper explores this issue by investigating a number of popular endmember extraction algorithms which are designed by different criteria. An extensive experiment-based study is also conducted for comparative analysis.