Does a simplex formed by endmembers really yield maximal volume?

One of commonly used criteria for finding an endmember set is based on the fact that for a given number of endmembers, p, a p-vertex simplex with its all p vertices specified by endmembers always yields the maximal volume. Since there are also other criteria that have been used for endmember extraction, an interesting issue arises: 'Does a p-vertex simplex with its all vertices specified by p endmembers really produce maximal volume?' In other words, 'Is the maximal simplex volume a better and more effective measure than other criteria currently being used by endmember extraction such as orthogonal projection, least squares error, etc.?' This paper explores this issue by investigating a number of popular endmember extraction algorithms designed by various criteria via a comparative study and analysis through real image experiments.