8.3 Simplex Growing Algorithm (SGA)

In this section, we present an SQ-EEA, called SGA developed by Chang et al. (2006), which can be considered another sequential version of SM N-FINDR. Unlike SC N-FINDR, which starts with a randomly generated p-vertex simplex and then successively replaces one vertex at a time via (8.1), SGA starts with one vertex and then begins to grow a simplex by one vertex at a time until it reaches p.

The key to making SGA work hinges on how to appropriately select new vertices to augment growing simplexes. According to N-FINDR for a given positive integer p, a simplex formed by p endmembers is the one that produces the maximal volume among all possible simplexes formed by any set of p data sample vectors. Using this as a criterion, SGA grows the current k-vertex simplex img to a (k + 1)-vertex simplex img by finding a new (k + 1)st vertex e(k) so that the new (k + 1)-vertex simplex img produces its volume that is not less than volumes of all possible (k + 1)-vertex simplexes img augmented by any other data sample vector r. The detailed implementation of the above growing simplex ...

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