11.5 Impact of Dimensionality Reduction on EEAs

Finally, this section investigates the impact of DR on the performance of EEAs. Most endmember extraction algorithms require dimensionality reduction to reduce computation complexity. For example, in order to calculate simplex volumes N-FINDR, SGA, and VCA need DR to reduce data dimensionality of a simplex or convex hull to avoid singularity problems in which case the number of components, q, to be retained after DR is set to the number of extracted endmembers, p. However, several questions may arise: does “p = q” always give the best performance? If more components are used to extract the same number of endmembers, that is, q > p, will it improve the performance of EEAs? The 15-panel HYDICE data in Figure 1.15(a) and (b) provide an excellent example to explore insights into these issues. The EEAs to be tested for performance evaluation are N-FINDR, SC N-FINDR, and SGA, all of which require simplex volume calculation that is closely related to data dimensionality reduction. Furthermore, because the inconsistency of these algorithms caused by the random initial endmembers might result in biased comparisons, ATGP is used as an EIA to generate the same initial endmembers shown in Figure 11.17 to initialize N-FINDR and SC N-FINDR, while IED-SGA is used to run SGA in the following experiments.

Figure 11.17 Nine endmembers generated by ATGP used to initialize the N-FINDR and SC N-FINDR in the following experiments.

Since VD estimated ...

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