9.2 Initialization Issues

From a viewpoint of algorithm design, three major issues determine the performance of an algorithm: initial conditions, stopping criteria, and learning rules. On some occasions, stopping criteria that set thresholds to terminate an algorithm are also closely related to initial conditions. Over the past few years, EEAs have been designed for finding endmembers which are mainly focused on the third issue, that is, learning rules. However, little work has been devoted to deal with algorithm initialization issues, which can be as important as learning rules as described in the following section.

9.2.1 Initial Conditions to Terminate an EEA

There are generally two initial conditions that can be used to terminate an EEA. One is to preset an error threshold, ε, to terminate an algorithm. Since the selection of an appropriate ε is usually data dependent, it is generally difficult to do so without prior knowledge about the data. If the value of ε is too small, the algorithm may take a long time to converge and may also run into a stability problem with fluctuating results. Besides, it may generate more endmembers than are actually needed. On the contrary, if the value of ε is too large, the algorithm may terminate earlier than it should. In this case, the set of generated endmembers may be insufficient and some desired endmembers will have to be left out. As an alternative, we may preset the number of endmembers needed to be generated, p. In this case, an alternative ...

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