Many endmember extraction algorithms (EEAs) have been developed to find endmembers that are assumed to be pure signatures in hyperspectral data. However, two issues arising in EEAs have not been addressed: one is the knowledge of the number of endmembers that must be provided a priori, and the other is the initialization of EEAs, where most EEAs initialize their endmember-searching processes by using randomly generated endmembers, which generally result in inconsistent final selected endmembers. Unfortunately, there has been no previous work reported on how to address these two issues, i.e., how to select a set of appropriate initial endmembers and how to determine the number of endmembers p. This paper takes up these two issues and describes two-stage processes to improve EEAs. First, a recently developed concept of virtual dimensionality (VD) is used to determine how many endmembers are needed to be generated for an EEA. Experiments show that the VD is an adequate measure for estimating p. Second, since EEAs are sensitive to initial endmembers, a properly selected set of initial endmembers can make significant improvements on the searching process. In doing so, a new concept of endmember initialization algorithm (EIA) is thus proposed, and four different algorithms are suggested for this purpose. It is surprisingly found that many EIA-generated initial endmembers turn out to be the final desired endmembers. A further objective is to demonstrate that EEAs implemented in conjunction with EIA-generated initial endmembers can significantly reduce the number of endmember replacements as well as the computing time during endmember search