If we wish to have a dynamic face recognition system that continuously
enlarges *D* in real-time as it views new individuals, it is possible to
recompute the PCA using more efficient iterative gradient search methods, such
as the one proposed by Roseborough and Murase [41]. However, we
shall only compute the eigenvectors once for a dataset of *N*=338 faces and
then reuse these eigenvectors on new faces which were not part of the original
dataset matrix *D*. This approach is based on the assumption that a large
enough initial training sample of 300+ mug-shot faces would populate the
``face-space'' cluster within the larger ``image-space'' quite adequately
(i.e., densely and extensively enough). Thus, new faces will simply fall
within the predetermined face-space region and hence are well approximated by
the span of the eigenvectors that were previously generated [44].

Figure shows a plot of the magnitude of the eigenvalues
versus their rank. The magnitude of an eigenvalue, ,
is equal to the
variance in the data set that is spanned by its corresponding eigenvector,
.
Thus, it is obvious that higher-order eigenvectors account for
less energy in the approximation of the data set since their eigenvalues have
low magnitudes. We choose to truncate the set of eigenvectors to the first 60
vectors. This reduced set of eigenvectors accounts for enough face-variance to
avoid excessively lossy compression. *M*=60 will be used throughout the
experiments [22]. The first 10 of our eigenvectors (also called
eigenfaces since they are formed from face images) are shown in
Figure .