Master Thesis - Department of Computer Science

4.5.1 Effect of Number of Training Samples on the Performance of Null
Space and Range Space
To demonstrate the effect of increasing number of training sample on the performance
of null space and range space, we compute the recognition accuracies of null space
and range space for Yale, ORL and PIE databases with different number of training
samples. For Yale and ORL databases, the accuracies are calculated for the number
of training samples per class ranging from two to nine. As the number of training
samples per class for PIE database is higher (42), the number of training samples is
varied in the range 2 to 18 (e.g. 2, 4, 6,..., 18). The image size has been kept as 25*25
for all databases. The null space technique used in our experimentation is adopted
from the method called Discriminative Common Vectors (DCV) [20].
The performance of null space and range space for Yale database is shown in
Table 4.1. The performance of null space is best when the number of training samples
per class is only two and three. Performance of null space decreases with increasing
number of samples and provides the minimum accuracy of 50% when number of
training samples is maximum (nine). This result validates the claim of negative
effect of increasing number of training samples on the performance of null space.
Initial increase in the number of training samples enhances performance of null space,
because the captured common features for each class hold more robust commonalities
present across samples containing variations in expression, illumination and pose. In
case of range space, the performance increases with increasing number of training
samples upto a certain point and again deteriorates. This performance trend can
be easily explained by stating that initial increase in number of samples drives the
discriminative information to the range space. However too many number of training
samples leads to a huge amount of intra-class variations which in turn effects the
overall accuracy.
The performances of null space and range space on ORL database with training
samples varying from two to nine are shown in Table 4.2. As the ORL database has
only pose variation, the increasing number of training samples helps the null space to
capture the common features which are robust and efficient for classification. So, the
performance of null space increases with increasing number of training samples and
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