Master Thesis - Department of Computer Science

Table 4.1: Effect of increasing number of training samples on the performance of null
space and range space for Yale database.
No. of Training Null Space Range Space
Samples
2 93.33 64.44
3 93.33 76.67
4 90.48 82.86
5 88.89 81.11
6 85.33 76.67
7 81.67 76.67
8 75.56 75.56
9 50.00 56.67
attains a maximum value 95.00% for eight training samples but again decreases down
to 92.00% for nine training samples due to the small size of null space. The perfor-
mance of range space exhibits an interesting behavior. The accuracy of range space
increases with increasing number of training samples for the following two reasons:
(i) the subspace learns more and more about the pose variations across the database
and (ii) discriminative informations go to range space due to the increase in the
number of training samples. Thus maximum accuracy for range space is obtained as
97.50% for eight training samples. But the further inclusion of more training samples
reduces the performance due to the following reasons: (i) the new training samples
does not provide any extra discriminatory information with respect to the informa-
tion already learned by the classifier from previous training samples, (ii) moreover,
they add confusing information to the discriminatory features.
For PIE database the performance of null space and range space is evaluated
and shown (see Table 4.3) for even number of training samples ranging from two (2)
to eighteen (18). The performances of null space and range space with increasing
number of training samples can be explained by a similar logic as described in case
of Yale and ORL databases. PIE has only illumination variation.
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