Master Thesis - Department of Computer Science

Table 4.3: Effect of increasing number of training samples on the performance of null
space and range space for PIE database.
No. of Training Null Space Range Space
Samples
2 80.21 40.17
4 82.58 72.36
6 88.33 75.28
8 90.44 89.75
10 93.49 97.55
12 55.33 94.56
14 53.87 94.44
16 50.58 95.90
18 39.86 96.04
robust and efficient for classification for higher number of training samples. The
common features extracted from a number of faces having expression variation
does not help in classifying the samples from the same class showing illumina-
tion variation. So, the performance of null space on Yale database is high with
very less number of training samples. On the other hand, the variability among
samples contributes in a different way in case of range space. Higher number
of training samples contributes to a large amount of intra-class variations in
range space. Thus, the information learned by range space from larger number
of training samples does not help in discrimination and adds to the degree of
confusion.
• On the contrary, ORL and PIE databases contain only a specific type of vari-
ability (pose for ORL and illumination for PIE). So, higher number of training
samples provides robust common features for null space and offers discrimi-
native information (instead of adding confusing information) to range space.
Hence, the performance increases with higher number of training samples in
the case of these two databases, unlike that in Yale database.
95