Master Thesis - Department of Computer Science

plored both of the spaces to capture and then combine discriminative directions for
enhancing discriminability across classes. Our approach efficiently exploit both the
spaces by combining them in two different levels: (i) Feature level and (ii) Decision
level.
For feature level fusion, we develop a dual space by combining the discriminative
features from both range space and null space of within-class scatter matrix Sw.
This allows us to utilize the whole set of discriminative directions present in an
entire face space. As every face has a unique decomposition in null space and range
space, we project all class means in both spaces to obtain two sets of projected
means. Now each of these sets are used separately to search for the directions that
discriminates them in that space. This step is equivalent to applying PCA on the
set of projected means separately. These two eigenmodels are then combined using:
1) Covariance Sum method and 2) Gramm-Schmidt Orthonormalization [42]. These
methods construct a new set of directions integrating the information from both
spaces. Then we reorder and select the best combination among those directions to
obtain the best discriminability across classes. The feature reordering and selection
is performed using two techniques: 1) Forward Selection and 2) Backward Selection
[39] on a validation set, based on a class separability criterion.
For decision level fusion, we extract two disjoint sets of optimal discriminatory
basis separately from null space and range space to obtain two different classifiers.
Then we combine the classifiers obtained on null space and range space using sum
rule and product rule, two classical decision fusion techniques developed by Kittler
[60],[59]. We also exploit each classifier separately using LDA and nonparametric
LDA to enhance class separability at classifier response level and then combine them
using sum rule. We denote the class scores provided by a classifier on a sample as
response vector. Basically, we use response vectors as features vectors at decision level
and employ LDA and nonparametric LDA to enhance class separability at classifier
output space. Response vectors on a validation set (disjoint from training and testing
sets of a database) is used as training data at decision level. Then the response
vectors on testing set of the database are recalculated in the eigenmodel to improve
combined classification accuracy.
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