Master Thesis - Department of Computer Science

iii) Project all class means onto null space and range space using the basis
vectors for range space only (see Eqn. 4.12-4.13). The sets of class means
projected on null space and range space are denoted by XNull and XRange,
respectively.
iv) Compute the scatter matrices, SNull and SRange of XNull and XRange, re-
spectively.
v) Perform eigen-analysis of SNull and SRange to obtain discriminatory direc-
tions W Null
opt
and W Null
opt
in null space and range space separately.
Let, DNull and DRange be two classifiers defined on the null space and
range space, respectively.
2. Decision Fusion of DNull and DRange.
i) Construct DP (x) for a test sample, x.
ii) Obtain ˜ D (using any one among (a) or (b) or (c))
(a) Apply sum rule to obtain ˜ D.
(b) Apply product rule to obtain ˜ D.
(c) Apply proposed method of decision fusion (see Fig. 4.4 given in sec-
tion 4.4.2) to obtain ˜ D.
iii) Use maximum membership rule to obtain crisp class labels for a test sample
x.
Experimental results for our proposed method is given in the following section.
4.5 Experimental Results and Discussion
We observe the performance of our proposed method on three public face databases:
Yale, ORL and PIE. Yale has 15 subjects with 11 samples per class. ORL and PIE
consist of 40 and 60 subjects with 10 and 42 samples per class respectively. More
details about these databases are provided in Section 3.4.1.
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