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