Master Thesis - Department of Computer Science
Master Thesis - Department of Computer Science
Master Thesis - Department of Computer Science
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We exploit classifier space in two ways:<br />
1. LDA and<br />
2. Nonparametric LDA.<br />
LDA and nonparametric LDA are discussed in Section 4.4.2.1 and Section 4.4.2.2,<br />
respectively.<br />
We combine face and fingerprint (two modalities for person authentication) using<br />
our proposed algorithm, described in this section. As already discussed in Section 5.2,<br />
our aim is to improve combined performance by conditionally replacing response<br />
vector Di(x) by our proposed measure, ¯ Di(x), in DP(x) to obtain ¯<br />
DP (x), classifier-<br />
wise by using train and validation response vector sets (obtained on two disjoint<br />
validation sets, validation1 and validation2).<br />
Now for each <strong>of</strong> the L classifier, we construct train, validation and test response<br />
vector sets, denoted by RV<br />
RV<br />
T R<br />
i<br />
, RV<br />
V A<br />
i<br />
and RV<br />
T S<br />
i<br />
T R<br />
i<br />
, RV<br />
V A<br />
i<br />
T S and RVi , where i = 1, 2, ..., L. Precisely,<br />
form the sets <strong>of</strong> the i th rows <strong>of</strong> the DP’s constructed from<br />
validation1 validation2 and test set feature vectors respectively. Now let validation1<br />
validation2 and test set feature vectors for i th classifier are denoted by:<br />
(i) validation1 feature vector set: {ux11 , ux21 M T R<br />
, . . . , ux i 1 12 mc M T R<br />
, ux , . . . , ux , . . . , ux i C },<br />
(ii) validation2 feature vector set: {vx11 , vx21 M V A<br />
, . . . , vx i 1 12 mc M V A<br />
, vx , . . . , vx , . . . , vx i C },<br />
and (iii) test feature vector set: {tx11 , tx21 M T S<br />
, . . . , tx<br />
i 1 , tx 12 , . . . , tx mc , . . . , tx M<br />
T S<br />
i C },<br />
where for i th classifier the number <strong>of</strong> response vectors per class for the three disjoint<br />
T R<br />
sets are M<br />
i , M<br />
V A<br />
i<br />
, M<br />
T S<br />
i<br />
respectively. The superscript “mc” on a feature vector (e.g.<br />
ux mc ) denotes the m th sample from c th class <strong>of</strong> the corresponding set. So the response<br />
vector sets can be visualized as:<br />
T R<br />
RVi ≡ {Di(ux 11 ), . . . , Di(ux<br />
V A<br />
RVi ≡ {Di(vx 11 ), . . . , Di(vx<br />
T S<br />
RVi ≡ {Di(tx 11 ), . . . , Di(tx<br />
M T R<br />
i 1<br />
), Di(ux 12 ), . . . , Di(ux mc M T R<br />
), . . . , Di(ux i<br />
M V A<br />
i 1<br />
), Di(vx 12 ), . . . , Di(vx mc M V A<br />
), . . . , Di(vx i<br />
M T S<br />
i 1 ), Di(tx 12 ), . . . , Di(tx mc ), . . . , Di(tx<br />
M T S<br />
i C )}.<br />
C )},<br />
C )},<br />
The steps <strong>of</strong> our algorithm is given below for L classifiers, even though we are<br />
dealing with the case where L = 2.<br />
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