Master Thesis - Department of Computer Science
Master Thesis - Department of Computer Science
Master Thesis - Department of Computer Science
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T R<br />
T S<br />
denoted by RVNull and RVNull and are represented as,<br />
RV<br />
RV<br />
T R<br />
Null ≡ {DNull(vx 1 1 ), DNull(vx 1 2 ), . . . , DNull(vx 1 V ), DNull(vx 2 1 ),<br />
. . . , DNull(vx 2 V ), . . . , DNull(vx i j), . . . , DNull(vx C V )} (4.36)<br />
T S<br />
Null ≡ {DNull(tx 1 1 ), DNull(tx 1 2 ), . . . , DNull(tx 1 S ), DNull(tx 2 1 ),<br />
. . . , DNull(tx 2 S), . . . , DNull(tx i j), . . . , DNull(tx C S )} (4.37)<br />
Considering “training response vector set”, RV<br />
T R<br />
Null<br />
, as training as well as testing set,<br />
we calculate an accuracy denoted by A Original<br />
Null , with the condition that same samples<br />
are never compared. So, the calculation <strong>of</strong> A Original<br />
Null<br />
1. For i = 1 to V ∗ C<br />
involves the following steps:<br />
(i) Select a response vector DNull(vxc j ) where i = (c − 1) ∗ V + j from the set<br />
T R RVNull .<br />
(ii) Calculate the Euclidean distance <strong>of</strong> DNull(vx c j) from all other response<br />
T R<br />
vectors in the set RVNull .<br />
(iii) Find the class label <strong>of</strong> the response vector providing minimum distance<br />
from DNull(vx c j) and assign it to DNull(vx c j).<br />
(iv) Cross check the obtained class label with the original label.<br />
2. Calculate A Original<br />
Null<br />
as<br />
Number <strong>of</strong> correctly labeled response vectors<br />
T otal number <strong>of</strong> response vectors<br />
<strong>of</strong> response vectors is V ∗ C in this case.<br />
Then RV<br />
T R<br />
Null<br />
∗100%. Total Number<br />
is used to construct an LDA or nonparametric LDA based eigen-<br />
model. As the length <strong>of</strong> a response vector is equal to the number <strong>of</strong> classes (C) present<br />
in a database, we obtain C eigenvectors in the eigenmodel. Let, the C eigenvectors in<br />
the order <strong>of</strong> decreasing eigenvalues be represented by EVNull = [e 1 Null, ...e i Null, ..., e C Null].<br />
We obtain C eigensubspaces ESV i Null ’s for i = 1, 2..., C where ith eigensubspace<br />
ESV i Null contains first i eigenvectors from the set EVNull. Thus C th eigensubspace,<br />
ESV C Null , is same as EVNull. The performance <strong>of</strong> i th eigensubspace ESV i Null<br />
on “train-<br />
ing response vector set”, which is denoted by A ESV i Null<br />
Null , is evaluated by projecting<br />
RV<br />
T R<br />
Null onto ESV i Null and calculating accuracy in the same manner as described for<br />
the calculation <strong>of</strong> A Original<br />
Null . For each eigensubspace, we compare its performance with<br />
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