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image is similar. The Gabor Wavelet features of r 1 frequency and eight directions are
first extracted from images number one to n+1 . Then the similarities between each of
train images and test image are evaluated according to equation 12, as discussed in the
previous section. It is obvious that in order to become these similarities comparable
they must be normalized in such a way that the sum of similarities vector of test
image becomes unit. So they are normalized in range [0,1]. After calculating each of
these similarities between each two training and test images, a similarity vector
named sim r1 which is a vector with n elements, is obtained. It is important to note that
the sim r1 i means the similarity between images number i and test image.
As the reader can guess, the problem mentioned here, is an n class problem. sim r1
can be also served as a simple classifier C r1 which uses image number 1 to n as its
train dataset. So as to the index of the maximum value in the vector can be considered
as class label of test image.
Considering sim r1 , r1
{ 0,...4 } there are five classifiers to classify the test image.
Now the majority-votes ensemble is employed to classify the test image. Assume that
the accuracy of classifier C r1 is denoted by p r1 , the weight vector w can
straightforwardly be calculated in the weighted-majority-votes ensemble.
5 Parameters of Classification
In the experiments, there exist 2×300 training images. Here there are 300 real classes,
2 images per each class denoted by TI i and VI i where i
{ 1,..300 }. Indeed one image
of class i is denoted by TI i and the other by VI i . 300 fixed images i.e. TI i , are selected
as training dataset. Running the algorithm 299 times, each time one of VI i is
considered as test image and the other 299 images as validation dataset. In z th running
of algorithm image VI z is selected as test image and images VI j where j
{ 1,...300 }-
{ VI z } are considered as validation dataset. Now we obtain 5 classifiers C r1 ,
r1
{ 0,...4 } based on sim r1 . To calculate the accuracies of C r1 the mentioned
validation dataset is used as following. The similarities between each pairs of images
denoted by TI i and VI i , where i
{ 1,..300 } and j
{ 1,...300 }-{ VI z } are evaluated
employing equation 13.
r
1
r
i
1
j
SIMILARITY
=
sim
(
I
)
(13)
i
,
j
It is obvious that these similarities must also again be normalized in order to
become them comparable. So they are again normalized in range [0,1] as mentioned
before. After calculating each of these similarities between each two of training
datasets, a similarity matrix named SIMILARITY r1 which is an n × n matrix, is
obtained. It is important to note that the SIMILARITY r1 i,j means the similarity between
image number i of training dataset and image number j of validation dataset and the
VI z th column of that matrix is invalid.
Now the accuracy of classifier C r1 , on the training data, is the number of training
data that correctly assigned to its correct class, divided to n . In other words, the
number of the columns which its maximum value is over matrix diagonal, divided to
n can be considered as the accuracy of this classifier as stated in equation 14.
Although it is obvious that diagonal elements of this matrix must be the largest in
their columns, it is not true in many cases.
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