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Fig. 10.5 Architecture of SVM-based late fusion method. In the fusion module, the vector x
is formed by the fusion of similarity matching scores in audio and visual domains, which are
respectively denoted by d a and d v . In the SVM, the input x and the support vector x i are nonlinearly
mapped (by
) into a feature space H , where dot products are computed. By the use of the kernel k ,
there two layers are in practice computed in one single step. The results are linearly combined by
weights v i , found by solving a quadratic program. The linear combination is fed into the function
˃ (
ˆ
x
)=
sgn
(
x
+
b
)
,where b is a bias
database, a subset of samples of x i ,
N T is used for training SVM to
learn a specific semantic concept defined by the positive class. This is described in
the following sections.
i
=
1
,
2
,...,
10.4.2
Support Vector Machine Learning
A mapping function f :
ˇ ₒ{±
1
}
is estimated by the input-output training data
[ 306 , 307 ],
(
x 1
,
y 1
) ,..., (
x i ,
y i ) ˇ ×{±
1
}
(10.20)
is some nonempty set that the patterns x i are taken from, and
the y i are the corresponding labels. It is assumed that the data were generated
independently from some unknown probability distribution P
The domain
ˇ
(
,
)
x
y
. The goal here
(
,
)
(
)=
is to learn a function that will correctly classify a new example
x
y
, i.e., f
x
y
for examples
(
x
,
y
)
that were also generated from P
(
x
,
y
)
. In other words, we choose
(
,
)
y such that
is in some sense similar to the training examples. To this end, we
need a similarity measure in
x
y
ˇ
, i.e.,
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