248
10: Pakorn Watanachaturaporn, Manoj K. Arora
Different Optimizers using Linear Kernel
30.00
25.00
~ 20.00
E
i= 15.00
OJ
I:
:;::;
~ 10.00
5.00
0.00
~ _ _ CD -G- LSV .. j
L>.
IR.~;:;~"'::'""::,,
~~~
~
\:)\:)\:J",,<;5
".
~
/
,
~
/
""~
L>.
dJ.A L>.
........
~~
"
Penalty Value (C)
Fig. 10.9. Testing time when using different optimizers on the hyperspectral image
10.4.3
Effect of Kernel Functions
The choice of a proper kernel function also plays an important role in SVM
based classification. Four types of kernels, namely the linear kernel, the polynomial kernel, the RBF kernel, and the sigmoid kernel have been investigated.
Five polynomial kernels with degrees varying from 2 to 7 have been used. Thus,
the effect of 9 kernel functions on the accuracy of classification implemented
using the LSVM optimizer and the pairwise multiclass method for different
values of the penalty parameter has been assessed. Classification of both multiand hyperspectral datasets has been performed. The variation in the overall
accuracy of multispectral classification over different C values is presented in
the form of plots drawn for different types of kernel functions (Fig. 10.10 to
Fig. 10.14).
It can be seen from these plots that the use of all the kernels, except the
sigmoid function, results in an accuracy of more than 90%. The sigmoid kernel could attain a maximum accuracy of 79% at C == O. 5, which gradually
dropped with any increase in C. This shows a relatively poor performance
of this kernel with respect to others. In contrast, all other kernels showed
an increase in accuracy as C increased and reached their maximum after
which accuracies remained constant in general. This shows that there is an
optimum C value for a particular kernel. Focusing on the performance of
only polynomial kernels, it can be seen that the polynomials with degrees 2
to 4 produced very low accuracies (of the order of 20%) when C was very
small. But the accuracy shoots up with a small increase in C. On the other
hand, the initial accuracy obtained from polynomials with higher degrees
(from 5 to 7) is high (of the order of 70% to 80%) at small C values. Also,
10: Pakorn Watanachaturaporn, Manoj K. Arora
Different Optimizers using Linear Kernel
30.00
25.00
~ 20.00
E
i= 15.00
OJ
I:
:;::;
~ 10.00
5.00
0.00
~ _ _ CD -G- LSV .. j
L>.
IR.~;:;~"'::'""::,,
~~~
~
\:)\:)\:J",,<;5
".
~
/
,
~
/
""~
L>.
dJ.A L>.
........
~~
"
Penalty Value (C)
Fig. 10.9. Testing time when using different optimizers on the hyperspectral image
10.4.3
Effect of Kernel Functions
The choice of a proper kernel function also plays an important role in SVM
based classification. Four types of kernels, namely the linear kernel, the polynomial kernel, the RBF kernel, and the sigmoid kernel have been investigated.
Five polynomial kernels with degrees varying from 2 to 7 have been used. Thus,
the effect of 9 kernel functions on the accuracy of classification implemented
using the LSVM optimizer and the pairwise multiclass method for different
values of the penalty parameter has been assessed. Classification of both multiand hyperspectral datasets has been performed. The variation in the overall
accuracy of multispectral classification over different C values is presented in
the form of plots drawn for different types of kernel functions (Fig. 10.10 to
Fig. 10.14).
It can be seen from these plots that the use of all the kernels, except the
sigmoid function, results in an accuracy of more than 90%. The sigmoid kernel could attain a maximum accuracy of 79% at C == O. 5, which gradually
dropped with any increase in C. This shows a relatively poor performance
of this kernel with respect to others. In contrast, all other kernels showed
an increase in accuracy as C increased and reached their maximum after
which accuracies remained constant in general. This shows that there is an
optimum C value for a particular kernel. Focusing on the performance of
only polynomial kernels, it can be seen that the polynomials with degrees 2
to 4 produced very low accuracies (of the order of 20%) when C was very
small. But the accuracy shoots up with a small increase in C. On the other
hand, the initial accuracy obtained from polynomials with higher degrees
(from 5 to 7) is high (of the order of 70% to 80%) at small C values. Also,