Geology Reference
In-Depth Information
es the learning process by changing the
representation of the data in the input space to a linear representation in a higher-
dimensional space called a feature space. A suitable choice of kernel allows the data
to become separable in the feature space despite being non-separable in the original
input space. Four standard kernels are usually used in classi
The role of the kernel function simpli
cation problems and
also in regression cases: linear, polynomial, radial basis, and sigmoid:
8
<
x
0
x
T
linear
ð
;
Þ
¼
x
0
d
x
T
polynomial
ð
;
þ
1
Þ
x
0
x
;
ð
4
:
62
Þ
2
x
0
:
Radial
exp
c
x
x
0
sigmoidal
tanh
ðc
x
:
þ
C
Þ
Currently, several types of support vector machine software are available. The
software used in this project was LIBSVM developed by Chih-Chung Chang and
Chih-Jen, and supported by the National Science Council of Taiwan. The source
code is written in C++. The choice of this software for our case studies in sub-
sequent chapters was made on its ease of use and dependability. The LIBSVM
model is capable of C-SVM classifi-
cation, one-class classifi-
cation,
ʽ
-SV classifi-
-
cation,
first trains the support
vector machine with a list of input vectors describing the training data.
Normalization of input vectors is important in SVM modeling. In SVM mod-
eling, we have performed analysis with
ʽ
-SV regression, and
ʵ
-SV regression. The software
-SVR using different kernel
functions such as linear, polynomial, radial, and sigmoid for three case studies in
this topic. These case studies chose different kernel and SVR models based on trial
and error experiments. The performance of
ʵ
-SVR and
ʽ
ʵ
-SVR with linear kernel was better than
that of
This topic recommends further exploration of the modeling of the selected two SVR
models, as the reason for over performance of one SVR over other in our case
studies is not clear. The SVM hypothesis suggests that the performance of SVM
depends on the slack parameter (
ʽ
ʵ
) and the cost factor (C). We have performed the
analysis, varying the
= 0.00001, and the cost parameters
C = 0.1 to C = 1000 in different case studies. The cost factor of error (C) assigns a
penalty for the number of vectors falling between the two hyperplanes in the
hypothesis. It suggests that, if the data is of good quality, the distance between the
two hyperplanes is narrowed down. If the data is noisy it is preferable to have a
smaller value of C which will not penalize the vectors [
14
]. So it is important to
ʵ
values between
ʵ
=1to
ʵ
nd
the optimum cost value for SVM modeling. To ascertain the optimum cost value,
the support vector machine with linear kernel has made different iterations with
different values of C for three case studies in this topic.
