Page 101 - Data Science Algorithms in a Week

Evolutionary Optimization of Support Vector Machines … 85

Figure 10. Representation of parameters in genetic algorithm.

s
The binary code i that represents each variable is transformed to an integer
according to the expression

N 1
m   s i 2 i
i 0

where N is the number of bits. This integer value is then scaled to a real number in the
[ , ] b
a
interval according to

b a


x a m
N
2  1

The precision depends on the range and the number of bits:


b a
  .
2  1
N

In addition, the LIBSVM program was modified to include a mixture of Gaussian
and polynomial kernel:


p e    u v 2   )   u v  d .  r

(1 p

Keerthi and Lin (2003) found that when a Gaussian RBF kernel is used for model
selection, there is no need to consider the linear kernel since it behaves as a linear kernel

for certain values of the parameters C and .

Fitness Function

The objective function is probably the most important part of the genetic algorithms
since it is problem-dependent. We need a way to measure the performance or quality of