The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
fitness function that combines the goals of high classification 
accuracy and low computation cost into one. 
Hyperspectral Images 
Testing Set 
Training Set 
Feature Gene 
Genetic Operations 
(Crossover, mutation) 
—. Classification accuracy 
'Are the termination tor testing subset 
conditions satisfied 
Fitness Evaluation 
Optimized Core Parameters and Feature Subset 
Figure.2. Flowchart of the GA-SVM wrapper approach 
2.3.1 Design of chromosome 
To optimize the kernel parameters and feature subset 
simultaneously, the chromosome was designed to comprise 
three parts, C, , and the features mask. The binary coding 
system was used to represent the chromosome. Fig. 3 shows the 
design of the binary chromosome. 
c 
Y 
/ 
c, 
...Ci... 
Cnc 
n 
f 
-A- 
U 
Because the number of features of hyperspectral data, i.e., the 
number of bands, is so large, traditional binary coding method 
will produce an enormously large solution space, which makes 
it impossible to find the optimal feature subset. Therefore a 
novel binary coding strategy was adopted, which set the length 
of chromosome different to the number of features. Suppose 
that the length of chromosome for the feature subset is nf, nf 
features were randomly selected from all the feature subset and 
sorted according to their identity number. A nf bits bit string 
was then generated and used as a mask for the selected nf 
features. Thus the number of solutions decreased from 2n to 
2nf*Cnfn. When nf is much less than n, computation efficiency 
will be improved greatly. 
2.3.2 Design of fitness function 
A fitness function is needed in the Genetic Algorithm to 
evaluate whether an individual is “fit” to survive. In the GA- 
SVM model, we used two criteria, namely classification 
accuracy and the number of selected features, to design the 
fitness function. The principle is that individuals with high 
classification accuracy and small number of features has a high 
fitness value, and thus high probability to be pass its genes to 
the next generation. A single objective fitness function that 
combines the two goals into one was designed to solve the 
multiple criteria problem. The formula is as below. 
fitness = w a x accuracy + 
Figure.3. Coding of chromosome 
In Figure. 3, Ci represents the ith bit’s value of bit string that 
represents parameter C, and nc is the number of bits 
representing parameter C; j represents the jth bit’s value of 
bit string that represents , and n is the number of bits 
representing parameter ; f k represents the mask value of kth 
feature, and nf is the number of bits representing the selected 
features, nc, n and nf can be modified according to the 
calculation precision and/or efficiency required. 
The bit strings representing the genotype of parameter C and 
should be transformed into phenotype by Eq. (1). Note that the 
precision of representing parameter depends on the length of the 
bit string (nc and n ), and the minimum and maximum value 
of the parameter is determined by the user. For chromosome 
representing the feature mask, the bit with value ‘ 1 ’ represents 
the feature is selected, and ‘0’ indicates feature is not selected. 
T(R,l) = min Ä + 
max ß — min ^ 
2' -1 
x d 
(1) 
T (R, 1) represents phenotype of the chromosome (or part of it) 
that has 1 bits, i.e. genes. minR and maxR represents the 
minimum and maximum value of parameter R; d represents the 
decimal value corresponding to the bit string; the number of bits 
representing the parameter 1 can be modified according to the 
calculation precision required. 
Where wa f] represents the weight value for classification 
accuracy, wf for the number of features; fi is the mask value of 
the ith feature, ‘ 1 ’ represents that feature i is selected; ‘ 0 ’ 
represents that feature i is not selected; wa can be adjusted to 
100% if accuracy is the most important. Generally, wa can be 
set from 75 to 100% according to user’s requirements. In our 
study, we set wa to 80% and wf to 20%. It can be inferred that 
high fitness value is determined by high classification and small 
feature number. 
2.3.3 Basic Steps of the GA-SVM method 
The basic steps of the GA-SVM method are as below: 
1) Create a initial population of certain size, i.e. a group 
individuals with different chromosomes. Each individual’s 
chromosome consists of three parts, namely parameter C, 
parameter and band subset of the hyperspectral data. The 
chromosomes of the initial population were randomly created. 
The size of the initial population should be determined properly 
by user to include as many possible solutions as possible. 
2) Calculate the fitness value of each individual in the initial 
population using Eq. (2) and rank them according to their 
fitness. To calculate the fitness value of an individual, or a 
chromosome, the genotypes are firstly converted to phenotypes, 
i.e. converting the binary codes to the parameter C and , and 
the identities of the selected features; These values, together 
with the training sets of the hyperspectral image, are then used 
as input to the SVM classifier to perform classification; After 
that, the classification accuracy is evaluated based on the 
testing sets; finally, fitness value of the individual is calculated 
using Eq. (2) based on the classification accuracy and number 
of selected features.