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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
In addition, the clonal select algorithm can control the quantity 
of the same antibodies by calculating the expected survival 
value. It contains a memory cell set which saves the better 
antibodies, so the immune algorithm can converge very fast. 
Feature selection problem has been transformed to an 
optimization problem under the constrain domain of S(m). Thus, 
it can be proved that dimensional reduction problems are multi 
objective optimization problems. 
3. THE DIMENSIONAL REDUCTION MODEL IN 
HYPERSPECTRAL IMAGE 
3.1 Evaluation criteria during the process of feature 
selection 
In feature selection, many indexes are designed to evaluate the 
selected bands. There are Joint entropy, determinant of 
covariance matrix, Bhattacharyya distance, OIF (Optional Index 
Factor), and so on (Swain P H, 1987; Sheffield C, 1985; Chavez 
P S, 1982). In this paper, OIF is used as the evaluation criterion. 
Is, 
OIF = —^ (3) 
n n 
I IK I 
¿=1 j=‘ 
In the above formula, Sj- is the standard deviation of the ith 
band, and R tj is the correlation coefficient between the ith band 
and the jth band. 
The amount of information of the selected bands conforms to 
direct ratio with OIF value of bands set. 
3.2 The mathematical expression of feature selection 
problem 
Suppose that P is the number of bands in the image, and A is 
the wavelength. All the wavelengths construct the 
Set S- j/l], A 2 • • • A p }. The progress of feature select will 
select N bands from S^ , and the result can be expressed as 
/1 = ^, A 2 ... /l N } . The entire probable As constitute a 
set S(m) . Then the object function F(A) could describe the 
progress of calculating OIF value of the selected bands 
i.e. \A i ,A 2 }■ Feature selection problem can be described 
in math as formula (4). 
min F(A) = OIF 
s.t. A. g S(m) 
Select A from S(m), and the A should minimize F(A). A is 
the decision variables( A = {A ] , A 2 ... A-^}), constrain domain 
A = {A | Aj e S(m),i = is said to the feasible 
domain of decision variables. The formula of calculating OIF 
has been shown on formula (3). 
3.3 Hyperspectral dimensional reduction model 
Inspired of immune system, this paper has built a Hyperspectral 
dimensional reduction model on the base of clonal selection 
algorithm. HDRM is displayed as below: 
1) All the wavelengths construct the set , and N bands 
constitute individual (feasible solution)/4,. In the space S(m) 
which is constituted of all the probable A , Select M A from 
S(m) to constitute original population S(/l) , which is a set of 
antibodies. With no influence on the result, Aj (i.e. the elements 
of A) are arranged from large to small. 
2) Select n best individuals to constitute a set Sn from S(A) 
through calculating the value of F{A) . On the progress of 
calculating F(A) , the A is referenced to the wavelengths Aj, 
and then to the corresponding images. So the OIF value which 
is also the value of F{A) is computed. The whole calculating is 
a progress of affinity estimation. 
3) Clone these n best individuals, and generate temporary 
population T(Ab). The clone size increases as the increasing of 
its OIF value. The quantity of clonal bodies is described as 
formula (5). 
^clone 
---- round 
(5) 
n c ione is the quantity of antibodies after an antibody is cloned. 
P is the increment index, n is the quantity of all the antibodies 
in T(Ab). round() is the rounding operation, i is the antibody's 
index which indicates the order of the OIF value(decreasing). 
4) A.fter cloning, the next step is mutation. The purpose is to 
carry out the effective global search. A mutation operation is 
used to temporary population T(Ab), and then a mature mature 
population T*(Ab) is generated. The larger OIF value, the more 
information the selected bands contain, and the less part the 
individual should be changed. The rule is shown in formula (6). 
Mutation rule: Suppose that A (A = {A\, A 2 ,... K N } )is selected 
to mutate. The model defines a variable CD to control the 
mutation, k elements( A { ) in A are chosen to change to the other 
wavelengths randomly, k conforms to inverse ratio with F(A) . 
k = round 
coxn 
(6)